Testset ES40FST

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
es40fst01	93	127	40	?s	44841522
es40fst02	82	105	40	?s	46811310
es40fst03	87	116	40	?s	49974157
es40fst04	55	55	40	?s	45289864
es40fst05	121	180	40	?s	51940413
es40fst06	92	123	40	?s	49753385
es40fst07	77	95	40	?s	45639009
es40fst08	98	137	40	?s	48745996
es40fst09	107	153	40	?s	51761789
es40fst10	107	152	40	?s	57136852
es40fst11	97	135	40	?s	46734214
es40fst12	67	75	40	?s	43843378
es40fst13	78	95	40	?s	51884545
es40fst14	98	134	40	?s	49166952
es40fst15	93	129	40	?s	50828067

The column DC classifies the difficulty of the instance.

L: 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.
P: 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.
NP: 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
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