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

Maciej Rysz, Foad Mahdavi Pajouh, Pavlo Krokhmal, Eduardo L. Pasiliao

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


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 , and 4.

Original languageEnglish (US)
Pages (from-to)89-108
Number of pages20
JournalAnnals of Operations Research
Issue number1
StatePublished - Mar 1 2018


  • coherent risk measures
  • combinatorial branch-and-bound
  • k-club
  • low-diameter clusters
  • stochastic graphs

ASJC Scopus subject areas

  • General Decision Sciences
  • Management Science and Operations Research


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