Algorithmica

, Volume 62, Issue 3, pp 787–806

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

  • Kazumasa Okumoto
  • Takuro Fukunaga
  • Hiroshi Nagamochi
Article

DOI: 10.1007/s00453-010-9483-0

Cite this article as:
Okumoto, K., Fukunaga, T. & Nagamochi, H. Algorithmica (2012) 62: 787. doi:10.1007/s00453-010-9483-0

Abstract

The submodular system k-partition problem is a problem of partitioning a given finite set V into k non-empty subsets V1,V2,…,Vk so that \(\sum_{i=1}^{k}f(V_{i})\) is minimized where f is a non-negative submodular function on V. In this paper, we design an approximation algorithm for the problem with fixed k. We also analyze the approximation factor of our algorithm for the hypergraph k-cut problem, which is a problem contained by the submodular system k-partition problem.

Keywords

Divide-and-conquer algorithmHypergraphMulticutSubmodular function

Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  • Kazumasa Okumoto
    • 1
  • Takuro Fukunaga
    • 2
  • Hiroshi Nagamochi
    • 2
  1. 1.Graduate School of EconomicsUniversity of TokyoTokyoJapan
  2. 2.Graduate School of InformaticsKyoto UniversityKyotoJapan