Abstract
Given a graph G=(V,E) with edge weights w e ∈ℝ, the optimum cooperation problem consists in determining a partition of the graph that maximizes the sum of weights of the edges with nodes in the same class plus the number of the classes of the partition. The problem is also known in the literature as the optimum attack problem in networks. Furthermore, a relevant physics application exists.
In this work, we present a fast exact algorithm for the optimum cooperation problem. Algorithms known in the literature require |V|−1 minimum cut computations in a corresponding network. By theoretical considerations and appropriately designed heuristics, we considerably reduce the numbers of minimum cut computations that are necessary in practice. We show the effectiveness of our method by presenting results on instances coming from the physics application. Furthermore, we analyze the structure of the optimal solutions.
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This work is supported by the German Science Foundation under contract Li 1675/1. Partially supported by the Marie Curie RTN Adonet 504438 funded by the EU.
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Fanghänel, D., Liers, F. A fast exact algorithm for the problem of optimum cooperation and the structure of its solutions. J Comb Optim 19, 369–393 (2010). https://doi.org/10.1007/s10878-009-9208-y
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DOI: https://doi.org/10.1007/s10878-009-9208-y