# A Fast Exact Algorithm for the Problem of Optimum Cooperation and Structure of Its Solutions

FanghÃ¤nel, Diana and Liers, Frauke
(2010)
*A Fast Exact Algorithm for the Problem of Optimum Cooperation and Structure of Its Solutions.*
**Published in: **
Journal of Combinatorial Optimization Vol. 19 (3).
pp. 369-393.

## Abstract

Given a graph with real edge weights, 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 n-1 minimum cut computations in a corresponding network, where n is the number of nodes in the graph. 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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ZAIK Number: | zaik2008-574 |
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Depositing User: | Diana FanghÃ¤nel |

Date Deposited: | 12 Jul 2011 00:00 |

Last Modified: | 09 Jan 2012 12:18 |

URI: | http://e-archive.informatik.uni-koeln.de/id/eprint/574 |