Identifying risk-averse low-diameter clusters in graphs with stochastic vertex weights

Maciej Rysz, Foad Mahdavi Pajouh, Pavlo Krokhmal () and Eduardo L. Pasiliao
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Maciej Rysz: National Research Council, Air Force Research Laboratory
Foad Mahdavi Pajouh: University of Massachusetts Boston
Pavlo Krokhmal: University of Arizona
Eduardo L. Pasiliao: Air Force Research Laboratory

Annals of Operations Research, 2018, vol. 262, issue 1, No 6, 89-108

Abstract: Abstract In this work, we study the problem of detecting risk-averse low-diameter clusters in graphs. It is assumed that the clusters represent k-clubs and that uncertain information manifests itself in the form of stochastic vertex weights whose joint distribution is known. The goal is to find a k-club of minimum risk contained in the graph. A stochastic programming framework that is based on the formalism of coherent risk measures is used to quantify the risk of a cluster. We show that the selected representation of risk guarantees that the optimal subgraphs are maximal clusters. A combinatorial branch-and-bound algorithm is proposed and its computational performance is compared with an equivalent mathematical programming approach for instances with $$k=2,3,$$ k = 2 , 3 , and 4.

Keywords: k-club; low-diameter clusters; stochastic graphs; coherent risk measures; combinatorial branch-and-bound (search for similar items in EconPapers)
Date: 2018
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DOI: 10.1007/s10479-016-2212-6

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