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In the k-partition problem (k-PP), one is given an edge-weighted undirectedgraph, and one must partition the node set into at most k subsets, in order tominimise (or maximise) the total weight of the edges that have their end-nodesin the same cluster. Various hierarchical variants of this problem have beenstudied in the context of data mining. We consider a 'two-level' variant thatarises in mobile wireless communications. We show that an exact algorithm basedon intelligent preprocessing, cutting planes and symmetry-breaking is capableof solving small- and medium-size instances to proven optimality, and providingstrong lower bounds for larger instances.

A Two-Level Graph Partitioning Problem Arising in Mobile Wireless Communications