On risk-averse maximum weighted subgraph problems

Maciej Rysz, Mohammad Mirghorbani, Pavlo Krokhmal () and Eduardo L. Pasiliao
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Maciej Rysz: University of Iowa
Mohammad Mirghorbani: University of Iowa
Pavlo Krokhmal: University of Iowa
Eduardo L. Pasiliao: Air Force Research Lab

Journal of Combinatorial Optimization, 2014, vol. 28, issue 1, No 10, 167-185

Abstract: Abstract In this work, we consider a class of risk-averse maximum weighted subgraph problems (R-MWSP). Namely, assuming that each vertex of the graph is associated with a stochastic weight, such that the joint distribution is known, the goal is to obtain a subgraph of minimum risk satisfying a given hereditary property. We employ a stochastic programming framework that is based on the formalism of modern theory of risk measures in order to find minimum-risk hereditary structures in graphs with stochastic vertex weights. The introduced form of risk function for measuring the risk of subgraphs ensures that optimal solutions of R-MWS problems represent maximal subgraphs. A graph-based branch-and-bound (BnB) algorithm for solving the proposed problems is developed and illustrated on a special case of risk-averse maximum weighted clique problem. Numerical experiments on randomly generated Erdös-Rényi graphs demonstrate the computational performance of the developed BnB.

Keywords: Risk-averse maximum weighted subgraph problem; Risk-averse maximum clique problem; Maximum weight clique problem; Stochastic weights; Coherent risk measures (search for similar items in EconPapers)
Date: 2014
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Citations: View citations in EconPapers (4)

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DOI: 10.1007/s10878-014-9718-0

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