Robust optimization of graph partitioning and critical node detection in analyzing networks

Authors:
Neng Fan;Panos M. Pardalos
Affiliations:
Center for Applied Optimization, Department of Industrial and Systems Engineering, University of Florida, Gainesville, FL;Center for Applied Optimization, Department of Industrial and Systems Engineering, University of Florida, Gainesville, FL
Venue:
COCOA'10 Proceedings of the 4th international conference on Combinatorial optimization and applications - Volume Part I
Year:
2010

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Abstract

The graph partitioning problem (GPP) consists of partitioning the vertex set of a graph into several disjoint subsets so that the sum of weights of the edges between the disjoint subsets isminimized. The critical node problem (CNP) is to detect a set of vertices in a graph whose deletion results in the graph having the minimum pairwise connectivity between the remaining vertices. Both GPP and CNP find many applications in identification of community structures or influential individuals in social networks, telecommunication networks, and supply chain networks. In this paper, we use integer programming to formulate GPP and CNP. In several practice cases, we have networks with uncertain weights of links. Some times, these uncertainties have no information of probability distribution. We use robust optimization models of GPP and CNP to formulate the community structures or influential individuals in such networks.