2400 lines
72 KiB
Plaintext
2400 lines
72 KiB
Plaintext
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/*
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----
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This file is part of SECONDO.
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Copyright (C) 2004-2008, University in Hagen, Faculty of Mathematics and
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Computer Science, Database Systems for New Applications.
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SECONDO is free software; you can redistribute it and/or modify
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it under the terms of the GNU General Public License as published by
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the Free Software Foundation; either version 2 of the License, or
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(at your option) any later version.
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SECONDO is distributed in the hope that it will be useful,
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but WITHOUT ANY WARRANTY; without even the implied warranty of
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MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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GNU General Public License for more details.
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You should have received a copy of the GNU General Public License
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along with SECONDO; if not, write to the Free Software
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Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
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----
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*/
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/*
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2 Part one - Determine relations and sql predicates using by the sql query
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2.1 Goal of part one
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Goal of part one is to determine any relation and any sql predicate
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used by sql query to be optimized. This information will be used by
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Part two to construct execution plans for secondo database to
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estimate the selectivity of joined predicates.
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2.2 The algorithm in few words
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1 Find any used sql predicate by using predicate pattern edge(0,A,B,\_,\_,\_).
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The zero as argument 1 means only edges should be used
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starting at start node. ???For the result B is an identifier
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of a marginal predicate ever and all edges using only one predicate
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match the pattern.??? A unifies with POG identifier
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of sql predicate unified with B.
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2 Based on unifiers of??? B the relations of sql query can be identified.
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The directly computed??? list could contain a relation twice:
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1 two instances of one relation (different aliases)
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2 one instance of one relation twice (used by different sql predicates)
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In the first case nothing is to be done. In the second case the
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second occurence of the relation shouldn't be added to the list of
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relations.
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3 A list is built containing the relations found. This list is stored as
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parameter of dynamic fact listOfRelations/1.
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4 Also based on unifiers of B the sql predicates of sql query are searched.
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5 The list of sql predicates generated before is stored as parameter of
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the dynamic fact listOfPredicates/1.
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*/
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/*
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2.3 The defined dynamic facts
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2.3.1 listOfPredicates/1
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The dynamic fact listOfPredicates/1 exists only once. The
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argument is
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a list containing the sql predicates of the sql query. The predicates
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are represented as a list of tuples. These tuples consist three elements:
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* the POG identifier of the sql predicate,
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* the relation of the sql predicate as predicate rel/3 and
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* the sql predicate itself.
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2.3.2 listOfRelations/1
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The dynamic fact listOfRelations/1 exists only once, too. The
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argument
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is also a list, but it contains the instances of the relations used
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by the sql predicates of the sql query. Each relation instance is
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represented by
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the predicate rel/3.The list is distinctive. Nevertheless it could contain
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one relation twice, if the relation is used with different aliases.
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2.3.2.1 instances of relations
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One relation can be used in a sql query more than one time
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by defining distinctive aliases.
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An instance of a relation is identified uniquely??? by an alias or just by
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the name of the relation if no alias was defined. Each sql predicate
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is exactly bundled with one relation instance.
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*/
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/*
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2.4 The implementation of the predicates
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2.4.1 findRelation/2
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The predicate is used to find a relation (arg 1) in an given list (arg 2)
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of relations. If arg 1 could be found in arg 2, so the predicate finishs
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successfully otherwise it fails.
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*/
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% the last element of list is reached and it unifies with arg1
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% (it means arg1 could be found in arg2) - predicate successful
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findRelation(Relation, Relation ):- % Relation found
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debug_writeln('findRelation 0').
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% the list is empty (arg1 should not be found in list before)
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% (it means arg1 could NOT be found in arg2) - predicate fails
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findRelation(Relation, [] ):- % Relation not found in list
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debug_writeln('findRelation 1 - ', Relation, '#'),
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fail.
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% the element heading the list is be able to unify with argument one
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% (it means arg1 could be found in arg2) - predicate successful
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findRelation(Relation, [ Relation | _ ]):- % Relation found
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debug_writeln('findRelation 3').
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% the element heading the list couldn't be unified with argument 1,
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% but the list is not empty
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% try again with the next top element of list
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findRelation(SearchFor, [ _ | Rest ]):-
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debug_writeln('findRelation 2'),
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findRelation(SearchFor, Rest).
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% just for debugging ???
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%findRelation(X,Y):-
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% % write some details
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% writeln('findRelation ? - unexpected call (internal error)'),
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% writeln(X),
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% writeln(Y),
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% fail. % the call failed - of course
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/*
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2.4.2 add\_relation/1
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The predicate appends the list of relations by the given
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relation (arg 1),
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if arg 1 is not still a part of the list. The list of relations is stored
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in fact listOfRelations/1.
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*/
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% the given relation is still a part of the list of relations -
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% do not add the relation
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add_relation(Relation):-
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listOfRelations(ListRelations),
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debug_writeln('add_relation 1 - ',
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Relation, ' // ', ListRelations),
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%!, % if relation not in list - add_relation 1 have to fail
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findRelation(Relation , ListRelations),
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!. % if Relation could be found - do not search again
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% append list of relations by the given relation
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add_relation(Relation):-
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debug_writeln('add_relation 2'),
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listOfRelations(OldList),
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retract(listOfRelations(OldList)),
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NewList = [ Relation | OldList ],
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asserta(listOfRelations(NewList)),
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debug_writeln('add_relation 2 - ', Relation, ' added'),
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!.
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/*
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2.4.3 add\_predicate/1
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The predicate appends the list of sql predicates always found
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by sql predicate (arg 1). Finally the list of sql predicates
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is stored as argument of fact listOfPredicates/1.
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*/
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add_predicate(Predicate):-
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listOfPredicates(OldList),
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retract(listOfPredicates(OldList)),
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NewList = [ Predicate | OldList ],
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asserta(listOfPredicates(NewList)),
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debug_writeln('add_predicate 1 - ', Predicate, ' added'),
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!.
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/*
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2.4.4 build\_list\_of\_predicates/1
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The predicate is the entry point of part one. It initiates
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the construction of the list of relations and the list of predicates
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finally stored as argument of facts listOfRelations/1 and
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listOfPredicates/1.
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**something to do ?**
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*/
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build_list_of_predicates:-
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% clean up environment
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retractall(listOfRelations(_)),
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retractall(listOfPredicates(_)),
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asserta(listOfPredicates([])),
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asserta(listOfRelations([])),
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!,
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% build list of relations and list of predicates
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% all edges starting at source of pog
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edge(0,PredIdent,Pr,_,_,_),
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debug_writeln(
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'build_list_of_predicates 1 - analyse edge ', Pr),
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% only select supports selects only currently
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Pr = select( _ , PredExpr ),
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% ??? hier wird ein Eingriff noetig, ist Relation wirklich
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% eindeutig (auch bei SubSelects)? oder besser erstes Arg
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% von select(...) nutzen
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PredExpr = pr( _ , Relation ),
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% memory structure to store a found predicate
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PredIdent2 is round(PredIdent),
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Predicate = [ PredIdent2 , Relation , PredExpr ],
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% PredIdent is used to ident the predicate in pog
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% Relation is used to group predicates of a relation
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% PredExpr is the predicate itself used for predcounts query
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add_relation(Relation), % add Relation to the listOfRelations
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% add Predicate to the listOfPredicates
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add_predicate(Predicate),
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fail. % loop for all edges matching edge(0,_,_,_,_,_)
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/*
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//characters [1] Type: [\underline{\it ] [}]
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*/
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/*
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3 Part two - construct all predcount execution plans
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3.1 The goal of Part two
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The goal of part two is the construction of execution plans of
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predcounts queries, ???which are able to run against
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secondo database. They are constructed using
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predicates "listOfPredicates/1"[1] and "listOfRelations/1" created by part one.
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Finally the part three will using the execution plans to collect statistics
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to bring??? the POG more detailed.
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3.2 The algorithm in few words
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1 *???Punkt sinnlos???*
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The used sql predicates and relations are stored as argument 1 of
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predicates listOfPredicates/1 and listOfRelations/1. (see part one)
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2 for each relation instance: creation of predcount execution plan
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1 collect all sql predicates using one relation instance
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2 construct predcount execution plan (one per relation instance)
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3 generate the list of POG identifiers of sql predicates used
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by the constructed predcount execution plan
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*/
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/*
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3.2.1 predcount execution plans
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The stream consuming sql operator predcount called with a list of
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sql predicates determine for each element of the stream which
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combination of given sql predicates are solved.
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Each sql predicate i given as parameter is identified by an identifier
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2\^i. This way of identifing allows to identify each combination of sql
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predicates just by sum the identifiers of each solved sql predicate.
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The result of the predcount operator is a stream of tuples. The count
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of tuples is 2\^(count of sql predicates). Each tuple consists of an
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identifier identifing a unique comination of solved sql predicates and
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number of tuples of the original stream solving this combination of
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sql predicates.
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The identifier does not correspond with the POG identifier
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of the sql predicate. (see section below)
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*/
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/*
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3.2.2 POG identifiers
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Each sql predicate has gotten an identifier in POG during parsing
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the sql query.
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To assign the collected statistics to the right edge of the POG,
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it's necessary to translate each identifier of the results of predcount
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to the corresponding identifier of the POG. This is done by predicate
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translate\_ident\_bits/3. (see part three for details)
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Part two supplies the translation by bundling the list of original POG
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identifiers to each constructed predcount execution plan.
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*/
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/*
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3.3 The defined dynamic facts
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none
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*/
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/*
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3.4 The implementation of the predicates
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3.4.1 build\_queries/1
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The predicate is the entry point of part two. The result is returned
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as the argument. The result is a list of tuples. One tupel per
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relation instance is created. Each tuple contains a query (second
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element) which represents the predcount execution plan for that
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relation instance. The first element of the tupel is the list of
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predicate identifiers called translation list. (see section 3.2.2
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above) The elements of the translation list are used in step 3 to
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translate the tupels responsed by predcount for the POG.
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*/
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build_queries(Queries):-
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% get list of relations created in step 1
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listOfRelations(RelationList),
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% build queries
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build_queries(RelationList, Queries).
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/*
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3.4.2 build\_queries/2
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The predicate implements a loop over all relation instances given
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as first argument.
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*/
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build_queries([], []). % end of recursion
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build_queries([ Relation | RRest], [ Query | QRest]):-
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debug_writeln('build_queries 2: ', Relation),
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% build tupel for relation Relation
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build_query(Relation, Query),
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% recursive call for other relations in list
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build_queries(RRest, QRest).
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/*
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3.4.3 build\_query/2
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The predicate constructs the tuple [ PredIdentList Query ]
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for the given relation (argument 1).
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*/
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build_query(Relation, [ PredIdentList , Query , Relation ]):-
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debug_writeln('build_query 1'),
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% build predcounts expression
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build_predcount_exprs(Relation, PredcountExpr,
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PredIdentList),
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% build relation expression
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build_relation_expr(Relation, RelationExpr),
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% concatinate string
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atom_concat(RelationExpr, PredcountExpr, ' consume;',
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'', '', Query).
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/*
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3.4.4 build\_relation\_expr/2
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The predicate builds relation expression " query relation feed \{alias\} " .
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Setting the alias is necessary to support direct using of sql predicates
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of the original query. In addition it prepares the future
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support of joins.
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*/
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build_relation_expr(Relation, RelationExpr):-
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debug_writeln('build_relation_expr - ', Relation),
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plan_to_atom(Relation, RelName), % determine relation
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% ??? add using of small relation / samples here
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% build alias if necessary
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build_alias_string(Relation, RelAliasString),
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atom_concat('query ', RelName, ' feed ', RelAliasString,
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'', RelationExpr). % concatinate string
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/*
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3.4.5 build\_alias\_string/2
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The predicate builds the relation alias expression " \{alias\} " .
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*/
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|
|
||
|
|
% vjo 2008-10-23 veraltet
|
||
|
|
% build_alias_string(rel(_,*,_), ''). % no alias necessary
|
||
|
|
% build_alias_string(rel(_,RelAlias,_), AliasString):-
|
||
|
|
% % create alias expression
|
||
|
|
% atom_concat(' {', RelAlias, '}', '', '', AliasString).
|
||
|
|
|
||
|
|
build_alias_string(rel(_,*), ''). % no alias necessary
|
||
|
|
build_alias_string(rel(_,RelAlias), AliasString):-
|
||
|
|
% create alias expression
|
||
|
|
atom_concat(' {', RelAlias, '}', '', '', AliasString).
|
||
|
|
|
||
|
|
|
||
|
|
/*
|
||
|
|
3.4.6 build\_predcount\_exprs/3
|
||
|
|
|
||
|
|
The predicate builds the predcounts expression string
|
||
|
|
" predcounts [ ... ] " .
|
||
|
|
|
||
|
|
*/
|
||
|
|
|
||
|
|
build_predcount_exprs(Relation, PredcountString, PredIdentList):-
|
||
|
|
debug_writeln('build_predcount_exprs - ', Relation),
|
||
|
|
% get list of predicates created by part one
|
||
|
|
listOfPredicates(ListOfPredicates),
|
||
|
|
% build list of predcounts expression elements and
|
||
|
|
% predicate translation list
|
||
|
|
build_predcount_expr(Relation, ListOfPredicates,
|
||
|
|
PredcountExpr, PredIdentList),
|
||
|
|
atom_concat(' predcounts [ ', PredcountExpr, ' ] ', '', '',
|
||
|
|
PredcountString).
|
||
|
|
|
||
|
|
|
||
|
|
/*
|
||
|
|
3.4.7 build\_predcount\_expr/4
|
||
|
|
|
||
|
|
The predicate builds the expression for each sql predicate of
|
||
|
|
predcounts expression string and concates the expression to the list
|
||
|
|
of predcount expressions (argument 3). It adds the POG identifier
|
||
|
|
of the sql predicate to the translation list (argument 4), too.
|
||
|
|
|
||
|
|
*/
|
||
|
|
|
||
|
|
build_predcount_expr(_, [], '', []):- % end of recursion
|
||
|
|
debug_writeln('build_predcount_expr 0').
|
||
|
|
build_predcount_expr(Relation,[ Predicate | Rest ], PredcountExpr,
|
||
|
|
PredIdentList):- % used if Predicate use Relation
|
||
|
|
Predicate = [ PredIdent, Relation, PredExprNew ],
|
||
|
|
PredExprNew = pr( PredExpr, _),
|
||
|
|
debug_writeln('build_predcount_expr 1: ', Relation,
|
||
|
|
' // ', Predicate),
|
||
|
|
% recursive call for other predicates in list
|
||
|
|
build_predcount_expr(Relation, Rest, PERest, PIRest),
|
||
|
|
%!, % if Predicate does not use Relation add_predcount fails
|
||
|
|
build_predicate_expression(PredIdent, PredExpr,
|
||
|
|
PredPredcountExpr),
|
||
|
|
build_comma_separated_string(PredPredcountExpr, PERest,
|
||
|
|
PredcountExpr),
|
||
|
|
% add predicate identifier of POG to list
|
||
|
|
PredIdentList = [ PredIdent | PIRest ].
|
||
|
|
build_predcount_expr(Relation,[ Predicate | Rest ], PredcountExpr,
|
||
|
|
PredIdentList):- % used if Predicate do not use Relation
|
||
|
|
debug_writeln('build_predcount_expr 2: ', Relation,
|
||
|
|
' // ', Predicate),
|
||
|
|
% recursive call for other predicates in list
|
||
|
|
build_predcount_expr(Relation, Rest,
|
||
|
|
PredcountExpr, PredIdentList).
