Abstract
A signed graph \(G=(V,E,s)\) is \(k\)-balanced if \(V\) can be partitioned into at most \(k\) sets in such a way that positive edges are found only within the sets and negative edges go between sets. We study the problem of finding a subgraph of \(G\) that is \(k\)-balanced and maximum according to the number of vertices. This problem has applications in clustering problems appearing in collaborative \(\times \) conflicting environments. We describe a 0-1 linear programming formulation for the problem and implement a first version of a branch-and-cut algorithm based on it. GRASP metaheuristics are used to implement the separation routines in the branch-and-cut. We also propose GRASP and ILS-VND procedures to solve heuristically the problem.
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Acknowledgements.
Rosa Figueiredo is supported by FEDER founds through COMPETE-Operational Programme Factors of Competitiveness and by Portuguese founds through the CIDMA (University of Aveiro) and FCT, within project PEst-C/MAT/UI4106/2011 with COMPETE number FCOMP-01-0124-FEDER-022690.
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Figueiredo, R., Frota, Y., Labbé, M. (2013). Solution of the Maximum \(k\)-Balanced Subgraph Problem. In: Nicosia, G., Pardalos, P. (eds) Learning and Intelligent Optimization. LION 2013. Lecture Notes in Computer Science(), vol 7997. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-44973-4_28
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DOI: https://doi.org/10.1007/978-3-642-44973-4_28
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