Approximation, Randomization, and Combinatorial Optimization.. Algorithms and Techniques

We consider the following general correlation-clustering problem [1]: given a graph with real edge weights (both positive and negative), partition the vertices into clusters to minimize the total absolute weight of cut positive edges and uncut negative edges. Thus, large positive weights (representing strong correlations between endpoints) encourage those endpoints to belong to a common cluster; large negative weights encourage the endpoints to belong to different clusters; and weights with small absolute value represent little information. In contrast to most clustering problems, correlation clustering specifies neither the desired number of clusters nor a distance threshold for clustering; both of these parameters are effectively chosen to be the best possible by the problem definition.

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