Detecting large risk-averse 2-clubs in graphs with random edge failures

• Published in: Annals of operations research Vol. 249; no. 1-2; pp. 55 - 73
• Main Authors: Mahdavi Pajouh, Foad, Moradi, Esmaeel, Balasundaram, Balabhaskar
• Format: Journal Article
• Language: English
• Published: New York Springer US 01.02.2017; Springer; Springer Nature B.V
• Subjects: Algorithms; Business and Management; Clubs; Combinatorics; Data mining; Decomposition; Failure; Graph theory; Graphs; Networks; Operations research; Operations Research/Decision Theory; Optimization; Pardalos60; Probabilistic methods; Probability theory; Risk; Risk aversion; Social networks; Studies; Theory of Computation; Uncertainty; Conditional value-at-risk; 2-club; Benders decomposition; Graph-based data mining
• ISSN: 0254-5330; 1572-9338
• DOI: 10.1007/s10479-016-2279-0

Detecting large 2-clubs in biological, social and financial networks can help reveal important information about the structure of the underlying systems. In large-scale networks that are error-prone, the uncertainty associated with the existence of an edge between two vertices can be modeled by assigning a failure probability to that edge. Here, we study the problem of detecting large “risk-averse” 2-clubs in graphs subject to probabilistic edge failures. To achieve risk aversion, we first model the loss in 2-club property due to probabilistic edge failures as a function of the decision (chosen 2-club cluster) and randomness (graph structure). Then, we utilize the conditional value-at-risk (CVaR) of the loss for a given decision as a quantitative measure of risk for that decision, which is bounded in the model. More precisely, the problem is modeled as a CVaR-constrained single-stage stochastic program. The main contribution of this article is a new Benders decomposition algorithm that outperforms an existing decomposition approach on a test-bed of randomly generated instances, and real-life biological and social networks.