|
||
|
|
|
||
|
|
|
||
|
|
% alt: add_predcount(Relation, Predicate, PERest, PIRest,
|
||
|
|
% PredcountExpr, PredIdentList). % build predicate expression for
|
||
|
|
% precounts expression
|
||
|
|
|
||
|
|
/*
|
||
|
|
3.4.8 build\_predicate\_expression/3
|
||
|
|
|
||
|
|
The predicate constructs one sql predicate expression for predcount
|
||
|
|
expression.
|
||
|
|
|
||
|
|
*/
|
||
|
|
|
||
|
|
build_predicate_expression(PredIdent, Expression, PredcountExpr):-
|
||
|
|
debug_writeln('build_predicate_expression'),
|
||
|
|
plan_to_atom(Expression, PredExpr),
|
||
|
|
atom_concat('P', PredIdent, ': ', PredExpr,
|
||
|
|
'', PredcountExpr).
|
||
|
|
|
||
|
|
|
||
|
|
/*
|
||
|
|
3.4.9 build\_comma\_separated\_string/3
|
||
|
|
|
||
|
|
Arg3 = Arg1 + ',' + Arg2
|
||
|
|
|
||
|
|
*/
|
||
|
|
|
||
|
|
build_comma_separated_string('', AtEnd, AtEnd).
|
||
|
|
build_comma_separated_string(AtBegin, '', AtBegin).
|
||
|
|
build_comma_separated_string(AtBegin, AtEnd, NewString):-
|
||
|
|
atom_concat(AtBegin, ',', AtEnd, '', '', NewString).
|
||
|
|
|
||
|
|
|
||
|
|
/*
|
||
|
|
3.4.10 add\_predcount/6
|
||
|
|
|
||
|
|
deprecated
|
||
|
|
|
||
|
|
*/
|
||
|
|
|
||
|
|
add_predcount(Relation, [ PredIdent , Relation , Expr ], PERest,
|
||
|
|
PIRest, PredcountExpr, PredIdentList):-
|
||
|
|
debug_writeln('add_predcount 1'),
|
||
|
|
build_predicate_expression(PredIdent, Expr, PredString),
|
||
|
|
build_comma_separated_string(PredString,
|
||
|
|
PERest, PredcountExpr),
|
||
|
|
PredIdentList = [ PredIdent | PIRest ].
|
||
|
|
add_predcount(Relation, Pred, PERest, PIRest, PERest, PIRest):-
|
||
|
|
% if Pred does not use Relation
|
||
|
|
debug_writeln('add_predcount 0: ', Relation, ' # ', Pred).
|
||
|
|
|
||
|
|
/*
|
||
|
|
4 Part three - execution of predcounts plans and
|
||
|
|
tranforming of the results for the POG
|
||
|
|
|
||
|
|
4.1 Goal of part three
|
||
|
|
|
||
|
|
After the construction of predcounts execution plans
|
||
|
|
in part two the plans
|
||
|
|
have to be executed now. The predcounts results have to be transformed
|
||
|
|
because
|
||
|
|
the identifiers used by operator predcounts don't generally match with the
|
||
|
|
identifiers used by POG. Finally the results are added to the POG.
|
||
|
|
|
||
|
|
4.2 Algorithm in few words
|
||
|
|
|
||
|
|
1 execute predcounts execution plan
|
||
|
|
|
||
|
|
2 transform the predicate identifiers (atom) of the operator predcounts
|
||
|
|
to the correspondig node identifiers used by the POG
|
||
|
|
|
||
|
|
4.3 Defined dynamic facts
|
||
|
|
|
||
|
|
none
|
||
|
|
|
||
|
|
4.4 Implementation of the predicates
|
||
|
|
|
||
|
|
4.4.1 calculate\_predcounts/2
|
||
|
|
|
||
|
|
The predicate is the entry point of part three. It uses the result of
|
||
|
|
part two as first argument and returns the result as second arguent.
|
||
|
|
It executes any given predcounts execution plan and transforms each predicate
|
||
|
|
identifiers of operator predcounts to POG's one using
|
||
|
|
translate\_ident\_bits.
|
||
|
|
|
||
|
|
*/
|
||
|
|
|
||
|
|
calculate_predcounts([], []):- % Rekursionsabschluss
|
||
|
|
retractall(predcounts_result(_,_)).
|
||
|
|
calculate_predcounts([[PredIDs , Query , Relation ] | QRest],
|
||
|
|
[PredCount | PRest]):-
|
||
|
|
% rekursiv alle predcounts-Plaene betrachten
|
||
|
|
calculate_predcounts(QRest,PRest),
|
||
|
|
% predcounts-Plan ausfuehren
|
||
|
|
secondo(Query, [_|[PredTupels]]),
|
||
|
|
% Wert fuer atom in Ergebnistupel in den Wert
|
||
|
|
% fuer POG uebersetzen
|
||
|
|
translate_ident_bits(PredTupels, PredIDs, PredCount),
|
||
|
|
% speichere predcounts Ergebnisse als Fakt
|
||
|
|
assert(predcounts_result(Relation, PredCount)).
|
||
|
|
|
||
|
|
/*
|
||
|
|
4.4.2 translate\_ident\_bits/3
|
||
|
|
|
||
|
|
The predicate transforms the predicate identifiers of the
|
||
|
|
operator predcounts
|
||
|
|
(argument one) to the node identifiers of POG (argument three) using
|
||
|
|
the translation tables given as a list (argument two).
|
||
|
|
Each atom of argument one is finally translated by using
|
||
|
|
calculate\_pog\_ident/3.
|
||
|
|
|
||
|
|
*/
|
||
|
|
|
||
|
|
translate_ident_bits([], _, []). % Rekursionsabschluss
|
||
|
|
translate_ident_bits([ InTupel | IRest], TranTab,
|
||
|
|
[ OutTupel | ORest]):-
|
||
|
|
% rekursiv alle alle Tupel durchgehen
|
||
|
|
translate_ident_bits(IRest, TranTab, ORest),
|
||
|
|
% Tupel zerlegen
|
||
|
|
InTupel = [ InAtom | Count ],
|
||
|
|
% Wert fuer Atom in korrespondierenden POG-Wert uebersetzen
|
||
|
|
calculate_pog_ident(InAtom, TranTab, OutAtom),
|
||
|
|
% Zieltupel zusammensetzen
|
||
|
|
OutTupel = [ OutAtom | Count].
|
||
|
|
|
||
|
|
|
||
|
|
/*
|
||
|
|
4.4.3 calculate\_pog\_ident/3
|
||
|
|
|
||
|
|
The predicate translate each atom identifier of the operator
|
||
|
|
predcounts to the corresponding node identifier of POG.
|
||
|
|
|
||
|
|
*/
|
||
|
|
|
||
|
|
calculate_pog_ident(0, [], 0). % Rekursionsabschluss
|
||
|
|
calculate_pog_ident(InAtom, [ TranElem | TRest ], OutAtom):-
|
||
|
|
% mod = Ganzzahl; restliche Bits
|
||
|
|
IRest is InAtom // 2,
|
||
|
|
IBit is InAtom - ( 2 * IRest),
|
||
|
|
calculate_pog_ident(IRest, TRest, ORest),
|
||
|
|
OBit is IBit * TranElem,
|
||
|
|
OutAtom is ORest + OBit.
|
||
|
|
calculate_pog_ident(_,_,_):-
|
||
|
|
writeln('Fehler bei translate_ident_bits').
|
||
|
|
|
||
|
|
/*
|
||
|
|
4. Implementation of interfaces for SecondoPL
|
||
|
|
|
||
|
|
4.1 Overview
|
||
|
|
|
||
|
|
An new independent optimizer option has to implement
|
||
|
|
two prolog predicates:
|
||
|
|
* traversePath/1 and
|
||
|
|
* translate/4
|
||
|
|
|
||
|
|
The goal of this section is to implement these both interfaces.
|
||
|
|
To provide the functionalities needed the predicates use the predicates
|
||
|
|
defined above as well as new predicates implemented within this section.
|
||
|
|
|
||
|
|
The new functionalities should:
|
||
|
|
* transform the data provided by predicates described above for their
|
||
|
|
usability within the already existing code and
|
||
|
|
* reimplement already existing code more generally (this should be avoided
|
||
|
|
in most cases)
|
||
|
|
|
||
|
|
4.2 The algorithm in few words
|
||
|
|
|
||
|
|
4.3 Defined dynamic facts
|
||
|
|
|
||
|
|
4.4 Implementation of the predicates
|
||
|
|
|
||
|
|
4.4.1 traversePath/1
|
||
|
|
|
||
|
|
not still implemented - it could possible look like the
|
||
|
|
implementation of entropy approach
|
||
|
|
|
||
|
|
----
|
||
|
|
traversePath(Path) :-
|
||
|
|
optimizerOption(correlations),
|
||
|
|
writeln('call traversePath(',Path,')'),
|
||
|
|
traversePath3(Path), !.
|
||
|
|
|
||
|
|
traversePath3([]).
|
||
|
|
traversePath3([costEdge(Source, Target, Term, Result, _, _) | Path]) :-
|
||
|
|
embedSubPlans(Term, Term2),
|
||
|
|
possiblyCorrectSelfJoins(Source, Target, Term2, Term3),
|
||
|
|
nextCounter(nodeCtr, Nc),
|
||
|
|
assert(nodePlan(Result, counter(Term3,Nc))),
|
||
|
|
assert(smallResultCounter(Nc, Source, Target, Result)),
|
||
|
|
traversePath2(Path).
|
||
|
|
----
|
||
|
|
|
||
|
|
4.4.2 translate1/4
|
||
|
|
|
||
|
|
not still implemented - it could also be implemented as within
|
||
|
|
the entropy aproach
|
||
|
|
|
||
|
|
----
|
||
|
|
translate1(Query, Stream3, Select2, Cost2) :-
|
||
|
|
writeln('call translation(',[Query, Stream3, Select2, Cost2],')'),
|
||
|
|
optimizerOption(correlations),
|
||
|
|
translate(Query, Stream1, Select, Cost1),
|
||
|
|
writeln('Query: ', Query),
|
||
|
|
writeln('Stream3: ', Stream3),
|
||
|
|
writeln('Select2: ', Select2),
|
||
|
|
writeln('Cost1: ', Cost1),
|
||
|
|
translateCorrelation(Stream1, Stream2, Cost1, Cost2).
|
||
|
|
----
|
||
|
|
|
||
|
|
*/
|
||
|
|
|
||
|
|
/*
|
||
|
|
4.4.3 translateCorrelation/4
|
||
|
|
|
||
|
|
currently not used and not checked
|
||
|
|
|
||
|
|
The implementation is derivated from translateEntropy/4.
|
||
|
|
|
||
|
|
*/
|
||
|
|
|
||
|
|
%translateCorrelation(Stream1, Stream2, Cost1, Cost2) :-
|
||
|
|
translateCorrelation(_, Stream2, _, _) :-
|
||
|
|
% VJO-ok: limit application to queries with a maximum of 8 predicates:
|
||
|
|
highNode(HN), HN > 1, HN < 256, !,
|
||
|
|
nl, write('*** Using Entropy-approach ************' ), nl, !,
|
||
|
|
|
||
|
|
% compute a new plan based on the cost annotations of
|
||
|
|
% the new selectivities computed by maximize_entropy
|
||
|
|
assignCorrelationCost,
|
||
|
|
writeln('Stream2 out: ',Stream2),
|
||
|
|
%bestPlan(Stream2, Cost2), !,
|
||
|
|
%warn_plan_changed(Stream1, Stream2),
|
||
|
|
!.
|
||
|
|
|
||
|
|
/*
|
||
|
|
4.4.4 assignCorrelationCost/0
|
||
|
|
|
||
|
|
not used and not tested currently
|
||
|
|
|
||
|
|
The predicate assignCorrelationCost/0 joins all the functionalities
|
||
|
|
needed to implement the correlations approach.
|
||
|
|
|
||
|
|
*/
|
||
|
|
|
||
|
|
assignCorrelationCost :-
|
||
|
|
|
||
|
|
find_all_calcable_nodes,
|
||
|
|
|
||
|
|
list_calcable_nodes, nl,
|
||
|
|
|
||
|
|
not(build_list_of_predicates),
|
||
|
|
|
||
|
|
listOfPredicates(LoP), writeln('listOfPredicates: ', LoP), nl,
|
||
|
|
listOfRelations(LoR), writeln('listOfRelations: ', LoR), nl,
|
||
|
|
|
||
|
|
build_queries(Queries),
|
||
|
|
|
||
|
|
writeln('Queries: ', Queries), nl,
|
||
|
|
|
||
|
|
calculate_predcounts(Queries, PredcountsResult),
|
||
|
|
|
||
|
|
writeln('PredcountsResult: ', PredcountsResult), nl,
|
||
|
|
|
||
|
|
calc_node_sels(NodeSels),
|
||
|
|
|
||
|
|
writeln('NodeSels=', NodeSels), nl,
|
||
|
|
|
||
|
|
calc_mpjp_sels(NodeSels, MP, JP),
|
||
|
|
|
||
|
|
nl, write('Marginal Sel.: MP ='), write( MP ),
|
||
|
|
nl, write('Conditional Sel.: JP =') , write( JP ), nl, nl,
|
||
|
|
|
||
|
|
% use predicate feasible/4 of entropy_opt.pl
|
||
|
|
feasible(MP, JP, MP2, JP2), !,
|
||
|
|
|
||
|
|
% call the predicate implemented in C++ which computes the
|
||
|
|
% remaining conditional probabilities.
|
||
|
|
write('calling maximize_entropy with:'), nl,
|
||
|
|
write( MP2 ), write(', ') , write( JP2 ), nl, nl,
|
||
|
|
maximize_entropy(MP2, JP2, Result), !,
|
||
|
|
|
||
|
|
% Funktionen koennen direkt uebernommen werden
|
||
|
|
createEntropyNode(Result),
|
||
|
|
assignEntropySizes,
|
||
|
|
createCostEdges.
|
||
|
|
|
||
|
|
|
||
|
|
/*
|
||
|
|
4.4.5 find_all_calcable_nodes/0
|
||
|
|
|
||
|
|
-> calcable_node(NodeIDint)
|
||
|
|
|
||
|
|
*/
|
||
|
|
|
||
|
|
find_all_calcable_nodes:-
|
||
|
|
retractall(calcable_node(_)),
|
||
|
|
not(find_all_calcable_nodes2).
|
||
|
|
|
||
|
|
find_all_calcable_nodes2:-
|
||
|
|
node(NodeID, Predicates, _),
|
||
|
|
all_preds_allowed(Predicates),
|
||
|
|
NodeIDint is round(NodeID),
|
||
|
|
assert(calcable_node(NodeIDint)),
|
||
|
|
fail.
|
||
|
|
|
||
|
|
/*
|
||
|
|
4.4.6 all_preds_allowed/1
|
||
|
|
|
||
|
|
used by find_all_calcable_nodes/0
|
||
|
|
|
||
|
|
*/
|
||
|
|
|
||
|
|
all_preds_allowed([]).
|
||
|
|
all_preds_allowed([ Predicate | Predicates ]):-
|
||
|
|
is_pred_allowed(Predicate),
|
||
|
|
all_preds_allowed(Predicates).
