Submitter | Variables | Constraints | Density | Status | Group | Objective | MPS File |
---|---|---|---|---|---|---|---|

Daniel Heinlein | 200787 | 22117 | 4.52141e-03 | open | selofsubspaces | -257* | a2864-99blp.mps.gz |

Clique problems arising from a selection problem of subspaces in the PG(7,2) with different prescribed variables and numerically instable linear programming relaxation.

Detailed explanation of the following tables can be found here.

Original | Presolved | |
---|---|---|

Variables | 200787 | 13824 |

Constraints | 22117 | 20893 |

Binaries | 200787 | 13824 |

Integers | 0 | 0 |

Continuous | 0 | 0 |

Implicit Integers | 0 | 0 |

Fixed Variables | 0 | 0 |

Nonzero Density | 0.00452141 | 0.00478629 |

Nonzeroes | 20078700 | 1382400 |

Original | Presolved | |
---|---|---|

Total | 22117 | 20893 |

Empty | 0 | 0 |

Free | 0 | 0 |

Singleton | 17 | 0 |

Aggregations | 0 | 0 |

Precedence | 0 | 0 |

Variable Bound | 0 | 0 |

Set Partitioning | 0 | 0 |

Set Packing | 21590 | 20384 |

Set Covering | 0 | 0 |

Cardinality | 0 | 0 |

Invariant Knapsack | 510 | 509 |

Equation Knapsack | 0 | 0 |

Bin Packing | 0 | 0 |

Knapsack | 0 | 0 |

Integer Knapsack | 0 | 0 |

Mixed Binary | 0 | 0 |

General Linear | 0 | 0 |

Indicator | 0 | 0 |

Available nonzero structure and decomposition information. Further information can be found here.

Decomposed structure of original problem (dec-file)

Decomposed structure after trivial presolving (dec-file)

value | min | median | mean | max | |
---|---|---|---|---|---|

Components | 0.301030 | ||||

Constraint % | 100.0000 | 100.0000 | 100.0000 | 100.0000 | |

Variable % | 99.8772 | 99.8772 | 99.8772 | 99.8772 | |

Score | 0.001228 |

Find solutions below. Download the archive containing all solutions from the Download page.

ID | Objective | Exact | Int. Viol | Cons. Viol | Obj. Viol | Submitter | Date | Description |
---|---|---|---|---|---|---|---|---|

1 | -257 | -257 | 0 | 0 | 0 | - | 2018-10-13 | Solution found during MIPLIB2017 problem selection. |

The following instances are most similar to a2864-99blp in the collection. This similarity analysis is based on 100 scaled instance features describing properties of the variables, objective function, bounds, constraints, and right hand sides.

Instance | Status | Variables | Binaries | Integers | Continuous | Constraints | Nonz. | Submitter | Group | Objective | Tags |
---|---|---|---|---|---|---|---|---|---|---|---|

cdc7-4-3-2 | open | 11811 | 11811 | 0 | 0 | 14478 | 259842 | Sascha Kurz | – | -296.0* | binary set_packing |

cod105 | easy | 1024 | 1024 | 0 | 0 | 1024 | 57344 | MIPLIB submission pool | – | -12 | benchmark binary benchmark_suitable set_packing |

z26 | open | 17937 | 17937 | 0 | 0 | 850513 | 1715613 | Daniel Bienstock | – | -1195.0* | binary variable_bound set_packing |

sorrell7 | open | 2048 | 2048 | 0 | 0 | 78848 | 157696 | Toni Sorrell | independentset | -198.0* | binary variable_bound |

sorrell3 | easy | 1024 | 1024 | 0 | 0 | 169162 | 338324 | Toni Sorrell | independentset | -16 | benchmark binary benchmark_suitable variable_bound |

```
@article{honold2016classification,
title = {Classification of large partial plane spreads in ${PG}(6, 2)$ and related combinatorial objects},
author = {Honold, Thomas and Kiermaier, Michael and Kurz, Sascha},
journal = {Journal of Geometry},
note = {arXiv preprint arXiv:1606.07655},
year = {to appear}
}
```

Last Update 2024 by Julian Manns

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