Article

Algorithmica

, Volume 62, Issue 3, pp 787-806

First online:

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

  • Kazumasa OkumotoAffiliated withGraduate School of Economics, University of Tokyo
  • , Takuro FukunagaAffiliated withGraduate School of Informatics, Kyoto University Email author 
  • , Hiroshi NagamochiAffiliated withGraduate School of Informatics, Kyoto University

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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. 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 algorithm Hypergraph Multicut Submodular function