Abstract
The clique partitioning problem can be described as follows. Given a complete graph G = (V, E) with edge weights w e ∈ IR for all e ∈ E, find a subset A ⊆ E such that the graph G′ = (V, A) consists of cliques, and such that 1 is minimal. Obviously, if all edge weights are nonnegative, then A = 0 is a (not necessarily unique) optimal clique partition; if all edge weights are nonpositive, then A = E is an optimal clique partition. However, for general edge weights the problem of finding a minimal weight clique partition is NP-hard [8].
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