TY - JOUR

T1 - A decomposition approach for solving a broadcast domination network design problem

AU - Shen, Siqian

AU - Smith, J. Cole

N1 - Funding Information:
Acknowledgements The authors gratefully acknowledge the comments of four anonymous referees and the Guest Editor, whose comments led to an improved presentation in this paper. Dr. Smith acknowledges the support of the Air Force Office of Scientific Research under Grants FA9550-07-1-0404 and FA9550-08-1-0189, and of the Defense Threat Reduction Agency under Grant HDTRA1-10-1-0050.

PY - 2013/11

Y1 - 2013/11

N2 - 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 fi assigned to each node i, such that for any node j in the graph, there exists some node k having a positive fk-value whose shortest distance to node j is no more than fk. 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.

AB - 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 fi assigned to each node i, such that for any node j in the graph, there exists some node k having a positive fk-value whose shortest distance to node j is no more than fk. 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.

KW - Benders decomposition

KW - Broadcast domination

KW - Cutting-plane algorithms

KW - Integer programming

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U2 - 10.1007/s10479-011-0962-8

DO - 10.1007/s10479-011-0962-8

M3 - Article

AN - SCOPUS:84886719583

VL - 210

SP - 333

EP - 360

JO - Annals of Operations Research

JF - Annals of Operations Research

SN - 0254-5330

IS - 1

ER -