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Testset ES100FST

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 
 es100fst01250 354 100 ?s 72522165 
 es100fst02339 522 100 ?s 75176630 
 es100fst03189 233 100 ?s 72746006 
 es100fst04188 235 100 ?s 74342392 
 es100fst05188 238 100 ?s 75670198 
 es100fst06301 452 100 ?s 74414990 
 es100fst07276 401 100 ?s 77740576 
 es100fst08210 276 100 ?s 73033178 
 es100fst09248 342 100 ?s 77952027 
 es100fst10229 312 100 ?s 75952202 
 es100fst11253 362 100 ?s 78674859 
 es100fst12266 385 100 ?s 76131099 
 es100fst13254 361 100 ?s 74604990 
 es100fst14198 253 100 ?s 78632795 
 es100fst15231 319 100 ?s 70446493 

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)