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On risk-averse maximum weighted subgraph problems

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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.

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Notes

  1. The rationale for the chosen terminology is explained in Remark 1.

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Acknowledgments

This work was supported in part by the U.S. Dept. of Air Force Grant FA8651-12-2-0010, AFOSR Grant FA9550-12-1-0142, and NSF Grant EPS1101284. The authors are grateful for the support from the AFRL Mathematical Modeling and Optimization Institute.

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Correspondence to Pavlo Krokhmal.

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Rysz, M., Mirghorbani, M., Krokhmal, P. et al. On risk-averse maximum weighted subgraph problems. J Comb Optim 28, 167–185 (2014). https://doi.org/10.1007/s10878-014-9718-0

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