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International Symposium on Algorithms and Computation

ISAAC 2009: Algorithms and Computation pp 55–64Cite as

Divide-and-Conquer Algorithms for Partitioning Hypergraphs and Submodular Systems

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5878))

Abstract

The submodular system k-partition problem is a problem of partitioning a given finite set V into k non-empty subsets V 1,V 2, ...,V k so that \(\sum_{i=1}^k f(V_i)\) is minimized where f is a non-negative submodular function on V, and k is a fixed integer. This problem contains the hypergraph k-cut problem. In this paper, we design the first exact algorithm for k = 3 and approximation algorithms for k ≥ 4. We also analyze the approximation factor for the hypergraph k-cut problem.

This work was partially supported by Grant-in-Aid for Scientific Research from the Ministry of Education, Culture, Sports, Science and Technology of Japan.

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Author information

Authors and Affiliations

  1. Graduate School of Economics, University of Tokyo, Japan

    Kazumasa Okumoto

  2. Department of Applied Mathematics and Physics, Graduate School of Informatics, Kyoto University, Japan

    Takuro Fukunaga & Hiroshi Nagamochi

Authors
  1. Kazumasa Okumoto
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  2. Takuro Fukunaga
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  3. Hiroshi Nagamochi
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Editor information

Editors and Affiliations

  1. Dept. of Electrical and Computer Engineering, University of Hawaii, Holmes Hall 483, 2540 Dole Street, 96822, Honolulu, HI, USA

    Yingfei Dong

  2. Department of Computer Science, University of Texas at Dallas, 75083, Dallas, TX, USA

    Ding-Zhu Du

  3. Department of Computer Science, University of California, 93106, Santa Barbara, CA, USA

    Oscar Ibarra

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© 2009 Springer-Verlag Berlin Heidelberg

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Okumoto, K., Fukunaga, T., Nagamochi, H. (2009). Divide-and-Conquer Algorithms for Partitioning Hypergraphs and Submodular Systems. In: Dong, Y., Du, DZ., Ibarra, O. (eds) Algorithms and Computation. ISAAC 2009. Lecture Notes in Computer Science, vol 5878. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-10631-6_8

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  • DOI: https://doi.org/10.1007/978-3-642-10631-6_8

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-10630-9

  • Online ISBN: 978-3-642-10631-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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