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Testset ES10FST

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 
 es10fst0118 20 10 ?s 22920745 
 es10fst0214 13 10 ?s 19134104 
 es10fst0317 20 10 ?s 26003678 
 es10fst0418 20 10 ?s 20461116 
 es10fst0512 11 10 ?s 18818916 
 es10fst0617 20 10 ?s 26540768 
 es10fst0714 13 10 ?s 26025072 
 es10fst0821 28 10 ?s 25056214 
 es10fst0921 29 10 ?s 22062355 
 es10fst1018 21 10 ?s 23936095 
 es10fst1114 13 10 ?s 22239535 
 es10fst1213 12 10 ?s 19626318 
 es10fst1318 21 10 ?s 19483914 
 es10fst1424 32 10 ?s 21856128 
 es10fst1516 18 10 ?s 18641924 

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)