### 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 Δ_{i} the number of non-zero coefficients in the ith constraints. Furthermore, we assume that Δ_{1}≥ Δ_{2}≥ ⋯ ≥ Δ_{m}. For this problem, Koufogiannakis and Young proposed a polynomial-time Δ_{1}-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 { Δ_{2}, min { Δ_{1}, 1 + Π} } , where Π is the maximum size of a connected component of the input submodular function.

Original language | English |
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Pages (from-to) | 2957-2971 |

Number of pages | 15 |

Journal | Algorithmica |

Volume | 80 |

Issue number | 10 |

DOIs | |

Publication status | Published - Oct 1 2018 |

### All Science Journal Classification (ASJC) codes

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