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Testset ES1000FST

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 . For solutions see also PV01a .

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 
 es1000fst012865 4267 1000 ?s 230535806 
 es1000fst022629 3793 1000 ?s 227886471 
 es1000fst032762 4047 1000 ?s 227807756 
 es1000fst042778 4083 1000 ?s 230200846 
 es1000fst052676 3894 1000 ?s 228330602 
 es1000fst062815 4162 1000 ?s 231028456 
 es1000fst072604 3756 1000 ?s 230945623 
 es1000fst082834 4207 1000 ?s 230639115 
 es1000fst092846 4187 1000 ?s 227745838 
 es1000fst102546 3620 1000 ?s 229267101 
 es1000fst112763 4038 1000 ?s 231605619 
 es1000fst122984 4484 1000 ?s 230904712 
 es1000fst132532 3615 1000 ?s 228031092 
 es1000fst142840 4200 1000 ?s 234318491 
 es1000fst152733 3997 1000 ?s 229965775 

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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