|
||
|
|
|
||
|
|
/*
|
||
|
|
4.4.7 is_pred_allowed/1
|
||
|
|
|
||
|
|
used by all_preds_allowed/1
|
||
|
|
|
||
|
|
*/
|
||
|
|
|
||
|
|
is_pred_allowed(pr(_, _)).
|
||
|
|
%vjo zu erweitern fuer join preds
|
||
|
|
|
||
|
|
/*
|
||
|
|
4.4.8 list_calcable_nodes/0
|
||
|
|
|
||
|
|
just lists all calculatable nodes
|
||
|
|
|
||
|
|
*/
|
||
|
|
|
||
|
|
list_calcable_nodes:-
|
||
|
|
write('calculatable nodes: '),
|
||
|
|
not(list_calcable_nodes2).
|
||
|
|
|
||
|
|
list_calcable_nodes2:-
|
||
|
|
calcable_node(NodeID),
|
||
|
|
write(NodeID), write(' '),
|
||
|
|
fail.
|
||
|
|
|
||
|
|
/*
|
||
|
|
4.4.9 add_predcounts_results/4
|
||
|
|
|
||
|
|
The predicate add_predcounts_results/4 offers to use the
|
||
|
|
correlations aproach within the entropy approach. To do so one has to
|
||
|
|
assert the fact corr (assert(corr)).
|
||
|
|
|
||
|
|
The predicate add_predcounts_results/0 is called by
|
||
|
|
assignEntropyCost/0 to append the cardinalities returned by the first plan
|
||
|
|
by the marginal and joint selectivities returned by predcounts plans.
|
||
|
|
|
||
|
|
*/
|
||
|
|
|
||
|
|
% if predcounts approach should not be additionally used
|
||
|
|
add_predcounts_results(_, _, _, _):-
|
||
|
|
not(corr),
|
||
|
|
writeln('do not additionally use predcounts approach').
|
||
|
|
|
||
|
|
add_predcounts_results(MP, JP, MPPC, JPPC):-
|
||
|
|
|
||
|
|
writeln('Nutze Correlations-Funktionen zur Erweiterung von JP'),
|
||
|
|
|
||
|
|
not(build_list_of_predicates),!,
|
||
|
|
build_queries(Queries),!,
|
||
|
|
calculate_predcounts(Queries, PredcountsResult),!,
|
||
|
|
find_all_calcable_nodes,!,
|
||
|
|
calc_node_sels(NodeSels),!,
|
||
|
|
calc_mpjp_sels(NodeSels, MP2, JP2),!,
|
||
|
|
|
||
|
|
nl, write('PredcountsResult = '), write( PredcountsResult ),
|
||
|
|
nl, write('Marginal Sel.: MP2 ='), write( MP2 ),
|
||
|
|
nl, write('Conditional Sel.: JP2 =') , write( JP2 ), nl, nl,
|
||
|
|
|
||
|
|
%join_lists(JP, JP2, JPPC),
|
||
|
|
merge_lists_j(JP, JP2, JPPC),!,
|
||
|
|
merge_lists_m(MP, MP2, MPPC),!,
|
||
|
|
|
||
|
|
nl, write('joined lists: MPjoined =') , write( MPPC ), nl,
|
||
|
|
nl, write(' JPjoined =') , write( JPPC ), nl, nl,
|
||
|
|
|
||
|
|
true.
|
||
|
|
|
||
|
|
/*
|
||
|
|
4.4.10 calc_node_sels/1
|
||
|
|
|
||
|
|
used by assignCorrelationCost/0
|
||
|
|
used by add_predcounts_results/4
|
||
|
|
|
||
|
|
*/
|
||
|
|
|
||
|
|
|
||
|
|
% call: calc_node_sels(NS).
|
||
|
|
calc_node_sels([ [ 0, 1 ] | NodeSels ]):-
|
||
|
|
retractall(predcounts_node_sel(_,_)),
|
||
|
|
NodeID = 0,
|
||
|
|
node_nodeid(Node, NodeID),
|
||
|
|
listOfRelations(Relations), !,
|
||
|
|
product_over_all_relations(Relations, Node, Node0Card),
|
||
|
|
store_node_sel(0, 1),
|
||
|
|
debug_writeln('Node ',NodeID,' Sel=1'),
|
||
|
|
NextNodeID is NodeID + 1,
|
||
|
|
calc_node_sels(NextNodeID, Relations, Node0Card, NodeSels).
|
||
|
|
calc_node_sels(NodeID, Relations, Node0Card, [ [NodeID,NodeSel] | NodeSels ]):-
|
||
|
|
% nicht NodeID=0
|
||
|
|
calcable_node(NodeID),
|
||
|
|
node_nodeid(Node, NodeID),
|
||
|
|
product_over_all_relations(Relations, Node, NodeCard),
|
||
|
|
NodeSel is NodeCard / Node0Card,
|
||
|
|
store_node_sel(NodeID, NodeSel),
|
||
|
|
debug_writeln('Node ',NodeID,' [Card,Sel]=',[NodeCard,NodeSel]),
|
||
|
|
NextNodeID is NodeID + 1,
|
||
|
|
calc_node_sels(NextNodeID, Relations, Node0Card, NodeSels).
|
||
|
|
calc_node_sels(NodeID, Relations, Node0Card, [ [NodeID,n/a] | NodeSels ]):-
|
||
|
|
% nicht NodeID=0
|
||
|
|
% nicht calcable_node(NodeID)
|
||
|
|
is_marginal_pred(NodeID),
|
||
|
|
% jetzt noch sicherstellen, dass NodeID auch existiert
|
||
|
|
%%node_nodeid(_, NodeID),
|
||
|
|
highNode(HN), NodeID =< HN,
|
||
|
|
debug_writeln('Node ',NodeID,' keine Selektivitaet'),
|
||
|
|
store_node_sel(NodeID, n/a),
|
||
|
|
NextNodeID is NodeID + 1,
|
||
|
|
calc_node_sels(NextNodeID, Relations, Node0Card, NodeSels).
|
||
|
|
calc_node_sels(NodeID, Relations, Node0Card, NodeSels):-
|
||
|
|
% nicht NodeID=0
|
||
|
|
% nicht calcable_node(NodeID)
|
||
|
|
% nicht is_marginal_pred(NodeID)
|
||
|
|
% jetzt noch sicherstellen, dass NodeID auch existiert
|
||
|
|
%%node_nodeid(_, NodeID),
|
||
|
|
highNode(HN), NodeID =< HN,
|
||
|
|
debug_writeln('Node ',NodeID,' nicht bearbeitet'),
|
||
|
|
NextNodeID is NodeID + 1,
|
||
|
|
calc_node_sels(NextNodeID, Relations, Node0Card, NodeSels).
|
||
|
|
calc_node_sels(NodeID, _, _, []):-
|
||
|
|
debug_writeln('beende mit NodeID: ',NodeID).
|
||
|
|
|
||
|
|
|
||
|
|
|
||
|
|
|
||
|
|
/*
|
||
|
|
5 A simple example
|
||
|
|
|
||
|
|
5.1 Overview
|
||
|
|
|
||
|
|
The following simple example explains the using of
|
||
|
|
|
||
|
|
* build\_list\_of\_predicates/0
|
||
|
|
|
||
|
|
* build\_queries/1
|
||
|
|
|
||
|
|
* calculate\_predcounts/2
|
||
|
|
|
||
|
|
5.2 Code example
|
||
|
|
|
||
|
|
The output that shows the content of variables is restructured
|
||
|
|
for easier understanding. Normally the variable's content is shown
|
||
|
|
within one line per variable. For easier reading and referencing
|
||
|
|
such a line is devided into more than one. Additionally these lines
|
||
|
|
are numerated.
|
||
|
|
|
||
|
|
----
|
||
|
|
F=[8,[2,3]]
|
||
|
|
----
|
||
|
|
|
||
|
|
For example such a original prolog output line would
|
||
|
|
devided as follows:
|
||
|
|
|
||
|
|
----
|
||
|
|
000 F=
|
||
|
|
001 [
|
||
|
|
002 8,
|
||
|
|
003 [
|
||
|
|
004 2,
|
||
|
|
005 3
|
||
|
|
006 ]
|
||
|
|
007 ]
|
||
|
|
----
|
||
|
|
|
||
|
|
Now it's possible to reference each element just by the
|
||
|
|
line's number.
|
||
|
|
|
||
|
|
In Prolog all structured data is represented as a list.
|
||
|
|
For simplifing the explanations below we decide between a list and
|
||
|
|
a tuple. Both structures are represented as a list in Prolog, but
|
||
|
|
a tuple is a list with a fixed len. In no case a list called
|
||
|
|
tuple will be composed of more or less elements as described in
|
||
|
|
this example.
|
||
|
|
|
||
|
|
For example the list of predicates is a typical list
|
||
|
|
because their len is determined by the sql query to be optimized.
|
||
|
|
The predicate description which the list of predicates is composed of
|
||
|
|
is a typical tuple. It ever contains of three element.
|
||
|
|
|
||
|
|
5.2.1 Preparation
|
||
|
|
|
||
|
|
----
|
||
|
|
1 ?- secondo('open database opt;').
|
||
|
|
Total runtime ... Times (elapsed / cpu): 0.010001sec / 0.01sec = 1.0001
|
||
|
|
Command succeeded, result:
|
||
|
|
|
||
|
|
** output truncated **
|
||
|
|
|
||
|
|
2 ?- setOption(entropy).
|
||
|
|
Total runtime ... Times (elapsed / cpu): 0.080001sec / 0.07sec = 1.14287
|
||
|
|
Switched ON option: 'entropy' - Use entropy to estimate selectivities.
|
||
|
|
|
||
|
|
Yes
|
||
|
|
----
|
||
|
|
|
||
|
|
Setting the option entropy is nessecary first to let the
|
||
|
|
system generate the dynamic facts edge/6. These facts are used
|
||
|
|
by later prolog praedicates to analyse the sql query to be
|
||
|
|
optimized.
|
||
|
|
|
||
|
|
After toggling on the Option entropy the sql query to be
|
||
|
|
optimized has to be entered.
|
||
|
|
|
||
|
|
----
|
||
|
|
3 ?- sql select count(*) from [ plz as a, plz as b ]
|
||
|
|
where [a:plz > 40000, b:plz < 50000, a:plz <50000].
|
||
|
|
|
||
|
|
Computing best Plan ...
|
||
|
|
Destination node 7 reached at iteration 6
|
||
|
|
Height of search tree for boundary is 1
|
||
|
|
|
||
|
|
Computing best Plan ...
|
||
|
|
Destination node 7 reached at iteration 6
|
||
|
|
Height of search tree for boundary is 1
|
||
|
|
|
||
|
|
Computing best Plan ...
|
||
|
|
Destination node 7 reached at iteration 6
|
||
|
|
Height of search tree for boundary is 1
|
||
|
|
|
||
|
|
Computing best Plan ...
|
||
|
|
Destination node 7 reached at iteration 6
|
||
|
|
Height of search tree for boundary is 1
|
||
|
|
|
||
|
|
Computing best Plan ...
|
||
|
|
Destination node 7 reached at iteration 6
|
||
|
|
Height of search tree for boundary is 1
|
||
|
|
|
||
|
|
Computing best Plan ...
|
||
|
|
Destination node 7 reached at iteration 6
|
||
|
|
Height of search tree for boundary is 1
|
||
|
|
|
||
|
|
Computing best Plan ...
|
||
|
|
Destination node 7 reached at iteration 6
|
||
|
|
Height of search tree for boundary is 1
|
||
|
|
|
||
|
|
Computing best Plan ...
|
||
|
|
Destination node 7 reached at iteration 6
|
||
|
|
Height of search tree for boundary is 1
|
||
|
|
|
||
|
|
Computing best Plan ...
|
||
|
|
Destination node 7 reached at iteration 6
|
||
|
|
Height of search tree for boundary is 1
|
||
|
|
|
||
|
|
Computing best Plan ...
|
||
|
|
Destination node 7 reached at iteration 6
|
||
|
|
Height of search tree for boundary is 1
|
||
|
|
|
||
|
|
Computing best Plan ...
|
||
|
|
Destination node 7 reached at iteration 6
|
||
|
|
Height of search tree for boundary is 1
|
||
|
|
|
||
|
|
Computing best Plan ...
|
||
|
|
Destination node 7 reached at iteration 6
|
||
|
|
Height of search tree for boundary is 1
|
||
|
|
|
||
|
|
No
|
||
|
|
----
|
||
|
|
|
||
|
|
After entering the sql query the option correlation
|
||
|
|
has to be toggled on. By doing this the option entropy
|
||
|
|
will be toggled off automatically.
|
||
|
|
|
||
|
|
----
|
||
|
|
4 ?- setOption(correlations).
|
||
|
|
Switched OFF option: 'entropy' - Use entropy to estimate selectivities.
|
||
|
|
% ./Correlations/correlations compiled 0.01 sec, 10,660 bytes
|
||
|
|
Switched ON option: 'correlations' - Try to take predicate interdependence into account.
|
||
|
|
|
||
|
|
Yes
|
||
|
|
----
|
||
|
|
|
||
|
|
5.2.2 Analyze the query to be opimized
|
||
|
|
|
||
|
|
This analysis is done by the prolog predicate
|
||
|
|
build\_list\_of\_predicates/0.
|
||
|
|
|
||
|
|
----
|
||
|
|
5 ?- build_list_of_predicates.
|
||
|
|
|
||
|
|
No
|
||
|
|
----
|
||
|
|
|
||
|
|
After calling the predicate build\_list\_of\_predicates/0
|
||
|
|
the dynamic facts listOfPredicates/1 and listOfRelations/1 were
|
||
|
|
created. The content of their arguments are shown below.
|
||
|
|
|
||
|
|
----
|
||
|
|
6 ?- listOfPredicates(X).
|
||
|
|
010 X =
|
||
|
|
020 [
|
||
|
|
030 [
|
||
|
|
031 4,
|
||
|
|
032 rel(plz, a),
|
||
|
|
033 pr(attr(a:pLZ, 1, u)<50000, rel(plz, a))
|
||
|
|
034 ],
|
||
|
|
040 [
|
||
|
|
041 2,
|
||
|
|
042 rel(plz, b),
|
||
|
|
043 pr(attr(b:pLZ, 1, u)<50000, rel(plz, b))
|
||
|
|
044 ],
|
||
|
|
050 [
|
||
|
|
051 1,
|
||
|
|
052 rel(plz, a),
|
||
|
|
053 pr(attr(a:pLZ, 1, u)>40000, rel(plz, a))
|
||
|
|
054 ]
|
||
|
|
060 ]
|
||
|
|
|
||
|
|
Yes
|
||
|
|
----
|
||
|
|
|
||
|
|
The content of X is the list of sql predicates found by
|
||
|
|
predicate build\_list\_of\_predicates/0 before. Each sql predicate found
|
||
|
|
is represented by one tuple (lines 30-34, 40-44 and 50-54).
|
||
|
|
Each tuple is composed of three elements: (sql joins are disallowed yet!)
|
||
|
|
|
||
|
|
1 POG identifier of the sql predicate (lines 31,41 and 51)
|
||
|
|
|
||
|
|
2 the relation instance of the sql predicate represented by fact rel/2
|
||
|
|
(lines 32, 42 and 52)
|
||
|
|
|
||
|
|
3 the sql predicate itself (lines 33, 43 and 53)
|
||
|
|
|
||
|
|
----
|
||
|
|
|
||
|
|
7 ?- listOfRelations(Y).
