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Testset ES500FST

These instances are the result of the following procedure. First there were files with random generated points in the plane on a 10,000,000 by 10,000,000 grid.
These points serve as terminals and were converted to rectalinear graphs with L1 edge weights, by building the Hanan grid (see Han66 ).

Then these graphs were preprocessed with GeoSteiner a Software for computing Full-Steiner-Sets by M. Zachariasen and D.M. Warme . For a description of the Algorithm see War97 and WWZ00 .

The original point sets are from the OR-Library named ES10 to ES10000 corresponding to the number of points given.

Some results on solving the smaller instances without FST-preprocessing are published in KM98 . Since there seems to be no reason why today someone should try to solve these instances without FST-preprocessing anymore we only list the preprocessed ones.

Here is an picture of es250fst01 with solution:
es250fst01 with solution

The files can be found in the download section.

Name   |V|    |E|    |T|    DC    Opt 
 es500fst011250 1763 500 ?s 162978810 
 es500fst021408 2056 500 ?s 160756854 
 es500fst031337 1933 500 ?s 162664661 
 es500fst041296 1879 500 ?s 164110997 
 es500fst051172 1627 500 ?s 160586161 
 es500fst061335 1932 500 ?s 164685074 
 es500fst071214 1700 500 ?s 160124233 
 es500fst081349 1972 500 ?s 161248138 
 es500fst091294 1853 500 ?s 162100435 
 es500fst101203 1679 500 ?s 155581203 
 es500fst111274 1808 500 ?s 161674316 
 es500fst121322 1918 500 ?s 164009591 
 es500fst131273 1814 500 ?s 161324201 
 es500fst141477 2204 500 ?s 165984329 
 es500fst151334 1927 500 ?s 160758467 

The column DC classifies the difficulty of the instance.

Solvable by usage of local preprocessing. Typical examples are the SD-Test, BD-n Tests and FST computations. Neither a global upper nor lower bound needs to be computed.
Solvable by polynomial time algorithms, like dual ascent in combination with primal heuristic, a integral LP formulation or advanced preprocessing like reduced cost criteria or the RCR-Test.
No polynomial time algorithm is known. Use of an exponential time enumeration sceme like Branch-and-Bound is neccessary.

The letter after class gives an impression how long it takes to solve the problem using state-of-the-art soft- and hardware. secounds means less than a minute (this includes instances which can be solved in fractions of a second). minutes means less than an hour. hours is less than a day and days is less than a week. weeks mean it takes really a long time to solve this instance. ? means the instance is not solved or the time is not known.

If the number in the Opt column is written in italics the optimum is not known. The number given is the best know upper bound.

Last Update : 2015/02/11 11:57:20 $ by Thorsten Koch
© 2001 by Konrad-Zuse-Zentrum für Informationstechnik Berlin (ZIB)