Approximating the minimum net expansion: Near optimal solutions to circuit partitioning problems

Abstract

We address the problem of finding an approximation to the minimum net expansion (MNE) of a hypergraph H=(V, E _h ), MNE is defined to be the minimum total weight of hyperedges with endpoints into two different sets divided by the number of nodes of the smaller set. We prove that a solution or a constant times optimal approximation to the optimization version of a multicommodity flow problem yields a logarithmic, to the number of nets, approximation of the minimum net expansion of the input hypergraph. This is a generalization of the result that Leighton and Rao proposed for graphs. Our flow problem can be solved or approximated to a constant factor of the optimal solution in polynomial time. Next, we show important applications of our result to achieve provably good solutions for a variety of partitioning and partitioning related problems on hypergraphs including bipartitioning, multiway partitioning and nonplanar net deletion. For several of the problems the solutions are within a polylogarithmic factor to the optimal solution.