|
||
|
|
|
||
|
|
110 Y =
|
||
|
|
120 [
|
||
|
|
130 rel(plz, b, l),
|
||
|
|
140 rel(plz, a, l)
|
||
|
|
150 ]
|
||
|
|
|
||
|
|
Yes
|
||
|
|
----
|
||
|
|
|
||
|
|
The content of Y is the distinctive list of relation instances
|
||
|
|
found by build\_list\_of\_predicates/0. Although two sql predicates use
|
||
|
|
the same relation PLZ the relation was added twice to the list
|
||
|
|
because the relation PLZ was used as relation instance a and relation
|
||
|
|
instance b within the sql query. On the other hand the relation instance
|
||
|
|
b was added just once, although the relation instance is used by
|
||
|
|
two predicates. For a more detailed explanation of relation instances
|
||
|
|
see the section instances of relations above.
|
||
|
|
|
||
|
|
5.2.3 Build predcounts queries and get the statistics
|
||
|
|
|
||
|
|
----
|
||
|
|
8 ?- build_queries(Queries), calculate_predcounts(Queries,Result).
|
||
|
|
0.init finished
|
||
|
|
Total runtime ... Times (elapsed / cpu): 1.91003sec / 1.91sec = 1.00002
|
||
|
|
0.init finished
|
||
|
|
Total runtime ... Times (elapsed / cpu): 0.530008sec / 0.54sec = 0.981496
|
||
|
|
210 Queries =
|
||
|
|
220 [
|
||
|
|
230 [
|
||
|
|
231 [2] |
|
||
|
|
232 query plz feed {b} predcounts [ P2: (.PLZ_b < 50000) ]
|
||
|
|
232 consume;
|
||
|
|
233 ],
|
||
|
|
240 [
|
||
|
|
241 [4, 1] |
|
||
|
|
242 query plz feed {a} predcounts [ P4: (.PLZ_a < 50000),
|
||
|
|
242 P1: (.PLZ_a > 40000) ] consume;
|
||
|
|
243 ]
|
||
|
|
250 ],
|
||
|
|
310 Result =
|
||
|
|
320 [
|
||
|
|
330 [
|
||
|
|
331 [2, 21470],
|
||
|
|
332 [0, 19797]
|
||
|
|
333 ],
|
||
|
|
340 [
|
||
|
|
341 [5, 3127],
|
||
|
|
342 [1, 19797],
|
||
|
|
343 [4, 18343],
|
||
|
|
344 [0, 0]
|
||
|
|
345 ]
|
||
|
|
350 ]
|
||
|
|
|
||
|
|
Yes
|
||
|
|
----
|
||
|
|
|
||
|
|
The variable Queries contains a list of tuples (lines
|
||
|
|
230-233 and 240-243). One tuple
|
||
|
|
corresponds with exactly one relation instance (lines 130
|
||
|
|
and 140)
|
||
|
|
found by build\_list\_of\_predicates/0. Each tuple is composed of two
|
||
|
|
elements:
|
||
|
|
|
||
|
|
1 the list of POG identifiers of the sql predicates used by
|
||
|
|
the predcounts execution plan (see element two); the order of the
|
||
|
|
POG identifiers corresponds with the order of using the sql predicates
|
||
|
|
within the predcounts execution plan
|
||
|
|
|
||
|
|
2 predcounts execution plan of one relation instance with all
|
||
|
|
sql predicates using this relation instance
|
||
|
|
|
||
|
|
The variable Result is unified with the list of results of
|
||
|
|
predcounts execution plans created by the predicate build\_queries/1.
|
||
|
|
(lines 232 and 242) Each result corresponds with one relation instance.
|
||
|
|
The order of predcounts results stored in Result matches the order of
|
||
|
|
predcounts execution plans in the variable Queries.
|
||
|
|
|
||
|
|
The predcounts result is a list of tuples. Each tuple is
|
||
|
|
composed of a element atom (first one) and an element count (second
|
||
|
|
one). An explanation of the tuple's meaning could be found in the
|
||
|
|
documentation of operator predcounts.
|
||
|
|
|
||
|
|
The predcounts's results stored in Result are already
|
||
|
|
transformed. What means transformed? This issue is discussed later in
|
||
|
|
this document detailed. In a short manner one could say, the identifiers
|
||
|
|
of the tuples (column atom) are transformed for using it directly to
|
||
|
|
identify nodes of the POG.
|
||
|
|
|
||
|
|
5.2.4 How are the predcounts results to be interpreted ?
|
||
|
|
|
||
|
|
Each predcounts result is exclusively calculated for
|
||
|
|
exact one relation instance. The tuples attribute atom identifies which
|
||
|
|
predicates a tuple has to solve and not to solve to increase the count value
|
||
|
|
of this tuple.
|
||
|
|
|
||
|
|
To understand the meaning of predcounts result the predcounts
|
||
|
|
execution plan of relation instance a (line 242) will be executed.
|
||
|
|
|
||
|
|
----
|
||
|
|
9 ?- secondo(query plz feed {a} predcounts [ P4: (.PLZ_a < 50000),
|
||
|
|
P1: (.PLZ_a > 40000) ] consume;', A).
|
||
|
|
0.init finished
|
||
|
|
Total runtime ... Times (elapsed / cpu): 0.940014sec / 0.89sec = 1.0562
|
||
|
|
|
||
|
|
410 A =
|
||
|
|
420 [
|
||
|
|
430 [rel,
|
||
|
|
431 [tuple,
|
||
|
|
432 [
|
||
|
|
433 [Atom, int],
|
||
|
|
434 [Count, int]
|
||
|
|
435 ]
|
||
|
|
436 ]
|
||
|
|
437 ],
|
||
|
|
440 [
|
||
|
|
441 [3, 3127],
|
||
|
|
442 [2, 19797],
|
||
|
|
443 [1, 18343],
|
||
|
|
444 [0, 0]
|
||
|
|
445 ]
|
||
|
|
450 ]
|
||
|
|
|
||
|
|
Yes
|
||
|
|
----
|
||
|
|
|
||
|
|
While looking at the listing above you will see the predcounts
|
||
|
|
result is a list of tuples and each tuple is composed of a value Atom
|
||
|
|
and a value Count.
|
||
|
|
|
||
|
|
To understand the value atom one has to imagine the value in
|
||
|
|
binary mode. So the value 1 is 01. The Count 18343 means that 18343 tuples
|
||
|
|
of the relation instance b solve the the predicate P4 but not the
|
||
|
|
predicate P1. (Please note the tuples must not solve the predicate P1.
|
||
|
|
This is in contradiction to the meaning of POG's nodes identifier.)
|
||
|
|
|
||
|
|
To determine how many tuples of relation instance a solves
|
||
|
|
the predicate P4 in independence of predicate P1, the values Count of
|
||
|
|
the result's tuples identified by 2 (binary 10) and 3 (binary 11)
|
||
|
|
has to be added. In the example you get a count of 18343 + 3127 = 21470.
|
||
|
|
|
||
|
|
5.2.5 Some Theory
|
||
|
|
|
||
|
|
5.2.5.1 Definitions
|
||
|
|
|
||
|
|
.
|
||
|
|
|
||
|
|
Be $Pi = \{ p_1, p_2, p_4, ..., p_{2^m} \}$ the set of predicates used
|
||
|
|
by the sql query to be optimized and $P_{N_i}$ the set of predicates
|
||
|
|
solved at POG's node $N_i$.
|
||
|
|
|
||
|
|
Be $R = \{R_0, R_1, \ldots, R_n \}$ the set of relation instances used by
|
||
|
|
the sql query to be optimized and $R_{N_i}$ the set of relation instances
|
||
|
|
used by the predicates of set $P_{N_i}$.
|
||
|
|
|
||
|
|
Be $C_{N_0} = R_0 \times R_1 \times \ldots \times R_n$ the
|
||
|
|
initial set of tupels at the start node $N_0$.
|
||
|
|
|
||
|
|
Be $r: P \rightarrow 2^R$ the function which determines the
|
||
|
|
relation instances $R_{p_i} \subseteq R$ used by the predicate
|
||
|
|
$p_i \in P$.
|
||
|
|
|
||
|
|
Be the cardinality $C_{N_i}$ the count of tuples which solves all
|
||
|
|
predicates $p \in P_{N_i}$.
|
||
|
|
|
||
|
|
Be the selectivity $S_{N_i} = \frac{C_{N_i}}{C_{N_0}}$.
|
||
|
|
|
||
|
|
Be $PC_{R_i} \subset \aleph \times \aleph$ the predcounts result. Each
|
||
|
|
element $t \in PC_{R_i}$ is composed of an attribute atom and an attribute
|
||
|
|
count. The elements of the tuple $t \in PC_{R_i}$ can be obtained
|
||
|
|
by the functions $a_{atom}: PC_{R_i} \rightarrow \aleph$ and
|
||
|
|
$a_{count}: PC_{R_i} \rightarrow \aleph$. In addition there is a function
|
||
|
|
$solved: PC_{R_i} \rightarrow P$ which determines the set of predicates
|
||
|
|
solved by the tuples $e \in R_i$ that are represented by tuple $t \in PC_{R_i}$
|
||
|
|
of predcounts result.
|
||
|
|
|
||
|
|
Be $card: R_{N_i} \times \aleph \rightarrow \aleph$ a function which
|
||
|
|
determines $\forall t \in R_{N_i}, n \le 2^{|P|}: card(t,n) = ???$
|
||
|
|
|
||
|
|
Be $CM_{R_i}$ the set of tuples $c_{R_i,\aleph} \in \aleph \times
|
||
|
|
\aleph$ of the the predcounts result. The elements of the tuple $c_{R_i,\aleph}$
|
||
|
|
can be obtained by the functions $a_{atom}(c_{R_i,\aleph}) \mapsto \aleph$ and
|
||
|
|
$a_{count}(c_{R_i,\aleph}) \mapsto \aleph$
|
||
|
|
|
||
|
|
Be $s: PC_{R_i} \rightarrow P$ the function which determines
|
||
|
|
the set of predicates solved by tuples represented by a tuple
|
||
|
|
of predcounts result PC. For example the $a_{atom}(R_i,3)=5$ returns
|
||
|
|
the set $\{p_4, p_1\}$.
|
||
|
|
|
||
|
|
5.2.5.2 Types of POG's nodes
|
||
|
|
|
||
|
|
.
|
||
|
|
|
||
|
|
While evaluating the predcounts results it's possible to devide
|
||
|
|
the set of POG's nodes into the following types of nodes:
|
||
|
|
|
||
|
|
** was ist mit Praedikaten, die keine Relation verwenden **
|
||
|
|
|
||
|
|
1. the start node $N_0$ with $|P_{N_0}| = 0$
|
||
|
|
|
||
|
|
2. nodes $N_i$ with $|P_{N_i}| = 1$ and $|R_{N_i}| = 1$
|
||
|
|
|
||
|
|
3. nodes $N_i$ with $|R_{N_i}| = 1$
|
||
|
|
|
||
|
|
4. nodes $N_i$ with $|R_{N_i}| > 1$ but
|
||
|
|
$\forall p \in P_{N_i}: |r(p)| = 1$
|
||
|
|
|
||
|
|
5. nodes $N_i$ with $\exists p \in P_{N_i}: |r(p)| \ge 2$
|
||
|
|
|
||
|
|
5.2.5.3 Determine the cardinalities
|
||
|
|
|
||
|
|
** Das folgende muesste eigentlich bewiesen werden - oder ? **
|
||
|
|
|
||
|
|
5.2.5.3.1 Node of type 1
|
||
|
|
|
||
|
|
Within a POG there exist only one node of type 1. This node is
|
||
|
|
the start node of the POG.
|
||
|
|
|
||
|
|
To determine the cardinality of node $N_0$ based on predcount results
|
||
|
|
the cardinalities $C_{R_i}$ of all relation instances have to calculated first.
|
||
|
|
This can be done by: $$C_{R_i} = \sum_t^{PC_{R_i}} a_{count}(t)$$
|
||
|
|
|
||
|
|
The cardinality $C_{N_0}$ can be calculated as follows:
|
||
|
|
$$C_{N_0} = \prod_{R_i}^R C_{R_i}$$
|
||
|
|
|
||
|
|
5.2.5.3.1 Nodes of type 2 and 3
|
||
|
|
|
||
|
|
The nodes of type 2 are all nodes which follows directly of the
|
||
|
|
POG's start node. At all of these nodes just one predicate was evaluated.
|
||
|
|
The predicate evaluated uses exactly one relation instance $R_{p_i} \in
|
||
|
|
R_{N_i}$ with $p_i \in P_{N_i}$.
|
||
|
|
|
||
|
|
|
||
|
|
The cardinality of these nodes $C_{N_i}$ can be obtained using
|
||
|
|
predcounts results $PC_{R_i}$:
|
||
|
|
$$C_{N_i} = C_{R_i}' * \prod_{R_j}^{R \setminus R_{N_i}} C_{R_j}$$
|
||
|
|
with
|
||
|
|
$$C_{R_i}' = \sum_t^{\{e \in PC_{R_i} { | } \forall p \in P_{N_i}:
|
||
|
|
p \in solved(e)\}}
|
||
|
|
a_{count}(t)$$
|
||
|
|
|
||
|
|
The way described above is also usable to determine the
|
||
|
|
cardinality $C_{N_i}$ of nodes of type 3.
|
||
|
|
|
||
|
|
5.2.5.3.1 Nodes of type 4
|
||
|
|
|
||
|
|
The nodes of type 4 includes all nodes except type 1,2,3 nodes and
|
||
|
|
nodes which includes join predicates. To obtain the cardinality of such
|
||
|
|
a node the following equation has to be solved:
|
||
|
|
$$C_{N_i} = \prod_{R_m}^{R_{N_i}} C_{R_m}' *
|
||
|
|
\prod_{R_j}^{R \setminus R_{N_i}} C_{R_j}$$ with
|
||
|
|
$$C_{R_m}' = \sum_t^{\{e \in PC_{R_m} { | } \forall p \in P_{N_i}:
|
||
|
|
p \in solved(e)\}} a_{count}(t)$$.
|
||
|
|
|
||
|
|
The both equations above are the general form of the equations
|
||
|
|
for type 1,2 and 3 nodes.
|
||
|
|
|
||
|
|
5.2.5.3.1 nodes of type 5
|
||
|
|
|
||
|
|
The nodes of type 5 are nodes including join predicates. The
|
||
|
|
source is not still able to deal with these predicates.
|
||
|
|
|
||
|
|
5.2.6 The cardinalities of the example's nodes
|
||
|
|
|
||
|
|
The sql query to be optimized contains three predicates (see lines 010 - 060):
|
||
|
|
|
||
|
|
* $P1: attr(a:pLZ, 1, u)>40000$
|
||
|
|
|
||
|
|
* $P2: attr(b:pLZ, 1, u)<50000$
|
||
|
|
|
||
|
|
* $P4: attr(a:pLZ, 1, u)<50000$
|
||
|
|
|
||
|
|
The three predicates uses two relation instances. Therefore two
|
||
|
|
predcounts execution plans were created (lines 232 and 242).
