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Testset ES30FST

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 
 es30fst0179 115 30 ?s 40692993 
 es30fst0271 97 30 ?s 40900061 
 es30fst0383 120 30 ?s 43120444 
 es30fst0480 115 30 ?s 42150958 
 es30fst0558 71 30 ?s 41739748 
 es30fst0683 119 30 ?s 39955139 
 es30fst0753 64 30 ?s 43761391 
 es30fst0869 93 30 ?s 41691217 
 es30fst0943 44 30 ?s 37133658 
 es30fst1048 52 30 ?s 42686610 
 es30fst1179 112 30 ?s 41647993 
 es30fst1246 48 30 ?s 38416720 
 es30fst1365 84 30 ?s 37406646 
 es30fst1453 58 30 ?s 42897025 
 es30fst15118 188 30 ?s 43035576 

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)