Minimum edge blocker dominating set problem

Foad Mahdavi Pajouh, Jose L. Walteros, Vladimir Boginski and Eduardo L. Pasiliao

European Journal of Operational Research, 2015, vol. 247, issue 1, 16-26

Abstract: This paper introduces and studies the minimum edge blocker dominating set problem (EBDP), which is formulated as follows. Given a vertex-weighted undirected graph and r > 0, remove a minimum number of edges so that the weight of any dominating set in the remaining graph is at least r. Dominating sets are used in a wide variety of graph-based applications such as the analysis of wireless and social networks. We show that the decision version of EBDP is NP-hard for any fixed r > 0. We present an analytical lower bound for the value of an optimal solution to EBDP and formulate this problem as a linear 0–1 program with a large number of constraints. We also study the convex hull of feasible solutions to EBDP and identify facet-inducing inequalities for this polytope. Furthermore, we develop the first exact algorithm for solving EBDP, which solves the proposed formulation by a branch-and-cut approach where nontrivial constraints are applied in a lazy fashion. Finally, we also provide the computational results obtained by using our approach on a test-bed of randomly generated instances and real-life power-law graphs.

Keywords: Network interdiction; Minimum weighted dominating set; NP-hardness; Branch-and-cut algorithm; Critical elements detection (search for similar items in EconPapers)
Date: 2015
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Citations: View citations in EconPapers (4)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:ejores:v:247:y:2015:i:1:p:16-26

DOI: 10.1016/j.ejor.2015.05.037

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