Divide-and-conquer algorithms for partitioning hypergraphs and submodular systems

Abstract

The submodular system k-partition problem is a problem of partitioning a given finite set V into k non-empty subsets V 1,V 2, ⋯ ,V k so that is minimized where f is a non-negative submodular function on V, and k is a fixed integer. This problem contains the hypergraph k-cut problem. In this paper, we design the first exact algorithm for k=3 and approximation algorithms for k≥4. We also analyze the approximation factor for the hypergraph k-cut problem. © 2009 Springer-Verlag Berlin Heidelberg.