An exact algorithm for robust influence maximization

• 成果类型: Article
• 署名作者: Nannicini, Giacomo; Sartor, Giorgio; Traversi, Emiliano; Calvo, Roberto Wolfler
• 署名单位: International Business Machines (IBM); IBM USA; SINTEF; Centre National de la Recherche Scientifique (CNRS); CNRS - Institute for Information Sciences & Technologies (INS2I); University of Cagliari
• 刊物名称: MATHEMATICAL PROGRAMMING
• ISSN/ISSBN: 0025-5610
• DOI: 10.1007/s10107-020-01507-z
• 发表日期: 2020
• 页码: 419-453

摘要

We propose a Branch-and-Cut algorithm for the robust influence maximization problem. The influence maximization problem aims to identify, in a social network, a set of given cardinality comprising actors that are able to influence the maximum number of other actors. We assume that the social network is given in the form of a graph with node thresholds to indicate the resistance of an actor to influence, and arc weights to represent the strength of the influence between two actors. In the robust version of the problem that we study, the node thresholds and arc weights are affected by uncertainty and we optimize over a worst-case scenario within given robustness budgets. We study properties of the robust solution and showthat even computing theworst-case scenario for given robustness budgets is NP-hard. We implement an exact Branch-and-Cut as well as a heuristic Branch-Cut-and-Price. Numerical experiments show that we are able to solve to optimality instances of size comparable to other exact approaches in the literature for the non-robust problem, and we can tackle the robust version with similar performance. On larger instances (= 2000 nodes), our heuristic Branch-Cutand-Price significantly outperforms a 2-opt heuristic. An extended abstract of this paper appeared in the proceedings of IPCO 2019.