Detecting large risk-averse 2-clubs in graphs with random edge failures
- First Online:
- 169 Downloads
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.
Keywords2-club Graph-based data mining Conditional value-at-risk Benders decomposition
- Center for Complex Networks Research (2007). Network databases. http://www3.nd.edu/~networks/resources.htm. Accessed Dec 2014.
- Grossman, J., Ion, P., & Castro, R.D. (1995). The Erdös number project. Online: http://www.oakland.edu/enp/. Accessed Dec 2014.
- KEGG BRITE Database (2014). Biomolecular relations in information transmission and expression. http://www.genome.jp/kegg/brite.html. Accessed Dec 2014.
- Rain, J.C., Selig, L., Reuse, H.D., Battaglia, V., Reverdy, C., Simon, S., Lenzen, G., Petel, F., Wojcik, J., Schachter, V., Chemama, Y., Labigne, A., & Legrain, P. (2004). The protein-protein interaction map of helicobacter pylori. Nature 409(6817):211–215, erratum in: Nature 409(6820):553 and 409(6821):743, 2001.Google Scholar
- Soleimani, H., & Govindan, K. (2014). Reverse logistics network design and planning utilizing conditional value at risk. European Journal of Operational Research, 237(2), 487–497. doi:10.1016/j.ejor.2014.02.030, http://www.sciencedirect.com/science/article/pii/S0377221714001635.
- Subramanian, D., & Huang, P. (2009). An efficient decomposition algorithm for static, stochastic, linear and mixed-integer linear programs with conditional value-at-risk constraints. Tech. Rep. RC24752, IBM Research Report.Google Scholar
- Uryasev, S. (2000). Conditional value-at-risk: optimization algorithms and applications. In: Computational Intelligence for Financial Engineering, 2000. (CIFEr) Proceedings of the IEEE/IAFE/INFORMS 2000 Conference on, IEEE, pp. 49–57.Google Scholar