On risk-averse maximum weighted subgraph problems

Maciej Rysz, Mohammad Mirghorbani, Pavlo Krokhmal, Eduardo L. Pasiliao

Research output: Contribution to journalArticle

10 Scopus citations

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.

Original languageEnglish (US)
Pages (from-to)167-185
Number of pages19
JournalJournal of Combinatorial Optimization
Volume28
Issue number1
DOIs
StatePublished - Jul 2014

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Keywords

  • Coherent risk measures
  • Maximum weight clique problem
  • Risk-averse maximum clique problem
  • Risk-averse maximum weighted subgraph problem
  • Stochastic weights

ASJC Scopus subject areas

  • Computer Science Applications
  • Discrete Mathematics and Combinatorics
  • Control and Optimization
  • Computational Theory and Mathematics
  • Applied Mathematics

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