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 |
---|---|---|---|---|---|

gap1307 | 342 | 552 | 17 | Ls | 549 |

gap1413 | 541 | 906 | 10 | Ls | 457 |

gap1500 | 220 | 374 | 17 | Ls | 254 |

gap1810 | 429 | 702 | 17 | Ls | 482 |

gap1904 | 735 | 1256 | 21 | Ps | 763 |

gap2007 | 2039 | 3548 | 17 | NPs | 1104 |

gap2119 | 1724 | 2975 | 29 | Ls | 1244 |

gap2740 | 1196 | 2084 | 14 | Ps | 745 |

gap2800 | 386 | 653 | 12 | Ls | 386 |

gap2975 | 179 | 293 | 10 | Ls | 245 |

gap3036 | 346 | 583 | 13 | Ps | 457 |

gap3100 | 921 | 1558 | 11 | Ps | 640 |

gap3128 | 10393 | 18043 | 104 | Ps | 4292 |

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.
**s**ecounds means less than a minute (this includes
instances which can be solved in fractions of a second).
**m**inutes means less than an hour. **h**ours is less than a
day and **d**ays is less than a week. **w**eeks 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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