A Note on Submodular Function Minimization with Covering Type Linear Constraints

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Abstract

In this paper, we consider the non-negative submodular function minimization problem with covering type linear constraints. Assume that there exist m linear constraints, and we denote by Δi the number of non-zero coefficients in the ith constraints. Furthermore, we assume that Δ1≥ Δ2≥ ⋯ ≥ Δm. For this problem, Koufogiannakis and Young proposed a polynomial-time Δ1-approximation algorithm. In this paper, we propose a new polynomial-time primal-dual approximation algorithm based on the approximation algorithm of Takazawa and Mizuno for the covering integer program with { 0 , 1 } -variables and the approximation algorithm of Iwata and Nagano for the submodular function minimization problem with set covering constraints. The approximation ratio of our algorithm is max { Δ2, min { Δ1, 1 + Π} } , where Π is the maximum size of a connected component of the input submodular function.

Original languageEnglish
Pages (from-to)2957-2971
Number of pages15
JournalAlgorithmica
Volume80
Issue number10
DOIs
Publication statusPublished - Oct 1 2018

All Science Journal Classification (ASJC) codes

  • Computer Science(all)
  • Computer Science Applications
  • Applied Mathematics

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