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We present a polynomial time dynamic programming algorithm for optimalpartitions in the shortest path metric induced by a tree. This resolves, amongother things, the exact complexity status of the optimal partition problems inone dimensional geometric metric settings. Our method of solution could be alsoof independent interest in other applications. We discuss also an extension ofour method to the class of metrics induced by the bounded treewidth graphs.

Optimal Cuts and Partitions in Tree Metrics in Polynomial Time