|
||
|
|
|
||
|
|
* $query plz feed \{b\} predcounts [ P2: (.PLZ\_b < 50000) ] consume;$
|
||
|
|
|
||
|
|
* $query plz feed \{a\} predcounts [ P4: (.PLZ\_a < 50000),
|
||
|
|
P1: (.PLZ_a > 40000) ] consume;$
|
||
|
|
|
||
|
|
The queries's result was stored in the variable Result as follows:
|
||
|
|
|
||
|
|
----
|
||
|
|
310 Result =
|
||
|
|
320 [
|
||
|
|
330 [
|
||
|
|
331 [2, 21470],
|
||
|
|
332 [0, 19797]
|
||
|
|
333 ],
|
||
|
|
340 [
|
||
|
|
341 [5, 3127],
|
||
|
|
342 [1, 19797],
|
||
|
|
343 [4, 18343],
|
||
|
|
344 [0, 0]
|
||
|
|
345 ]
|
||
|
|
350 ]
|
||
|
|
----
|
||
|
|
|
||
|
|
Using the predcounts result's above we get:
|
||
|
|
|
||
|
|
* $R = \{ R_a, R_b \}$
|
||
|
|
|
||
|
|
* $PC_{R_a} = \{ (5,3127), (1,19797), (4,18343), (0,0) \}$
|
||
|
|
|
||
|
|
* $PC_{R_b} = \{ (2,21470), (0,19797) \}$
|
||
|
|
|
||
|
|
By adding some values we get additionally:
|
||
|
|
$$C_{R_a} = \sum_t^{PC_{R_a}} a_{count}(t) = 3127 + 19797 + 18343 + 0 = 41267$$
|
||
|
|
$$C_{R_b} = \sum_t^{PC_{R_b}} a_{count}(t) = 21470 + 19797 = 41267$$
|
||
|
|
|
||
|
|
At first all nodes of the example's POG are of the type 1 to 4.
|
||
|
|
So the cardinality of each POG's node can be obtained by using the
|
||
|
|
equations for type 4 nodes.
|
||
|
|
|
||
|
|
|
||
|
|
5.2.6.1 node $N_0$ (type 1)
|
||
|
|
|
||
|
|
$P_{N_0} = \emptyset$ and $R_{N_0} = \emptyset$
|
||
|
|
|
||
|
|
$$C_{N_0} = \prod_{R_i}^R C_{R_i} $$
|
||
|
|
$$ C_{N_0} = \prod_{R_i}^{\{ R_a, R_b\}} C_{R_i} $$
|
||
|
|
$$ C_{N_0} = C_{R_a} * C_{R_b} $$
|
||
|
|
$$ C_{N_0} = 41267 * 41267 $$
|
||
|
|
$$ C_{N_0} = 1702965289 $$
|
||
|
|
|
||
|
|
5.2.6.2 node $N_1$ (type 2)
|
||
|
|
|
||
|
|
$P_{N_1} = \{ p_1 \}$ and $R_{N_1} = \{ R_a \}$
|
||
|
|
|
||
|
|
$$ C_{N_1} = C_{R_{N_1}}' * \prod_{R_i}^{R \setminus R_{N_1}} C_{R_i}$$
|
||
|
|
$$ C_{N_1} = C_{R_a}' * \prod_{R_i}^{R \setminus \{ R_a \}} C_{R_i} $$
|
||
|
|
$$ C_{N_1} = C_{R_a}' * \prod_{R_i}^{\{ R_b \}} C_{R_i} $$
|
||
|
|
$$ C_{N_1} = C_{R_a}' * C_{R_b} $$
|
||
|
|
$$ C_{N_1} = \left( \sum_t^{\{e \in PC_{R_a} { | } \forall p \in \{ p_1 \}:
|
||
|
|
p \in solved(e)\}} a_{count}(t) \right) * C_{R_b} $$
|
||
|
|
$$ C_{N_1} = \left( \sum_t^{\{ (5,3127), (1,19797) \}} a_{count}(t)
|
||
|
|
\right) * C_{R_b} $$
|
||
|
|
$$ C_{N_1} = ( 3127 + 19797 ) * 41267$$
|
||
|
|
$$ C_{N_1} = 946004708 $$
|
||
|
|
|
||
|
|
5.2.6.3 node $N_2$ (type 2)
|
||
|
|
|
||
|
|
$P_{N_2} = \{ p_2 \}$ and $R_{N_2} = \{ R_b \}$
|
||
|
|
|
||
|
|
$$ C_{N_2} = C_{R_b}' * C_{R_a} $$
|
||
|
|
$$ C_{N_2} = \left( \sum_t^{\{e \in PC_{R_b} { | } \forall p \in \{ p_2 \}:
|
||
|
|
p \in solved(e)\}} a_{count}(t) \right) * C_{R_a} $$
|
||
|
|
$$ C_{N_2} = \left( \sum_t^{\{ (2,21470) \}} a_{count}(t)
|
||
|
|
\right) * C_{R_a} $$
|
||
|
|
$$ C_{N_2} = ( 21470 ) * 41267$$
|
||
|
|
$$ C_{N_2} = 886002490 $$
|
||
|
|
|
||
|
|
5.2.6.4 node $N_4$ (type 2)
|
||
|
|
|
||
|
|
$P_{N_4} = \{ p_4 \}$ and $R_{N_4} = \{ R_a \}$
|
||
|
|
|
||
|
|
$$ C_{N_4} = C_{R_a}' * C_{R_b} $$
|
||
|
|
$$ C_{N_4} = \left( \sum_t^{\{e \in PC_{R_a} { | } \forall p \in \{ p_4 \}:
|
||
|
|
p \in solved(e)\}} a_{count}(t) \right) * C_{R_b} $$
|
||
|
|
$$ C_{N_4} = \left( \sum_t^{\{ (5,3127), (4,18343) \}} a_{count}(t)
|
||
|
|
\right) * C_{R_b} $$
|
||
|
|
$$ C_{N_4} = ( 3127 + 18343 ) * 41267$$
|
||
|
|
$$ C_{N_4} = 886002490 $$
|
||
|
|
|
||
|
|
5.2.6.4 node $N_5$ (type 3)
|
||
|
|
|
||
|
|
$P_{N_5} = \{ p_1, p_4 \}$ and $R_{N_5} = \{ R_a \}$
|
||
|
|
|
||
|
|
$$ C_{N_4} = C_{R_a}' * C_{R_b} $$
|
||
|
|
$$ C_{N_4} = \left( \sum_t^{\{e \in PC_{R_a} { | } \forall p \in \{ p_1, p_4 \}:
|
||
|
|
p \in solved(e)\}} a_{count}(t) \right) * C_{R_b} $$
|
||
|
|
$$ C_{N_4} = \left( \sum_t^{\{ (5,3127) \}} a_{count}(t)
|
||
|
|
\right) * C_{R_b} $$
|
||
|
|
$$ C_{N_4} = ( 3127 ) * 41267$$
|
||
|
|
$$ C_{N_4} = 129041909 $$
|
||
|
|
|
||
|
|
|
||
|
|
5.2.6.5 node $N_3$ (type 4)
|
||
|
|
|
||
|
|
$P_{N_3} = \{ p_1, p_2 \}$ and $R_{N_3} = \{ R_a, R_b \}$
|
||
|
|
|
||
|
|
$$ C_{N_3} = \prod_{R_m}^{R_{N_3}} C_{R_m}' *
|
||
|
|
\prod_{R_j}^{R \setminus R_{N_3}} C_{R_j} $$
|
||
|
|
$$ C_{N_3} = \prod_{R_m}^{\{R_a, R_b\}} C_{R_m}' *
|
||
|
|
\prod_{R_j}^{R \setminus \{ R_a, R_b \}} C_{R_j} $$
|
||
|
|
$$ C_{N_3} = \prod_{R_m}^{\{R_a, R_b\}} C_{R_m}' *
|
||
|
|
\prod_{R_j}^{\emptyset} C_{R_j} $$
|
||
|
|
$$ C_{N_3} = \prod_{R_m}^{\{R_a, R_b\}} C_{R_m}'$$
|
||
|
|
$$ C_{N_3} = C_{R_a}' * C_{R_b}' $$
|
||
|
|
|
||
|
|
** aus nachfolgender Formel ergibt sich noch ein Fehler (p in Durchschnitt!) **
|
||
|
|
|
||
|
|
$$ C_{N_3} = \sum_t^{\{e \in PC_{R_a} { | } \forall p \in P_{N_3}:
|
||
|
|
p \in solved(e)\}} a_{count}(t) *
|
||
|
|
\sum_t^{\{e \in PC_{R_b} { | } \forall p \in P_{N_3}:
|
||
|
|
p \in solved(e)\}} a_{count}(t)$$.
|
||
|
|
|
||
|
|
** denn eigentlich muss folgendes herauskommen {p1} statt {p1,p2} **
|
||
|
|
|
||
|
|
$$ C_{N_3} = \sum_t^{\{e \in PC_{R_a} { | } \forall p \in \{ p_1 \}:
|
||
|
|
p \in solved(e)\}} a_{count}(t) *
|
||
|
|
\sum_t^{\{e \in PC_{R_b} { | } \forall p \in \{ p_2 \}:
|
||
|
|
p \in solved(e)\}} a_{count}(t)$$
|
||
|
|
$$ C_{N_3} = \sum_t^{\{ (5,3127), (1,19797) \}} a_{count}(t) *
|
||
|
|
\sum_t^{\{ (2,21470) \}} a_{count}(t) $$
|
||
|
|
$$ C_{N_3} = ( 3127 + 19797 ) * 21470 $$
|
||
|
|
$$ C_{N_3} = 22924 * 21470 $$
|
||
|
|
$$ C_{N_3} = 492178280 $$
|
||
|
|
|
||
|
|
|
||
|
|
5.2.6.5 node $N_6$ (type 4)
|
||
|
|
|
||
|
|
dto
|
||
|
|
|
||
|
|
5.2.6.5 node $N_7$ (type 4)
|
||
|
|
|
||
|
|
dto
|
||
|
|
|
||
|
|
|
||
|
|
5.2.7 What means transformed in case of the result set?
|
||
|
|
|
||
|
|
** der Abschnitt muss woanders hin **
|
||
|
|
|
||
|
|
To explain let us look at the native??? results of the
|
||
|
|
predcounts execution plans.
|
||
|
|
|
||
|
|
----
|
||
|
|
66 ?- secondo('query plz feed {b} predcounts [ P2: (.PLZ_b < 50000) ]
|
||
|
|
consume;', Z).
|
||
|
|
0.init finished
|
||
|
|
Total runtime ... Times (elapsed / cpu): 0.800012sec / 0.61sec = 1.3115
|
||
|
|
|
||
|
|
410 Z =
|
||
|
|
420 [
|
||
|
|
430 [rel, [tuple, [[Atom, int], [Count, int]]]],
|
||
|
|
440 [
|
||
|
|
441 [1, 21470],
|
||
|
|
442 [0, 19797]
|
||
|
|
443 ]
|
||
|
|
450 ]
|
||
|
|
|
||
|
|
Yes
|
||
|
|
67 ?- secondo(, A).
|
||
|
|
0.init finished
|
||
|
|
Total runtime ... Times (elapsed / cpu): 0.940014sec / 0.89sec = 1.0562
|
||
|
|
|
||
|
|
510 A =
|
||
|
|
520 [
|
||
|
|
530 [rel, [tuple, [[Atom, int], [Count, int]]]],
|
||
|
|
540 [
|
||
|
|
541 [3, 3127],
|
||
|
|
542 [2, 19797],
|
||
|
|
543 [1, 18343],
|
||
|
|
544 [0, 0]
|
||
|
|
545 ]
|
||
|
|
550 ]
|
||
|
|
|
||
|
|
Yes
|
||
|
|
----
|
||
|
|
|
||
|
|
As you can see??? the tuples of the result are identified by
|
||
|
|
0 and 1. The tuple identified by 0 shows the number of rows of the
|
||
|
|
relation plz doesn't solve??? the sql predicate " PLZ < 50000 " . The
|
||
|
|
other tuple shows the number of rows solve the sql predicate. But
|
||
|
|
where should these results are written at the POG?
|
||
|
|
|
||
|
|
For each predcounts execution plan there was created a
|
||
|
|
transformation list (lines 231 and 241). For the example we have to
|
||
|
|
look at the first one. The list contains just one element. So the only
|
||
|
|
one predicate of predcounts operator corresponds with this element.
|
||
|
|
This means 21470 rows of plz solve the predicate identified with 2 in
|
||
|
|
the POG and 19797 rows don't do so???. So one is able to set the
|
||
|
|
cardinalty of node 2 (binary: 010) to 21470. The value 19797 cann't
|
||
|
|
be used directly. To used this value one have to combine them with
|
||
|
|
the result tuples of the other predcounts queries identified with
|
||
|
|
atom = 0.
|
||
|
|
|
||
|
|
Let's have a look at the second predounts query (lines 242),
|
||
|
|
their transformation list (line 241) and their native result list (lines
|
||
|
|
540-545). The predcounts query builds statistics of two predicates P4
|
||
|
|
and P1. Using the transformation list one is able to determine the
|
||
|
|
identifiers of the predicates within the POG. Within the POG the
|
||
|
|
predicate P1 is identified by 1 (binary 001) and the predicate P4
|
||
|
|
by 4 (binary 100). Within the predcounts result set the predicate P4
|
||
|
|
is identified by 2 (binary 010) and P1 by 1 (binary 001). To transform
|
||
|
|
the identifiers (column atom) of the native result set the identifiers
|
||
|
|
have to be changed by the following way:
|
||
|
|
|
||
|
|
1 Each identifier of the tuples (lines 541-544) is composed of
|
||
|
|
the predicate identifiers. By looking at the identifiers in binary mode
|
||
|
|
you are able to recognize this. The identifier is the sum??? of all
|
||
|
|
of the identifiers of solved predicates. In case of the example it means:
|
||
|
|
|
||
|
|
* atom=3 - binary 11 - predicates 1 and 2 are solved
|
||
|
|
|
||
|
|
* atom=2 - binary 10 - predicate 2 is solved AND predicate 1 is not
|
||
|
|
|
||
|
|
* atom=1 - binary 01 - predicate 1 is solved AND predicate 2 is not
|
||
|
|
|
||
|
|
* atom=0 - binary 00 - predicates 1 and 2 are not solved
|
||
|
|
|
||
|
|
2 The transformation list (line 241) means:
|
||
|
|
|
||
|
|
* predicate 1 is identified by 1 within the POG
|
||
|
|
|
||
|
|
* predicate 2 is identified by 4 within the POG
|
||
|
|
|
||
|
|
3 In case of predicate 1 there is nothing to do.
|
||
|
|
|
||
|
|
4 In case of predicate 2 it's identifier has to be changed to 4.
|
||
|
|
|
||
|
|
5 As you've seen above in the case of a solved predicate 2 the bit
|
||
|
|
2\^2 is set. (atom=3 and atom=2) To transform the tuples for using
|
||
|
|
for POG the bit 2i\^3 has to be set instead of bit 2i\^2. For the
|
||
|
|
result 11 has to be transformed to 101 and 10 to 100.
|
||
|
|
|
||
|
|
|
||
|
|
|
||
|
|
** hier weiter **
|
||
|
|
|
||
|
|
|
||
|
|
----
|
||
|
|
66 ?-
|
||
|
|
----
|
||
|
|
|
||
|
|
|
||
|
|
*/
|
||
|
|
/*
|
||
|
|
1 Helper predicates
|
||
|
|
|
||
|
|
The following predicates are used for easier programming and
|
||
|
|
understanding of the main code.
|
||
|
|
|
||
|
|
1.1 debug\_write
|
||
|
|
|
||
|
|
---- debug_write(Message)
|
||
|
|
----
|
||
|
|
|
||
|
|
The predicate debug\_write writes the given message to
|
||
|
|
the screen
|
||
|
|
without a trailing newline. The message is only written
|
||
|
|
if the fact debug\_level(X) with X greater then 0 is set.
