Greedy splitting algorithms for approximating multiway partition problems |
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Authors: | Liang Zhao Hiroshi Nagamochi Toshihide Ibaraki |
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Institution: | (1) Dept. Information Science, Faculty of Engineering, Utsunomiya University, Yoto 7-1-2, Utsunomiya 321-8585, Japan;(2) Dept. Information and Computer Sciences, Toyohashi University of Technology, Toyohashi, Aichi 441-8580, Japan;(3) Dept. Applied Mathematics and Physics, Graduate School of Informatics, Kyoto University, Kyoto 606-8501, Japan |
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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,...,Vk} of V that satisfies for all i and minimizes f(V1)+f(V2)+···+f(Vk), 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.Mathematics Subject Classification (1991): 20E28, 20G40, 20C20Acknowledgement 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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Keywords: | Approximation algorithm Hypergraph partition k-way cut Multiterminal cut Multiway partition problem Submodular function |
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