### Abstract

We consider an optimization problem that integrates network design and broadcast domination decisions. Given an undirected graph, a feasible broadcast domination is a set of nonnegative integer powers f_{i} assigned to each node i, such that for any node j in the graph, there exists some node k having a positive f_{k}-value whose shortest distance to node j is no more than f_{k}. The cost of a broadcast domination solution is the sum of all node power values. The network design problem constructs edges that decrease the minimum broadcast domination cost on the graph. The overall problem we consider minimizes the sum of edge construction costs and broadcast domination costs. We show that this problem is NP-hard in the strong sense, even on unweighted graphs. We then propose a decomposition strategy, which iteratively adds valid inequalities based on optimal broadcast domination solutions corresponding to the first-stage network design solutions. We demonstrate that our decomposition approach is computationally far superior to the solution of a single large-scale mixed-integer programming formulation.

Original language | English (US) |
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Pages (from-to) | 333-360 |

Number of pages | 28 |

Journal | Annals of Operations Research |

Volume | 210 |

Issue number | 1 |

DOIs | |

State | Published - Nov 1 2013 |

Externally published | Yes |

### Keywords

- Benders decomposition
- Broadcast domination
- Cutting-plane algorithms
- Integer programming

### ASJC Scopus subject areas

- Decision Sciences(all)
- Management Science and Operations Research