|
||
|
|
|
||
|
|
*/
|
||
|
|
|
||
|
|
debug_write(_):- % if X=0 then no debugging messages
|
||
|
|
% if fact debug_level is not set retract fails
|
||
|
|
retract((debug_level(X))),
|
||
|
|
% reassert the fact
|
||
|
|
assert((debug_level(X))),
|
||
|
|
% X=0 no debug output requested
|
||
|
|
X=0,
|
||
|
|
!.
|
||
|
|
% write debugging messages without concated newline
|
||
|
|
debug_write(Message):-
|
||
|
|
% if fact debug_level is not set retract fails
|
||
|
|
retract((debug_level(X))),
|
||
|
|
% reassert the fact
|
||
|
|
assert((debug_level(X))),
|
||
|
|
% X>0 debug output requested
|
||
|
|
X > 0,
|
||
|
|
% write debug message
|
||
|
|
write(Message),
|
||
|
|
!.
|
||
|
|
debug_write(_). % in any other case ignore call of debug_write
|
||
|
|
|
||
|
|
/*
|
||
|
|
1.2 debug\_writeln
|
||
|
|
|
||
|
|
---- debug_writeln(message)
|
||
|
|
debug_writeln(Msg1, Msg2)
|
||
|
|
debug_writeln(Msg1, Msg2, Msg3)
|
||
|
|
debug_writeln(Msg1, Msg2, Msg3, Msg4)
|
||
|
|
debug_writeln(Msg1, Msg2, Msg3, Msg4, Msg5)
|
||
|
|
debug_writeln(Msg1, Msg2, Msg3, Msg4, Msg5, Msg6)
|
||
|
|
----
|
||
|
|
|
||
|
|
The predicates debug\_writeln write the given message(s) to the
|
||
|
|
screen. The
|
||
|
|
given message(s) are concatinated without any delimiter but a newline
|
||
|
|
will be appended behind??? the last message. The message(s) are only
|
||
|
|
written if the fact debug\_level(X) with X greater then 0 is set.
|
||
|
|
|
||
|
|
*/
|
||
|
|
|
||
|
|
% if X=0 then no debugging messages
|
||
|
|
debug_writeln(_):-
|
||
|
|
% if fact debug_level is not set retract fails
|
||
|
|
retract((debug_level(X))),
|
||
|
|
% reassert the fact
|
||
|
|
assert((debug_level(X))),
|
||
|
|
% X=0 no debug output requested
|
||
|
|
X=0,
|
||
|
|
!.
|
||
|
|
% write debugging messages concated newline
|
||
|
|
debug_writeln(Message):-
|
||
|
|
retract((debug_level(X))),
|
||
|
|
assert((debug_level(X))),
|
||
|
|
X > 0,
|
||
|
|
debug_write(Message),
|
||
|
|
writeln(''),
|
||
|
|
!.
|
||
|
|
debug_writeln(_).
|
||
|
|
|
||
|
|
/*
|
||
|
|
The following three predicates write two up to four messages
|
||
|
|
using the predicates debug\_write/1 and debug\_writeln/1
|
||
|
|
|
||
|
|
*/
|
||
|
|
|
||
|
|
% write two messages
|
||
|
|
debug_writeln(Msg1,Msg2):-
|
||
|
|
debug_write(Msg1),
|
||
|
|
debug_writeln(Msg2).
|
||
|
|
|
||
|
|
%write three messages
|
||
|
|
debug_writeln(Msg1,Msg2,Msg3):-
|
||
|
|
debug_write(Msg1),
|
||
|
|
debug_write(Msg2),
|
||
|
|
debug_writeln(Msg3).
|
||
|
|
|
||
|
|
% write four messages
|
||
|
|
debug_writeln(Msg1,Msg2,Msg3,Msg4):-
|
||
|
|
debug_write(Msg1),
|
||
|
|
debug_write(Msg2),
|
||
|
|
debug_write(Msg3),
|
||
|
|
debug_writeln(Msg4).
|
||
|
|
|
||
|
|
% write five messages
|
||
|
|
debug_writeln(Msg1,Msg2,Msg3,Msg4,Msg5):-
|
||
|
|
debug_write(Msg1),
|
||
|
|
debug_write(Msg2),
|
||
|
|
debug_write(Msg3),
|
||
|
|
debug_write(Msg4),
|
||
|
|
debug_writeln(Msg5).
|
||
|
|
|
||
|
|
% write six messages
|
||
|
|
debug_writeln(Msg1,Msg2,Msg3,Msg4,Msg5,Msg6):-
|
||
|
|
debug_write(Msg1),
|
||
|
|
debug_write(Msg2),
|
||
|
|
debug_write(Msg3),
|
||
|
|
debug_write(Msg4),
|
||
|
|
debug_write(Msg5),
|
||
|
|
debug_writeln(Msg6).
|
||
|
|
|
||
|
|
/*
|
||
|
|
1.3 atom\_concat/6
|
||
|
|
|
||
|
|
---- atom_concat(Txt1, Txt2, Txt3, Txt4, Txt5, Rslt)
|
||
|
|
----
|
||
|
|
|
||
|
|
The predicate atom\_concat/6 concatinates five strings to one. It uses
|
||
|
|
the already defined predicate atom\_concat/3.
|
||
|
|
|
||
|
|
*/
|
||
|
|
|
||
|
|
% concat more than two strings
|
||
|
|
atom_concat(Txt1, Txt2, Txt3, Txt4, Txt5, Rslt):-
|
||
|
|
atom_concat(Txt1, Txt2, TMP1),
|
||
|
|
atom_concat(TMP1, Txt3, TMP2),
|
||
|
|
atom_concat(TMP2, Txt4, TMP3),
|
||
|
|
atom_concat(TMP3, Txt5, Rslt).
|
||
|
|
|
||
|
|
|
||
|
|
/*
|
||
|
|
|
||
|
|
7 several code
|
||
|
|
|
||
|
|
*/
|
||
|
|
|
||
|
|
|
||
|
|
% die folgende Konstruktion is noetig, weil die nodeID
|
||
|
|
% neuerdings float ist
|
||
|
|
% falls nodeid integer in fact node/3 ist
|
||
|
|
node_nodeid(Node, NodeID):-
|
||
|
|
debug_writeln('node_nodeid 0 - ',Node,',',NodeID),
|
||
|
|
integer(NodeID),
|
||
|
|
node(NodeID, A, B),
|
||
|
|
Node = node(NodeID, A, B).
|
||
|
|
% falls in fact float verwendet, aber int angefordert wird
|
||
|
|
node_nodeid(Node, NodeID):-
|
||
|
|
debug_writeln('node_nodeid 1 - ',Node,',',NodeID),
|
||
|
|
integer(NodeID),
|
||
|
|
Id is 1.0 * NodeID,
|
||
|
|
node_nodeid(Node, Id).
|
||
|
|
% falls in fact float verwendet und float angefordert wird
|
||
|
|
node_nodeid(Node, NodeID):-
|
||
|
|
debug_writeln('node_nodeid 2 - ',Node,',',NodeID),
|
||
|
|
number(NodeID),
|
||
|
|
node(NodeID, A, B),
|
||
|
|
Node = node(NodeID, A, B).
|
||
|
|
% falls node gegeben und id angefordert ist, id dann als int
|
||
|
|
node_nodeid(Node, NodeID):-
|
||
|
|
debug_writeln('node_nodeid 3 - ',Node,',',NodeID),
|
||
|
|
Node = node(Id, _, _),
|
||
|
|
% wenn keine Node angegeben wurde, sondern nur bisher keine Node
|
||
|
|
% mit der NodeID gefunden wurde, dann ist mit nachfolgender
|
||
|
|
% ZEile auch dieser Zweig beendet
|
||
|
|
node(Id, _, _),
|
||
|
|
NodeID is round(Id).
|
||
|
|
|
||
|
|
list_nodes:-
|
||
|
|
node(A,B,_), write(A), write(' '), writeln(B), fail.
|
||
|
|
|
||
|
|
|
||
|
|
|
||
|
|
|
||
|
|
% speichern der PC-Ergs in Fakten: predcount_result(Relation, PCResult)
|
||
|
|
% call: node_nodeid(N,1), listOfRelations(R), !, product_over_all_relations(R, N, C).
|
||
|
|
|
||
|
|
is_rel_used_by_node(Relation, Node):-
|
||
|
|
Node = node(N, Predicates, _),
|
||
|
|
is_rel_used_by_preds(Relation, Predicates),
|
||
|
|
debug_writeln(Relation, ' is used by node ',N).
|
||
|
|
is_rel_used_by_node(Relation, Node):-
|
||
|
|
Node = node(N, _, _),
|
||
|
|
debug_writeln(Relation, ' is not used by node ',N),
|
||
|
|
fail.
|
||
|
|
|
||
|
|
is_rel_used_by_preds(Relation, []):-
|
||
|
|
debug_writeln(' kein Predicat, das ', Relation,' benutzt'),
|
||
|
|
fail.
|
||
|
|
is_rel_used_by_preds(Relation, [ Predicate | _ ]):-
|
||
|
|
is_rel_used_by_pred(Relation, Predicate),
|
||
|
|
debug_writeln(Relation, ' is used by ', Predicate).
|
||
|
|
is_rel_used_by_preds(Relation, [ Predicate | Predicates ]):-
|
||
|
|
debug_writeln(Relation, ' is not used by ', Predicate),
|
||
|
|
is_rel_used_by_preds(Relation, Predicates).
|
||
|
|
|
||
|
|
% hier werden derzeit keine joins oder relfreie Preds betrachtet
|
||
|
|
is_rel_used_by_pred(Relation, Predicate):-
|
||
|
|
Predicate = pr(_, Relation).
|
||
|
|
|
||
|
|
|
||
|
|
%all_preds_of_nodeid_allowed(NodeID):-
|
||
|
|
% node(NodeID, Predicates, _),
|
||
|
|
% writeln('pruefe Node ',NodeID,' with ',Predicates),
|
||
|
|
% all_preds_allowed(Predicates).
|
||
|
|
|
||
|
|
%all_preds_allowed([]).
|
||
|
|
%all_preds_allowed([ Predicate | Predicates ]):-
|
||
|
|
% is_pred_allowed(Predicate),
|
||
|
|
% all_preds_allowed(Predicates).
|
||
|
|
|
||
|
|
%is_pred_allowed(pr(_, _)).
|
||
|
|
|
||
|
|
|
||
|
|
|
||
|
|
|
||
|
|
% Rekursionsabschluss
|
||
|
|
product_over_all_relations([], node(N,_,_) , 1):-
|
||
|
|
debug_writeln('product_over_all_relations: prod=1 node=', N).
|
||
|
|
% fuer alle C'(R(i))
|
||
|
|
product_over_all_relations([ Relation | Relations ], Node, ProdNew):-
|
||
|
|
Node = node(N, _, _),
|
||
|
|
is_rel_used_by_node(Relation, Node),
|
||
|
|
predcounts_result(Relation, PCResult),
|
||
|
|
sum_conded_over_rels_pcresult(PCResult, Relation, Node, Sum),
|
||
|
|
debug_writeln('Summe_bedingte ueber(Rm=', Relation,' & Ni=',N,') = ',Sum),
|
||
|
|
product_over_all_relations(Relations, Node, Prod),
|
||
|
|
ProdNew is Prod * Sum,
|
||
|
|
debug_writeln('product_over_all_relations(C_): prod=',ProdNew,' node=',N),
|
||
|
|
debug_writeln(' prod=',Prod,'*',Sum).
|
||
|
|
% fuer alle C(R(i))
|
||
|
|
product_over_all_relations([ Relation | Relations ], Node, ProdNew):-
|
||
|
|
Node = node(N, _, _),
|
||
|
|
predcounts_result(Relation, PCResult),
|
||
|
|
sum_over_rels_pcresult(PCResult, Sum),
|
||
|
|
debug_writeln('Summe ueber(Rm=', Relation,' & Ni=',N,') = ',Sum),
|
||
|
|
product_over_all_relations(Relations, Node, Prod),
|
||
|
|
ProdNew is Prod * Sum,
|
||
|
|
debug_writeln('product_over_all_relations(C): prod=',ProdNew,' node=',N),
|
||
|
|
debug_writeln(' prod=',Prod,'*',Sum).
|
||
|
|
product_over_all_relations(A, B, C):-
|
||
|
|
write('Error: product_over_all_relations: unexpected call '), write(A), write(','),
|
||
|
|
write(B),write(','),writeln(C).
|
||
|
|
|
||
|
|
% Summe fuer unabhaengige Relationen
|
||
|
|
sum_over_rels_pcresult([], 0):-
|
||
|
|
debug_writeln(' sum_over_rels_pcresult: sum=0').
|
||
|
|
sum_over_rels_pcresult([ [ PCAtom , PCCount ] | PCResult ], SumNew):-
|
||
|
|
number(PCAtom),
|
||
|
|
number(PCCount),
|
||
|
|
sum_over_rels_pcresult(PCResult, Sum),
|
||
|
|
SumNew is Sum + PCCount,
|
||
|
|
debug_writeln(' nutze PCTupel ',[ PCAtom , PCCount ],' fuer Summe').
|
||
|
|
sum_over_rels_pcresult(A, B):-
|
||
|
|
write(' Error: sum_over_rels_pcresult: unexpected call '), write(A), write(','),
|
||
|
|
write(B).
|
||
|
|
|
||
|
|
% Summe fuer abhaengige Relationen
|
||
|
|
% Summe ueber PCTupel
|
||
|
|
sum_conded_over_rels_pcresult([], _, node(N, _, _), 0):-
|
||
|
|
debug_writeln(' sum_conded_over_rels_pcresult: sum=0 ', 'node=', N).
|
||
|
|
sum_conded_over_rels_pcresult([ [ PCAtom , PCCount ] | PCResult ], Relation, Node, SumNew):-
|
||
|
|
number(PCAtom),
|
||
|
|
number(PCCount),
|
||
|
|
sum_conded_over_rels_pcresult(PCResult, Relation, Node, Sum),
|
||
|
|
calc_rel_preds_mask(Relation, RelMask),
|
||
|
|
Node = node(NodeID, _, _),
|
||
|
|
MaskedNodeID is RelMask /\ round(NodeID),
|
||
|
|
condition_pctuple([ PCAtom , PCCount ], MaskedNodeID, Count),
|
||
|
|
SumNew is Sum + Count,
|
||
|
|
debug_writeln(' nutze ', Count, ' fuer PCTupel ',
|
||
|
|
[ PCAtom , PCCount ],' fuer Summe').
|
||
|
|
sum_conded_over_rels_pcresult(A, _, B, C):-
|
||
|
|
write(' Error: sum_conded_over_rels_pcresult: unexpected call '), write(A), write(','),
|
||
|
|
write(B), write(','), write(C).
|
||
|
|
|
||
|
|
|
||
|
|
condition_pctuple([ PCAtom , PCCount ], MaskedNodeID, Count):-
|
||
|
|
is_node_matching_atom(MaskedNodeID, PCAtom),
|
||
|
|
Count = PCCount.
|
||
|
|
condition_pctuple([ PCAtom , PCCount ], _, 0):-
|
||
|
|
debug_writeln(' PCTuple ',[ PCAtom , PCCount ],'zaehlt nicht').
