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A Note on Submodular Function Minimization with Covering Type Linear Constraints | Algorithmica

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A Note on Submodular Function Minimization with Covering Type Linear Constraints

Author:

Naoyuki KamiyamaAuthors Info & Claims

Algorithmica, Volume 80, Issue 10

Pages 2957 - 2971

https://doi.org/10.1007/s00453-017-0363-8

Published: 01 October 2018 Publication History

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 $$\varDelta _i$$Δでるたi the number of non-zero coefficients in the ith constraints. Furthermore, we assume that $$\varDelta _1 \ge \varDelta _2 \ge \cdots \ge \varDelta _m$$Δでるた1źΔでるた2źźźΔでるたm. For this problem, Koufogiannakis and Young proposed a polynomial-time $$\varDelta _1$$Δでるた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 $$\{0,1\}$${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 $$\max \{\varDelta _2, \min \{\varDelta _1, 1 + \varPi \}\}$$max{Δでるた2,min{Δでるた1,1+ź}}, where $$\varPi $$ź is the maximum size of a connected component of the input submodular function.

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Cited By

Shi YZhang ZDu D(2018)A Bicriteria Approximation Algorithm for Minimum Submodular Cost Partial Multi-Cover ProblemAlgorithmic Aspects in Information and Management10.1007/978-3-030-04618-7_6(62-73)Online publication date: 3-Dec-2018
https://dl.acm.org/doi/10.1007/978-3-030-04618-7_6

Index Terms

A Note on Submodular Function Minimization with Covering Type Linear Constraints
1. Mathematics of computing
  1. Mathematical analysis
    1. Functional analysis
      1. Approximation
2. Theory of computation
  1. Design and analysis of algorithms

Index terms have been assigned to the content through auto-classification.

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cover image Algorithmica

Algorithmica Volume 80, Issue 10

October 2018

247 pages

ISSN:0178-4617

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Copyright © Copyright © 2018 Springer Science+Business Media, LLC, part of Springer Nature.

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Springer-Verlag

Berlin, Heidelberg

Publication History

Published: 01 October 2018

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Cited By

Shi YZhang ZDu D(2018)A Bicriteria Approximation Algorithm for Minimum Submodular Cost Partial Multi-Cover ProblemAlgorithmic Aspects in Information and Management10.1007/978-3-030-04618-7_6(62-73)Online publication date: 3-Dec-2018
https://dl.acm.org/doi/10.1007/978-3-030-04618-7_6

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