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 ofThe files can be found in the download section.

Name | |V| | |E| | |T| | DC | Opt |
---|---|---|---|---|---|

es40fst01 | 93 | 127 | 40 | ?s | 44841522 |

es40fst02 | 82 | 105 | 40 | ?s | 46811310 |

es40fst03 | 87 | 116 | 40 | ?s | 49974157 |

es40fst04 | 55 | 55 | 40 | ?s | 45289864 |

es40fst05 | 121 | 180 | 40 | ?s | 51940413 |

es40fst06 | 92 | 123 | 40 | ?s | 49753385 |

es40fst07 | 77 | 95 | 40 | ?s | 45639009 |

es40fst08 | 98 | 137 | 40 | ?s | 48745996 |

es40fst09 | 107 | 153 | 40 | ?s | 51761789 |

es40fst10 | 107 | 152 | 40 | ?s | 57136852 |

es40fst11 | 97 | 135 | 40 | ?s | 46734214 |

es40fst12 | 67 | 75 | 40 | ?s | 43843378 |

es40fst13 | 78 | 95 | 40 | ?s | 51884545 |

es40fst14 | 98 | 134 | 40 | ?s | 49166952 |

es40fst15 | 93 | 129 | 40 | ?s | 50828067 |

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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