Min-max multiway cut

We propose the MIN-MAX MULTIWAY CUT problem, a variant of the traditional MULTIWAY CUT problem, but with the goal of minimizing the maximum capacity (rather than the sum or average capacity) leaving a part of the partition. The problem is motivated by data partitioning in Peer-to-Peer networks. The min-max objective function forces the solution not to overload any given terminal, and hence may lead to better solution quality. We prove that the MIN-MAX MULTIWAY CUT is NP-hard even on trees, or with only a constant number of terminals. Our main result is an O(log(3) n)-approximation algorithm for general graphs, and an O(log(2) n)approximation for graphs excluding any fixed graph as a minor (e.g., planar graphs). We also give a (2 + epsilon)-approximation algorithm for the special case of graphs with bounded treewidth.