On risk-averse maximum weighted subgraph problems

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

Research output: Contribution to journalArticle

10 Citations (Scopus)

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
Externally publishedYes

Fingerprint

Coherent Risk Measures
Stochastic programming
Stochastic Programming
Stochastic systems
Graph theory
Risk Analysis
Risk analysis
Stochastic Systems
Subgraph
Graph in graph theory
Hereditary Properties
Risk Function
Risk Measures
Branch and Bound Algorithm
Branch-and-bound
Vertex of a graph
Erdös
Clique
Joint Distribution
Optimal Solution

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

Cite this

On risk-averse maximum weighted subgraph problems. / Rysz, Maciej; Mirghorbani, Mohammad; Krokhmal, Pavlo; Pasiliao, Eduardo L.

In: Journal of Combinatorial Optimization, Vol. 28, No. 1, 07.2014, p. 167-185.

Research output: Contribution to journalArticle

Rysz, Maciej ; Mirghorbani, Mohammad ; Krokhmal, Pavlo ; Pasiliao, Eduardo L. / On risk-averse maximum weighted subgraph problems. In: Journal of Combinatorial Optimization. 2014 ; Vol. 28, No. 1. pp. 167-185.
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