Mathematical Programming

, Volume 102, Issue 1, pp 167–183 | Cite as

Greedy splitting algorithms for approximating multiway partition problems

  • Liang ZhaoEmail author
  • Hiroshi Nagamochi
  • Toshihide Ibaraki


Given a system (V,T,f,k), where V is a finite set, Open image in new window is a submodular function and k≥2 is an integer, the general multiway partition problem (MPP) asks to find a k-partition Open image in new window ={V1,V2,...,V k } of V that satisfies Open image in new window for all i and minimizes f(V1)+f(V2)+···+f(V k ), where Open image in new window is a k-partition of Open image in new window 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.


Approximation algorithm Hypergraph partition k-way cut Multiterminal cut Multiway partition problem Submodular function 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Liang Zhao
    • 1
    Email author
  • Hiroshi Nagamochi
    • 2
  • Toshihide Ibaraki
    • 3
  1. 1.Dept. Information Science, Faculty of EngineeringUtsunomiya UniversityUtsunomiyaJapan
  2. 2.Dept. Information and Computer SciencesToyohashi University of TechnologyToyohashi, AichiJapan
  3. 3.Dept. Applied Mathematics and Physics, Graduate School of InformaticsKyoto UniversityKyotoJapan

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