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Greedy splitting algorithms for approximating multiway partition problems

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Abstract.

Given a system (V,T,f,k), where V is a finite set, is a submodular function and k≥2 is an integer, the general multiway partition problem (MPP) asks to find a k-partition ={V1,V2,...,V k } of V that satisfiesfor all i and minimizes f(V1)+f(V2)+···+f(V k ), where is a k-partition of hold. MPP formulation captures a generalization in submodular systems of many NP-hard problems such as k-way cut, multiterminal cut, target split and their generalizations in hypergraphs. This paper presents a simple and unified framework for developing and analyzing approximation algorithms for various MPPs.

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Authors and Affiliations

  1. Dept. Information Science, Faculty of Engineering, Utsunomiya University, Yoto 7-1-2, Utsunomiya, 321-8585, Japan

    Liang Zhao

  2. Dept. Information and Computer Sciences, Toyohashi University of Technology, Toyohashi, Aichi, 441-8580, Japan

    Hiroshi Nagamochi

  3. Dept. Applied Mathematics and Physics, Graduate School of Informatics, Kyoto University, Kyoto, 606-8501, Japan

    Toshihide Ibaraki

Authors
  1. Liang Zhao
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  2. Hiroshi Nagamochi
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  3. Toshihide Ibaraki
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Corresponding author

Correspondence to Liang Zhao.

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Mathematics Subject Classification (1991): 20E28, 20G40, 20C20

Acknowledgement This research is partially supported by the Scientific Grant-in-Aid from Ministry of Education, Science, Sports and Culture of Japan. The authors would like to thank the anonymous referees for their valuable comments and suggestions.

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Zhao, L., Nagamochi, H. & Ibaraki, T. Greedy splitting algorithms for approximating multiway partition problems . Math. Program. 102, 167–183 (2005). https://doi.org/10.1007/s10107-004-0510-2

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  • DOI: https://doi.org/10.1007/s10107-004-0510-2

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