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

Austin Buchanan | 150 | 7822 | 8.86312e-02 | hard | 2hopcds | 41.0 | v150d30-2hopcds.mps.gz |

A problem in wireless networks. The objective is to select a minimum number of relay nodes so that any two nonadjacent nodes can communicate by way of the chosen relay nodes in at most s hops, where s is a problem input. The 2-hop case of this problem can be formulated as a set cover/hitting set problem with n binary variables and n^2 constraints: _{ k N(i) N(j) } x_k for nonadjacent node pairs {i,j}. Despite the formulation’s simplicity, instances with as few as 120 variables are left unsolved after one hour using Gurobi 7.0.2.

Detailed explanation of the following tables can be found here.

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

Variables | 150 | 148 |

Constraints | 7822 | 6228 |

Binaries | 150 | 148 |

Integers | 0 | 0 |

Continuous | 0 | 0 |

Implicit Integers | 0 | 0 |

Fixed Variables | 0 | 0 |

Nonzero Density | 0.0886312 | 0.0883098 |

Nonzeroes | 103991 | 81399 |

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

Total | 7822 | 6228 |

Empty | 0 | 0 |

Free | 0 | 0 |

Singleton | 2 | 0 |

Aggregations | 0 | 0 |

Precedence | 0 | 0 |

Variable Bound | 4 | 4 |

Set Partitioning | 0 | 0 |

Set Packing | 0 | 0 |

Set Covering | 7816 | 6224 |

Cardinality | 0 | 0 |

Invariant Knapsack | 0 | 0 |

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 % | 98.6667 | 98.6667 | 98.6667 | 98.6667 | |

Score | 0.013333 |

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

2 | 41 | 41 | 0 | 0 | 0 | Ishibashi Yasumi | 2020-08-28 | Solved with NuOpt using 16 threads within 60 hours |

1 | 41 | 41 | 0 | 0 | 0 | - | 2018-10-10 | Solution found during MIPLIB2017 problem selection |

The following instances are most similar to v150d30-2hopcds 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 |
---|---|---|---|---|---|---|---|---|---|---|---|

glass-sc | easy | 214 | 214 | 0 | 0 | 6119 | 63918 | Marc Pfetsch | maxfeassub | 23 | benchmark binary benchmark_suitable set_covering |

iis-glass-cov | easy | 214 | 214 | 0 | 0 | 5375 | 56133 | Marc Pfetsch | iis | 20.99999999999999 | binary benchmark_suitable set_covering |

iis-hc-cov | easy | 297 | 297 | 0 | 0 | 9727 | 142971 | Marc Pfetsch | iis | 17 | binary benchmark_suitable set_covering |

seymour | easy | 1372 | 1372 | 0 | 0 | 4944 | 33549 | W. Cook, P. Seymour | – | 423 | benchmark binary benchmark_suitable variable_bound set_covering |

ramos3 | open | 2187 | 2187 | 0 | 0 | 2187 | 32805 | F. Ramos | – | 186.0* | binary set_covering |

```
@UNPUBLISHED{buchanan2017,
author = {Buchanan, Austin and Validi, Hamidreza},
title = {The optimal design of low-latency virtual backbones},
note = {Manuscript in preparation},
year = {2017}
}
```

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