|
||
|
|
|
||
|
|
is_node_matching_atom(NodeID, PCAtom):-
|
||
|
|
% check wether PCTuple represents rows matching predicates
|
||
|
|
% solved at node NodeID
|
||
|
|
NodeID is NodeID /\ PCAtom,
|
||
|
|
debug_writeln(' MaskedNodeId ', NodeID, ' matches PCAtom ',PCAtom).
|
||
|
|
is_node_matching_atom(N, PCAtom):-
|
||
|
|
debug_writeln(' MaskedNodeId ', N, ' does not match PCAtom ',PCAtom),
|
||
|
|
fail.
|
||
|
|
|
||
|
|
|
||
|
|
calc_rel_preds_mask(Relation, Mask):-
|
||
|
|
listOfPredicates(Predicates),
|
||
|
|
%debug_writeln('check: ',Predicates, ' # ', Relation),
|
||
|
|
calc_rel_preds_mask2(Predicates, Relation, Mask),
|
||
|
|
%debug_writeln('Relation=',Relation,' mask=',Mask),
|
||
|
|
true.
|
||
|
|
|
||
|
|
calc_rel_preds_mask2([], _, 0).
|
||
|
|
calc_rel_preds_mask2([ Predicate | Predicates ], Relation, MaskNew):-
|
||
|
|
Predicate = [ PredID, Relation, _ ],
|
||
|
|
calc_rel_preds_mask2(Predicates, Relation, Mask),
|
||
|
|
MaskNew is Mask \/ PredID,
|
||
|
|
%debug_writeln('calc_rel_preds_mask2: ',PredID,' added to ',Mask),
|
||
|
|
true.
|
||
|
|
calc_rel_preds_mask2([ Predicate | Predicates ], Relation, Mask):-
|
||
|
|
Predicate = [ PredID, _, _ ],
|
||
|
|
calc_rel_preds_mask2(Predicates, Relation, Mask),
|
||
|
|
%debug_writeln('calc_rel_preds_mask2: ',PredID,' not added to ',Mask),
|
||
|
|
PredID = PredID.
|
||
|
|
|
||
|
|
|
||
|
|
writeln(Msg1, Msg2):-
|
||
|
|
write(Msg1), writeln(Msg2).
|
||
|
|
writeln(Msg1, Msg2, Msg3):-
|
||
|
|
write(Msg1), writeln(Msg2, Msg3).
|
||
|
|
writeln(Msg1, Msg2, Msg3, Msg4):-
|
||
|
|
write(Msg1), writeln(Msg2, Msg3, Msg4).
|
||
|
|
writeln(Msg1, Msg2, Msg3, Msg4):-
|
||
|
|
write(Msg1), writeln(Msg2, Msg3, Msg4).
|
||
|
|
writeln(Msg1, Msg2, Msg3, Msg4, Msg5):-
|
||
|
|
write(Msg1), writeln(Msg2, Msg3, Msg4, Msg5).
|
||
|
|
writeln(Msg1, Msg2, Msg3, Msg4, Msg5, Msg6):-
|
||
|
|
write(Msg1), writeln(Msg2, Msg3, Msg4, Msg5, Msg6).
|
||
|
|
|
||
|
|
%is_nodeid_covered_by_pcresult(NodeID):-
|
||
|
|
% predcounts_result(Relation, PCResult),
|
||
|
|
% is_nodeid_covered_by_pcresult2(NodeID, PCResult).
|
||
|
|
|
||
|
|
%is_nodeid_covered_by_pcresult2(_, []).
|
||
|
|
%is_nodeid_covered_by_pcresult2(NodeID, [ [ NodeID , _ ] | _ ]).
|
||
|
|
%is_nodeid_covered_by_pcresult2(NodeID, [ [ PCAtom , _ ] | PCResult ]):-
|
||
|
|
% is_nodeid_covered_by_pcresult2(NodeID, PCResult).
|
||
|
|
|
||
|
|
|
||
|
|
|
||
|
|
store_node_sel(NodeID, NodeSel):-
|
||
|
|
retractall(predcounts_node_sel(NodeID, _)),
|
||
|
|
assert(predcounts_node_sel(NodeID, NodeSel)).
|
||
|
|
|
||
|
|
|
||
|
|
is_marginal_pred(NodeID):-
|
||
|
|
lowest_bitmask(NodeID, LMask),
|
||
|
|
!,
|
||
|
|
NodeID =:= NodeID /\ LMask.
|
||
|
|
|
||
|
|
lowest_bitmask(Value, _):-
|
||
|
|
Value =:= 0,
|
||
|
|
writeln('Error: lowest_bitmask: Value can not be 0!').
|
||
|
|
lowest_bitmask(Value, LowestMask):-
|
||
|
|
number(Value),
|
||
|
|
ValueInt is round(Value),
|
||
|
|
lowest_bitmask(1, ValueInt, LowestMask).
|
||
|
|
lowest_bitmask(Mask, Value, _):-
|
||
|
|
Mask > Value,
|
||
|
|
writeln('Error: lowest_bitmask: Mask is greater than Value!',[Mask, Value]).
|
||
|
|
lowest_bitmask(Mask, Value, LowestMask):-
|
||
|
|
X is Value /\ Mask,
|
||
|
|
X =:= Mask,
|
||
|
|
LowestMask = Mask.
|
||
|
|
lowest_bitmask(Mask, Value, LowestMask):-
|
||
|
|
MaskNeu is Mask << 1,
|
||
|
|
lowest_bitmask(MaskNeu, Value, LowestMask).
|
||
|
|
|
||
|
|
previous_nodeid(NodeID, _):-
|
||
|
|
NodeID =:= 0,
|
||
|
|
writeln('Error: previous_nodeid: There is no previous node of node 0').
|
||
|
|
previous_nodeid(NodeID, PrevNodeID):-
|
||
|
|
number(NodeID),
|
||
|
|
NodeInt is round(NodeID),
|
||
|
|
lowest_bitmask(NodeInt, Mask),
|
||
|
|
PrevNodeID is NodeInt - Mask.
|
||
|
|
|
||
|
|
|
||
|
|
%calc_mpjp_sels([ [ NodeID , _ ] | NodeSels ], MP, JP):-
|
||
|
|
% NodeID =:= 7,
|
||
|
|
% writeln('ignore node: 7'),
|
||
|
|
% calc_mpjp_sels(NodeSels, MP, JP).
|
||
|
|
%calc_mpjp_sels([ [ NodeID , _ ] | NodeSels ], MP, JP):-
|
||
|
|
% NodeID =:= 6,
|
||
|
|
% writeln('ignore node: 6'),
|
||
|
|
% calc_mpjp_sels(NodeSels, MP, JP).
|
||
|
|
% es entstehen zuviele MP: calc_mpjp_sels([], [ [ 0 , 1 ] ], []).
|
||
|
|
calc_mpjp_sels([], [], []).
|
||
|
|
calc_mpjp_sels([ [ NodeID , _ ] | NodeSels ], MP, JP):-
|
||
|
|
NodeID =:= 0,
|
||
|
|
calc_mpjp_sels(NodeSels, MP, JP).
|
||
|
|
calc_mpjp_sels([ [ NodeID , NodeSel ] | NodeSels ], MP, JP):-
|
||
|
|
NodeID =\= 0,
|
||
|
|
previous_nodeid(NodeID, PrevNodeID),
|
||
|
|
calc_mpjp_sels2(PrevNodeID, [ [ NodeID , NodeSel ] | NodeSels ],
|
||
|
|
MP, JP).
|
||
|
|
|
||
|
|
|
||
|
|
calc_mpjp_sels2(PrevNodeID, [ [ 8 , n/a ] | NodeSels ],
|
||
|
|
[ [ 8, 0.0003 ] | MP ], JP):-
|
||
|
|
NodeID=8,
|
||
|
|
PrevNodeID =:= 0,
|
||
|
|
debug_writeln('Sondernode ',NodeID),
|
||
|
|
% falls nicht berechenbare node, dann dummy node [0,1] in MP
|
||
|
|
calc_mpjp_sels(NodeSels, MP, JP).
|
||
|
|
calc_mpjp_sels2(PrevNodeID, [ [ NodeID , n/a ] | NodeSels ],
|
||
|
|
[ [ 0, 1 ] | MP ], JP):-
|
||
|
|
PrevNodeID =:= 0,
|
||
|
|
writeln('nicht berechbare node ',NodeID),
|
||
|
|
% falls nicht berechenbare node, dann dummy node [0,1] in MP
|
||
|
|
debug_writeln('dummy: ',[ PrevNodeID , NodeID , n/a ]),
|
||
|
|
calc_mpjp_sels(NodeSels, MP, JP).
|
||
|
|
calc_mpjp_sels2(PrevNodeID, [ [ NodeID , NodeSel ] | NodeSels ],
|
||
|
|
[ [ NodeID , NodeSel ] | MP ],
|
||
|
|
[ [ PrevNodeID , NodeID , NodeSel ] | JP ]):-
|
||
|
|
PrevNodeID =:= 0,
|
||
|
|
calc_mpjp_sels(NodeSels, MP, JP).
|
||
|
|
calc_mpjp_sels2(PrevNodeID, [ [ NodeID , NodeSel ] | NodeSels ], MP,
|
||
|
|
% [ [ PrevNodeID , NodeID , EdgeSel ] | JP ]):-
|
||
|
|
[ [ PrevNodeID , NodeID , NodeSel ] | JP ]):-
|
||
|
|
PrevNodeID =\= 0,
|
||
|
|
% neu, da Berechnung edgesel offensichtlich anderes
|
||
|
|
%predcounts_node_sel(PrevNodeID, PrevNodeSel),
|
||
|
|
%EdgeSel is NodeSel / PrevNodeSel,
|
||
|
|
%writeln('add: ',[ PrevNodeID , NodeID , EdgeSel ]),
|
||
|
|
calc_mpjp_sels(NodeSels, MP, JP).
|
||
|
|
|
||
|
|
|
||
|
|
|
||
|
|
|
||
|
|
|
||
|
|
merge_lists_m(MP, [], MP).
|
||
|
|
merge_lists_m(MP, [ [ Ni, S ] | MP2 ], MP3):-
|
||
|
|
Nf is 0.0 + Ni,
|
||
|
|
not_in_list_m(Nf, MP),
|
||
|
|
append_list_m(MP, [ Ni, S ], MP4),
|
||
|
|
merge_lists_m(MP4, MP2, MP3).
|
||
|
|
merge_lists_m(MP, [ _ | MP2 ], MP3):-
|
||
|
|
merge_lists_m(MP, MP2, MP3).
|
||
|
|
|
||
|
|
merge_lists_j(JP, [], JP).
|
||
|
|
merge_lists_j(JP, [ [ NVi , NBi, S ] | JP2 ], JP3):-
|
||
|
|
NBf is 0.0 + NBi,
|
||
|
|
NVf is 0.0 + NVi,
|
||
|
|
not_in_list_j([NVf, NBf], JP),
|
||
|
|
append_list_j(JP, [ NVi , NBi, S ], JP4),
|
||
|
|
merge_lists_j(JP4, JP2, JP3).
|
||
|
|
merge_lists_j(JP, [ _ | JP2 ], JP3):-
|
||
|
|
merge_lists_j(JP, JP2, JP3).
|
||
|
|
|
||
|
|
append_list_m([], [ V, S ], [[ Vi, S ]]):-
|
||
|
|
V =:= 0,
|
||
|
|
Vi is round(V).
|
||
|
|
append_list_m([], [ V, S ], [[ Vf, S ]]):-
|
||
|
|
V =\= 0,
|
||
|
|
Vf is 0.0 + V.
|
||
|
|
append_list_m([], A, B):-
|
||
|
|
writeln('ERROR: append_list(',[[], A, B],') sollte nie eintreten').
|
||
|
|
append_list_m([ E | LIR ], T, [ E | LOR ]):-
|
||
|
|
append_list_m(LIR, T, LOR).
|
||
|
|
|
||
|
|
append_list_j([], [ V, B, S ], [[ Vi, Bf, S ]]):-
|
||
|
|
V =:= 0,
|
||
|
|
Vi is round(V),
|
||
|
|
Bf is 0.0 + B.
|
||
|
|
append_list_j([], [ V, B, S ], [[ Vf, Bf, S ]]):-
|
||
|
|
V =\= 0,
|
||
|
|
Vf is 0.0 + V,
|
||
|
|
Bf is 0.0 + B.
|
||
|
|
append_list_j([], A, B):-
|
||
|
|
writeln('ERROR: append_list(',[[], A, B],') sollte nie eintreten').
|
||
|
|
append_list_j([ E | LIR ], T, [ E | LOR ]):-
|
||
|
|
append_list_j(LIR, T, LOR).
|
||
|
|
|
||
|
|
|
||
|
|
|
||
|
|
%join_lists(JP, [], JP).
|
||
|
|
%join_lists(JP, [ [ NVi, NBi, S ] | JP2 ], [ [ NVf, NBf, S ] | JPR ]):-
|
||
|
|
% NBf is 0.0 + NBi,
|
||
|
|
% NVf is 0.0 + NVi,
|
||
|
|
% not_in_list([NVf, NBf], JP),
|
||
|
|
% writeln('join_lists: add ', [NVf, NBf]),
|
||
|
|
% join_lists(JP, JP2, JPR).
|
||
|
|
%join_lists(JP, [ _ | JP2 ], JPR):-
|
||
|
|
% join_lists(JP, JP2, JPR).
|
||
|
|
|
||
|
|
not_in_list_m(T,JP):-
|
||
|
|
writeln('not_in_list(', [T, JP], ')'),
|
||
|
|
fail.
|
||
|
|
not_in_list_m(_, []):-
|
||
|
|
writeln('really not in list').
|
||
|
|
not_in_list_m(V1, [ [V2, _] | _ ]):-
|
||
|
|
V1 =:= V2,
|
||
|
|
writeln('not_in_list failed'),
|
||
|
|
fail.
|
||
|
|
not_in_list_m(V1, [ [V2, _] | JP ]):-
|
||
|
|
V1 =\= V2,
|
||
|
|
not_in_list_m(V1, JP).
|
||
|
|
|
||
|
|
not_in_list_j(T,JP):-
|
||
|
|
writeln('not_in_list(', [T, JP], ')'),
|
||
|
|
fail.
|
||
|
|
not_in_list_j(_, []):-
|
||
|
|
writeln('really not in list').
|
||
|
|
not_in_list_j([V1, B1], [ [V2, B2, _] | _ ]):-
|
||
|
|
V1 =:= V2,
|
||
|
|
B1 =:= B2,
|
||
|
|
writeln('not_in_list failed'),
|
||
|
|
fail.
|
||
|
|
not_in_list_j([V1, B1], [ [_, B2, _] | JP ]):-
|
||
|
|
B1 =\= B2,
|
||
|
|
not_in_list_j([V1, B1], JP).
|
||
|
|
not_in_list_j([V1, B1], [ [V2, _, _] | JP ]):-
|
||
|
|
V1 =\= V2,
|
||
|
|
not_in_list_j([V1, B1], JP).
