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

Falk Hueffner | 9182 | 17712 | 3.26726e-04 | easy | huefner | 1224 | tanglegram6.mps.gz |

The NP-hard Balanced Subgraph problem (variant of MaxCut) encoded as ILPs. Real-world instances from two applications from bioinformatics, finding monotone subsystems in gene regulatory networks (http://dx.doi.org/10.1007/s10878-009-9212-2) and finding optimal layouts of tanglegrams (http://dx.doi.org/10.1007/978-3-642-11269-0).

Imported from the MIPLIB2010 submissions.

Detailed explanation of the following tables can be found here.

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

Variables | 9182 | 9182 |

Constraints | 17712 | 17712 |

Binaries | 9182 | 9182 |

Integers | 0 | 0 |

Continuous | 0 | 0 |

Implicit Integers | 0 | 0 |

Fixed Variables | 0 | 0 |

Nonzero Density | 0.000326726 | 0.000326726 |

Nonzeroes | 53136 | 53136 |

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

Total | 17712 | 17712 |

Empty | 0 | 0 |

Free | 0 | 0 |

Singleton | 0 | 0 |

Aggregations | 0 | 0 |

Precedence | 0 | 0 |

Variable Bound | 0 | 0 |

Set Partitioning | 0 | 0 |

Set Packing | 0 | 0 |

Set Covering | 14214 | 3498 |

Cardinality | 0 | 0 |

Invariant Knapsack | 3498 | 14214 |

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 | 0.845098 | ||||

Constraint % | 0.0056500 | 3.29155 | 0.0225836 | 19.6590 | |

Variable % | 0.0326726 | 6.57990 | 0.0653452 | 39.1963 | |

Score | 0.120437 |

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 | 1224 | 1224 | 0 | 0 | 0 | - | 2018-10-12 | Solution found during MIPLIB2017 problem selection. |

The following instances are most similar to tanglegram6 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 |
---|---|---|---|---|---|---|---|---|---|---|---|

tanglegram4 | easy | 56048 | 56048 | 0 | 0 | 110404 | 331212 | Falk Hueffner | huefner | 10696 | binary benchmark_suitable set_covering invariant_knapsack |

toll-like | easy | 2883 | 2883 | 0 | 0 | 4408 | 13224 | Falk Hueffner | huefner | 610 | binary benchmark_suitable set_covering invariant_knapsack |

vpphard2 | easy | 199999 | 199999 | 0 | 0 | 198450 | 648340 | C. Cardonha | – | 81 | binary decomposition benchmark_suitable set_partitioning cardinality invariant_knapsack |

vpphard | easy | 51471 | 51471 | 0 | 0 | 47280 | 372305 | C. Cardonha | – | 5 | binary decomposition benchmark_suitable set_partitioning cardinality invariant_knapsack |

30_70_45_095_100 | easy | 10976 | 10975 | 0 | 1 | 12526 | 46640 | J. Walser | 30_70 | 3 | binary decomposition benchmark_suitable precedence variable_bound set_covering mixed_binary |

`No bibliographic information available`

Last Update Jul 31, 2019 by Gregor Hendel

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