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Testset ES50FST

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 
 es50fst01118 160 50 ?s 54948660 
 es50fst02125 177 50 ?s 55484245 
 es50fst03128 182 50 ?s 54691035 
 es50fst04106 138 50 ?s 51535766 
 es50fst05104 135 50 ?s 55186015 
 es50fst06126 182 50 ?s 55804287 
 es50fst07143 211 50 ?s 49961178 
 es50fst0883 96 50 ?s 53754708 
 es50fst09139 202 50 ?s 53456773 
 es50fst10139 207 50 ?s 54037963 
 es50fst11100 131 50 ?s 52532923 
 es50fst12110 149 50 ?s 53409291 
 es50fst1392 116 50 ?s 53891019 
 es50fst14120 167 50 ?s 53551419 
 es50fst15112 147 50 ?s 52180862 

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)