On the chance-constrained minimum spanning k-core problem

Juan Ma () and Balabhaskar Balasundaram ()
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Juan Ma: Turner Broadcasting System, Inc.
Balabhaskar Balasundaram: Oklahoma State University

Journal of Global Optimization, 2019, vol. 74, issue 4, No 9, 783-801

Abstract: Abstract A graph is called a k-core if every vertex has at least k neighbors. If the parameter k is sufficiently large relative to the number of vertices, a k-core is guaranteed to possess 2-hop reachability between all pairs of vertices. Furthermore, it is guaranteed to preserve those pairwise distances under arbitrary single-vertex deletion. Hence, the concept of a k-core can be used to produce 2-hop survivable network designs, specifically to design inter-hub networks. Formally, given an edge-weighted graph, the minimum spanningk-core problem seeks a spanning subgraph of the given graph that is a k-core with minimum total edge weight. For any fixed k, this problem is equivalent to a generalized graph matching problem and can be solved in polynomial time. This article focuses on a chance-constrained version of the minimum spanning k-core problem under probabilistic edge failures. We first show that this probabilistic version is NP-hard, and we conduct a polyhedral study to strengthen the formulation. The quality of bounds produced by the strengthened formulation is demonstrated through a computational study.

Keywords: Chance-constrained optimization; Minimum spanning k-core; Hop-constrained survivable network design (search for similar items in EconPapers)
Date: 2019
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DOI: 10.1007/s10898-018-0714-2

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