Divide-and-Conquer Algorithms for Partitioning Hypergraphs and Submodular Systems

  • Authors:

  • Kazumasa Okumoto;Takuro Fukunaga;Hiroshi Nagamochi

  • Affiliations:

  • Graduate School of Economics, University of Tokyo, Japan;Department of Applied Mathematics and Physics, Graduate School of Informatics, Kyoto University, Japan;Department of Applied Mathematics and Physics, Graduate School of Informatics, Kyoto University, Japan

  • Venue:
  • ISAAC '09 Proceedings of the 20th International Symposium on Algorithms and Computation
  • Year:
  • 2009

Quantified Score

Hi-index 0.00

Visualization

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 $\sum_{i=1}^k f(V_i)$ 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 驴 4. We also analyze the approximation factor for the hypergraph k-cut problem.