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 PD00 , and PV01c .

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

alut0787 | 1160 | 2089 | 34 | Ps | 982 |

alut0805 | 966 | 1666 | 34 | Ps | 958 |

alut1181 | 3041 | 5693 | 64 | Ps | 2353 |

alut2010 | 6104 | 11011 | 68 | Ps | 3307 |

alut2288 | 9070 | 16595 | 68 | NPs | 3843 |

alut2566 | 5021 | 9055 | 68 | NPs | 3073 |

alut2610 | 33901 | 62816 | 204 | Pm | 12239 |

alut2625 | 36711 | 68117 | 879 | NPm | 35459 |

alut2764 | 387 | 626 | 34 | Ls | 640 |

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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