Testset DMXA

These instances are grid graphs with rectangular holes. They come from a VLSI application (see JMRW94 ).

They were introduced in KM98 . More information can be found among others in UdAR99 and PD00 .

Here is an image of alue7080 PS DjVu with solution made by E. Uchoa .

This is a picture of diw0495 with solution.

The files can be found in the download section.

Name   |V|    |E|    |T|    DC    Opt
dmxa0296233 386 12 Ls 344
dmxa03682050 3676 18 Ps 1017
dmxa04541848 3286 16 Ls 914
dmxa0628169 280 10 Ls 275
dmxa0734663 1154 11 Ls 506
dmxa0848499 861 16 Ps 594
dmxa0903632 1087 10 Ps 580
dmxa10103983 7108 23 Ls 1488
dmxa1109343 559 17 Ps 454
dmxa1200770 1383 21 Ps 750
dmxa1304298 503 10 Ls 311
dmxa1516720 1269 11 Ls 508
dmxa17211005 1731 18 Ps 780
dmxa18012333 4137 17 Ps 1365

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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