|
||
|
|
|
||
|
|
% orginal feasible geht von fester REihenfolge aus,
|
||
|
|
% dass ist aber nicht mehr gegeben
|
||
|
|
/* in constrast to the implementation of feasible there isn't an order of
|
||
|
|
edges within the list of joint selectivities */
|
||
|
|
feasible(MP, JP, MP2, JP2):-
|
||
|
|
% only if corr is set
|
||
|
|
corr,
|
||
|
|
writeln('feasible(corr): ', [MP, JP, MP2, JP2]),
|
||
|
|
% for easier access
|
||
|
|
store_all_marginal([[0, 1]]),
|
||
|
|
store_all_marginal(MP),
|
||
|
|
store_all_joint(JP),
|
||
|
|
!,
|
||
|
|
|
||
|
|
% for all nodes except node 0, start with node 1
|
||
|
|
adjust_nodes(1.0), % parameter have to be real
|
||
|
|
!,
|
||
|
|
|
||
|
|
% rebuild lists
|
||
|
|
load_all_marginal(MP2),
|
||
|
|
load_all_joint(_), % Daten werden nicht mehr benoetigt
|
||
|
|
load_all_targetSels(JP2),
|
||
|
|
writeln('my feasible: MP2=',MP2),
|
||
|
|
writeln(' JP2=',JP2),
|
||
|
|
true.
|
||
|
|
|
||
|
|
adjust_nodes(N):-
|
||
|
|
highNode(HN),
|
||
|
|
HN >= N,
|
||
|
|
|
||
|
|
writeln('adjust_nodes(',N,'): try'),
|
||
|
|
|
||
|
|
% Menge aller Vorgaenger ermitteln
|
||
|
|
setof(PrevNodeID, edge(PrevNodeID, N, _, _, _, _), PrevNodeIDs),
|
||
|
|
|
||
|
|
% determine upper and lower limit for node N
|
||
|
|
get_lower_limit(N, PrevNodeIDs, LowerLimit),
|
||
|
|
get_upper_limit(N, PrevNodeIDs, UpperLimit),
|
||
|
|
|
||
|
|
% determine most exact edge selectivity
|
||
|
|
best_edge_selectivity(N, PrevNodeIDs, BestSel),
|
||
|
|
number(BestSel),
|
||
|
|
|
||
|
|
% check edge selectivity againts limits
|
||
|
|
adjust_edge_selectivity(LowerLimit, UpperLimit, BestSel, Selectivity),
|
||
|
|
|
||
|
|
% store adjusted selectivity
|
||
|
|
retractall(targetSelectivity(N, _)),
|
||
|
|
assert(targetSelectivity(N, Selectivity)),
|
||
|
|
|
||
|
|
writeln('adjust_nodes(',N,'): ',[N, Selectivity]),
|
||
|
|
|
||
|
|
% adjust next node
|
||
|
|
NN is N + 1,
|
||
|
|
adjust_nodes(NN).
|
||
|
|
adjust_nodes(N):-
|
||
|
|
highNode(HN),
|
||
|
|
HN >= N,
|
||
|
|
% ignore node
|
||
|
|
writeln('adjust_nodes(',N,'): ignored'),
|
||
|
|
% adjust next node
|
||
|
|
NN is N + 1,
|
||
|
|
adjust_nodes(NN).
|
||
|
|
adjust_nodes(N):-
|
||
|
|
writeln('finish adjust_nodes with ',N),
|
||
|
|
highNode(HN),
|
||
|
|
N > HN.
|
||
|
|
|
||
|
|
adjust_edge_selectivity(LowerLimit, UpperLimit, Selectivity, Selectivity):-
|
||
|
|
Selectivity < 0.99 * UpperLimit,
|
||
|
|
Selectivity > 1.01 * LowerLimit.
|
||
|
|
adjust_edge_selectivity(_, UpperLimit, BestSel, Selectivity):-
|
||
|
|
BestSel >= 0.99 * UpperLimit,
|
||
|
|
Selectivity is 0.99 * UpperLimit.
|
||
|
|
adjust_edge_selectivity(LowerLimit, _, BestSel, Selectivity):-
|
||
|
|
BestSel =< 1.01 * LowerLimit,
|
||
|
|
Selectivity is 1.01 * LowerLimit.
|
||
|
|
|
||
|
|
get_lower_limit(N, PrevNodeIDs, LowerLimit):-
|
||
|
|
% start with minimum value of selectivity 0
|
||
|
|
get_lower_limit(N, PrevNodeIDs, 0, LowerLimit).
|
||
|
|
|
||
|
|
get_lower_limit(_, [], LowerLimit, LowerLimit).
|
||
|
|
get_lower_limit(N, [ PrevNodeID | PrevNodeIDs ], LowerLimitOld, LowerLimitNew):-
|
||
|
|
%writeln('get_lower_limit: ',[N,PrevNodeID,LowerLimitOld,LowerLimitNew]),
|
||
|
|
% determine selectivity of previous node in path
|
||
|
|
targetSelectivity(PrevNodeID, PrevNodeSel), % muss exisitieren
|
||
|
|
LastPred is N - PrevNodeID,
|
||
|
|
targetSelectivity(LastPred, LastPredSel), % muss nicht existieren
|
||
|
|
number(LastPredSel),
|
||
|
|
% calculate new lower limit candidate
|
||
|
|
LowerLimitTmp is PrevNodeSel + LastPredSel - 1,
|
||
|
|
% determine next lower limit
|
||
|
|
LowerLimitTmp2 is max(LowerLimitTmp, LowerLimitOld),
|
||
|
|
%writeln('get_lower_limit: ',[N,PrevNodeID,LowerLimitOld,PrevNodeSel,LastPredSel,LowerLimitTmp]),
|
||
|
|
% recursive next
|
||
|
|
get_lower_limit(N, PrevNodeIDs, LowerLimitTmp2, LowerLimitNew).
|
||
|
|
get_lower_limit(N, [ _ | PrevNodeIDs ], LowerLimitOld, LowerLimitNew):-
|
||
|
|
% recursive next
|
||
|
|
get_lower_limit(N, PrevNodeIDs, LowerLimitOld, LowerLimitNew).
|
||
|
|
|
||
|
|
get_upper_limit(N, PrevNodeIDs, UpperLimit):-
|
||
|
|
% start with maximum value of selectivity 1
|
||
|
|
get_upper_limit(N, PrevNodeIDs, 1, UpperLimit).
|
||
|
|
|
||
|
|
get_upper_limit(_, [], UpperLimit, UpperLimit).
|
||
|
|
get_upper_limit(N, [ PrevNodeID | PrevNodeIDs], UpperLimitOld, UpperLimitNew):-
|
||
|
|
% determine selectivity of previous node in path
|
||
|
|
targetSelectivity(PrevNodeID, PrevNodeSel), % muss exisitieren
|
||
|
|
get_lower_selectivity(PrevNodeSel, UpperLimitOld, UpperLimitTmp1),
|
||
|
|
% determine marginal sel of last applied predicate
|
||
|
|
LastPred is N - PrevNodeID,
|
||
|
|
get_lastpred_selectivity(LastPred, LastPredSel), % muss nicht existieren
|
||
|
|
get_lower_selectivity(UpperLimitTmp1, LastPredSel, UpperLimitTmp2),
|
||
|
|
% recursive next
|
||
|
|
get_upper_limit(N, PrevNodeIDs, UpperLimitTmp2, UpperLimitNew).
|
||
|
|
|
||
|
|
get_upper_selectivity(Sel, n/a, Sel).
|
||
|
|
get_upper_selectivity(Sel1, Sel2, Sel):-
|
||
|
|
number(Sel2),
|
||
|
|
Sel is max(Sel1, Sel2).
|
||
|
|
|
||
|
|
get_lower_selectivity(Sel, n/a, Sel).
|
||
|
|
get_lower_selectivity(Sel1, Sel2, Sel):-
|
||
|
|
number(Sel2),
|
||
|
|
Sel is min(Sel1, Sel2).
|
||
|
|
|
||
|
|
best_edge_selectivity(N, PrevNodeIDs, BestEdgeSel):-
|
||
|
|
% still one edge selectivity has to exist
|
||
|
|
% it garanties??? that BestEdgeSel is a number ever
|
||
|
|
joint(_, N, _),
|
||
|
|
best_edge_selectivity(N, PrevNodeIDs, n/a, BestEdgeSel).
|
||
|
|
best_edge_selectivity(N, _, BestEdgeSel):-
|
||
|
|
targetSelectivity(N, BestEdgeSel).
|
||
|
|
best_edge_selectivity(_, _, n/a).
|
||
|
|
|
||
|
|
best_edge_selectivity(_, [], BestEdgeSel, BestEdgeSel).
|
||
|
|
best_edge_selectivity(N, [ PrevNodeID | PrevNodeIDs], BestEdgeSelOld,
|
||
|
|
BestEdgeSelNew):-
|
||
|
|
get_edge_selectivity(N, PrevNodeID, EdgeSel),
|
||
|
|
best_edge_selectivity2(BestEdgeSelOld, EdgeSel, BestEdgeSelTmp),
|
||
|
|
best_edge_selectivity(N, PrevNodeIDs, BestEdgeSelTmp, BestEdgeSelNew).
|
||
|
|
|
||
|
|
best_edge_selectivity2(n/a, Sel, Sel):-
|
||
|
|
number(Sel).
|
||
|
|
best_edge_selectivity2(Sel, n/a, Sel):-
|
||
|
|
number(Sel).
|
||
|
|
best_edge_selectivity2(Sel1, Sel2, Sel):-
|
||
|
|
number(Sel1),
|
||
|
|
number(Sel2),
|
||
|
|
Sel is min(Sel1, Sel2).
|
||
|
|
|
||
|
|
get_lastpred_selectivity(LastPred, LastPredSel):-
|
||
|
|
targetSelectivity(LastPred, LastPredSel).
|
||
|
|
get_lastpred_selectivity(_, n/a).
|
||
|
|
|
||
|
|
get_edge_selectivity(NodeID, PrevNodeID, Selectivity):-
|
||
|
|
joint(PrevNodeID, NodeID, Selectivity).
|
||
|
|
get_edge_selectivity(_, _, n/a).
|
||
|
|
|
||
|
|
/*
|
||
|
|
|
||
|
|
----
|
||
|
|
|
||
|
|
%adjust_node(_, [], TargetSel, TargetSel).
|
||
|
|
%adjust_node(N, [ PrevNodeID | PrevNodeIDs], TargetSelOld, TargetSelNew):-
|
||
|
|
%writeln('try to adjust for [NodeID, PrevID]: ',[N,PrevNodeID]),
|
||
|
|
%
|
||
|
|
% % determine selectivity of previous node in path
|
||
|
|
% targetSelectivity(PrevNodeID, PrevNodeSel), % muss exisitieren
|
||
|
|
% % determine marginal sel of last applied predicate
|
||
|
|
% LastPred is N - PrevNodeID,
|
||
|
|
% get_lastpred_selectivity(LastPred, LastPredSel), % muss nicht existieren
|
||
|
|
% % nur wenn Kante gegeben sonst n/a
|
||
|
|
% get_edge_selectivity(N, PrevNodeID, EdgeSelectivity),
|
||
|
|
%
|
||
|
|
% % ??? welche ZielSel ist besser?
|
||
|
|
% TargetSelTmp is better_selectivity(EdgeSelectivity, TargetSelOld),
|
||
|
|
%
|
||
|
|
%adjusted2(prev,last,TargetSelOld,dest),
|
||
|
|
%
|
||
|
|
% % ??? store adjusted selectivity as fact targetSelectivity
|
||
|
|
% %store_target_selectivity(N, PrevNodeSel, LastPredSel, EdgeSelectivity)
|
||
|
|
% adjust_target_selectivity(N, PrevNodeSel, LastPredSel, EdgeSelectivity)
|
||
|
|
% adjust_node(N, PrevNodeIDs, TargetSel2, TargetSelNew).
|
||
|
|
%adjust_node(N, [ _ | PrevNodeIDs], TargetSelOld, TargetSelNew):-
|
||
|
|
% adjust_node(N, PrevNodeIDs, TargetSelOld, TargetSelNew).
|
||
|
|
%
|
||
|
|
%adjusted2(PNS, LPS, ES, RTN):-
|
||
|
|
% number(PNS),
|
||
|
|
% number(LPS),
|
||
|
|
% number(ES),
|
||
|
|
% adjusted(PNS, LPS, ES, RTN).
|
||
|
|
%adjusted2(PPS, n/a, ES, RTN):-
|
||
|
|
% number(PNS),
|
||
|
|
% number(ES),
|
||
|
|
% adjusted(PNS, ES, RTN).
|
||
|
|
%
|
||
|
|
%
|
||
|
|
%adjust_target_selectivity(TID, PNSel, LPSel, EdgeSel):-
|
||
|
|
% targetSelectivity(TID, LastTargetSelectivity),
|
||
|
|
% number(LastTargetSelectivity),
|
||
|
|
% adjusted(PNSel, LPSel, EdgeSel, AdjustedSel),
|
||
|
|
% AdjustedSel2 is min(AdjustedSel, LastTargetSelectivity),
|
||
|
|
% store_node_selectivity([TID, AdjustedSel2]).
|
||
|
|
%
|
||
|
|
%adjust_target_selectivity(TID, PNSel, LPSel, EdgeSel):-
|
||
|
|
% adjusted(PNSel, LPSel, EdgeSel, AdjustedSel),
|
||
|
|
% store_node_selectivity([TID, AdjustedSel]).
|
||
|
|
%
|
||
|
|
%adjusted_corr(PNSel, LPSel, EdgeSel, AdjustedSel):-
|
||
|
|
|
||
|
|
----
|
||
|
|
|
||
|
|
*/
|
||
|
|
|
||
|
|
load_all_marginal(MP):-
|
||
|
|
setof([Pred, Sel], marginal(Pred, Sel), MP),
|
||
|
|
retractall(marginal(_, _)).
|
||
|
|
|
||
|
|
load_all_joint(JP):-
|
||
|
|
setof([PV, PB, Sel], joint(PV, PB, Sel), JP),
|
||
|
|
retractall(joint(_, _, _)).
|
||
|
|
|
||
|
|
load_all_targetSels(TS):-
|
||
|
|
setof([NodeID, Sel], targetSelectivity(NodeID, Sel), TS),
|
||
|
|
retractall(targetSelectivity(_, _)).
|
||
|
|
|
||
|
|
store_node_selectivity([ NodeID, Selectivity ]):-
|
||
|
|
retractall(adjustedNodeSelectivity(NodeID, _)),
|
||
|
|
assert(adjustedNodeSelectivity(NodeID, Selectivity)).
|
||
|
|
|
||
|
|
store_all_marginal([]).
|
||
|
|
store_all_marginal([ [ 0, S ] | Rest ]):-
|
||
|
|
retractall(targetSelectivity(P, _)),
|
||
|
|
assert(targetSelectivity(P, S)),
|
||
|
|
store_all_marginal(Rest).
|
||
|
|
store_all_marginal([ [ P, S ] | Rest ]):-
|
||
|
|
retractall(targetSelectivity(P, _)),
|
||
|
|
retractall(marginal(P, _)),
|
||
|
|
assert(marginal(P, S)),
|
||
|
|
assert(targetSelectivity(P, S)),
|
||
|
|
store_all_marginal(Rest).
|
||
|
|
|
||
|
|
store_all_joint([]).
|
||
|
|
store_all_joint([ [ 0, PB, S ] | Rest ]):-
|
||
|
|
store_all_marginal([[PB, S]]),
|
||
|
|
store_all_joint(Rest).
|
||
|
|
store_all_joint([ [ PV, PB, S ] | Rest ]):-
|
||
|
|
retractall(targetSelectivity(PB, _)),
|
||
|
|
retractall(joint(PV, PB, _)),
|
||
|
|
assert(joint(PV, PB, S)),
|
||
|
|
assert(targetSelectivity(PB, S)),
|
||
|
|
store_all_joint(Rest).
|
||
|
|
|
||
|
|
|