secondo/bin/Scripts3/DeterminingSmallCoresPD.sec

/*
//paragraph [10] title: [{\Large \bf ]  [}]
//[Contents] [\tableofcontents]
//[ue] [\"{u}]



[10] Determining SmallCores


[Contents] 

1 Overview

This script is for determining core points to partition a relation ~Pois~ by theese core points.

It is a commented script suitable for viewing with ~pdview~. To be run with 

----    @%Scripts/DeterminingSmallCoresPD.sec or
	@&Scripts/DeterminingSmallCoresPD.sec
----

The algorithm is the following:

1) Take a sample from relation ~Pois~.

2) For each sample point, determine the distance to its kth nearest neighbor and add this distance as the radius.

3) For each sample point p, compute the set of other sample points intersecting p. Store p if it has the smallest number among all intersecting tuples.


2 Preparations

Preparations: 

  * include the MainMemory2Algebra in makefile.algebras and recompile secondo

  * get the desired shape-file from download.geofabrik.de

  * create and open a database

  * import relation ~Pois~ using the script "importGermanyOsm.psec"

Determine SizeSample

*/

let SizeSample = 1000;

let k = 50;

/*
3 Take a Sample

Take a sample from the relation ~Pois~ and rename attribute GeoData

*/

let SamplePoints = Pois 
  feedNth[(Pois count) div SizeSample, FALSE] 
  renameattr[Center: GeoData]
  consume;

/*
4 Further Arrangements

If necessary delete prior objects.

*/

#delete SamplePoints;
#delete Core;
#delete Core_Box;
#delete SmallCore;
#delete CoreDel;

/*
Create an empty relation ~Core~ with equal structure of ~SamplePoints~

*/

let Core = SamplePoints feed 
  extend[N: 0, Radius: 0.0, Box: bbox(.Center),
  C: [const region value ()]]
  head[0] consume;

/*
Create an empty rtree

*/

let Core_Box = Core creatertree[Box];

/*
Create an empty relation ~SmallCore~ with equal structure of ~Core~

*/

let SmallCore = Core;

/*
Create an empty relation ~CoreDel~ with equal structure of ~Core~

*/
let CoreDel = Core;

/*
Delete all main memory objects

*/

query memclear();

/*
Create a MainMemoryTree based on relation ~SamplePoints~

*/

query SamplePoints feed letmconsume["SamplePoints"]
  mcreateMtree[Center, "SamplePoints_Center"];


/*
5 Determine the distance to the kth nearest neighbor

Extend each tuple of ~SamplePoints~ with the distance to its kth nearest neighbor (Radius) and number them by attribut N. 
Furthermore extend each tuple with a shape approximating a cirle (C) with the computed radius and a MBR (Box) enclosing this circle.
Store these tuples in relation ~Core~ and in a rtree ~CoreBox~ based on attribute Box.

*/

query SamplePoints feed addcounter[N, 1] 
  extend[Radius: fun(t: TUPLE)
    distance(attr(t, Center), "SamplePoints_Center" mdistScan2[attr(t, Center)] 
      head[k] tail[1] "SamplePoints" gettuples extract[Center]) ]
  extend[Box: enlargeRect(bbox(.Center), .Radius, .Radius)] 
  extend[C: circle(.Center, .Radius, 20)]
  Core insert
  Core_Box insertrtree[Box]
  count;

#Typing "query Core" in the GUI will show all SamplePoints 
#with their approximated circles and MBR's.

/*
6 Compute intersecting circles

For each point p in Core, compute the set of other sample points P from Core whose associated circle intersects its circle. If p has the smallest number N among all elements it intersects, then insert it into a set ~SmallCore~. (Rows 1 - 5) 
Remove from ~Core~ all elements whose circles intersect circles from ~SmallCore~. (Rows 7 - 9) This is done as follows: In ~CoreDel~ store alle tuples of the relation ~Core~ intersecting tuples of ~SmallCore~. Computing the difference between ~Core~ and ~CoreDel~, means to remove all tuples of ~CoreDel~ from ~Core~.  
The loop terminates if ~Core~ is empty.

*/

while (Core count) > 0 do
{ query Core feed filter[fun(t: TUPLE) 
    Core_Box Core windowintersects[attr(t, Box)] min[N] = attr(t, N)]
  SmallCore insert
  count
|
  update CoreDel := SmallCore feed loopsel
    [Core_Box Core windowintersects[.Box]] consume
|
  update Core := Core feed sort CoreDel feed sort mergediff consume
|
  update Core_Box := Core creatertree[Box]
}
endwhile;

#Typing "query SmallCore" in the GUI (Hoese-Viewer) will show all tuples, 
#which could have been placed, with their approximated circles and MBR's.