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Bisubmodular Function Minimization

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Integer Programming and Combinatorial Optimization (IPCO 2001)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2081))

Abstract

This paper presents the first combinatorial, polynomial-time algorithm for minimizing bisubmodular functions, extending the scaling algorithm for submodular function minimization due to Iwata, Fleischer, and Fujishige. A bisubmodular function arises as a rank function of a delta-matroid. The scaling algorithm naturally leads to the first combinatorial polynomial-time algorithm for testing membership in delta- matroid polyhedra. Unlike the case of matroid polyhedra, it remains open to develop a combinatorial strongly polynomial algorithm for this problem.

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Author information

Authors and Affiliations

  1. Graduate School of Engineering Science, Osaka University, Toyonaka, Osaka, 560-8531, Japan

    Satoru Fujishige

  2. Graduate School of Information Science and Technology University of Tokyo, Tokyo, 113-8656, Japan

    Satoru Iwata

Authors
  1. Satoru Fujishige
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  2. Satoru Iwata
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Editor information

Editors and Affiliations

  1. Instituut voor Informatica en Informatiekunde, Universiteit Utrecht, Padualaan 14, 3584, CH Utrecht, The Netherlands

    Karen Aardal

  2. CWI, Kruislaan 413, 1098, SJ Amsterdam, The Netherlands

    Bert Gerards

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© 2001 Springer-Verlag Berlin Heidelberg

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Fujishige, S., Iwata, S. (2001). Bisubmodular Function Minimization. In: Aardal, K., Gerards, B. (eds) Integer Programming and Combinatorial Optimization. IPCO 2001. Lecture Notes in Computer Science, vol 2081. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45535-3_13

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  • DOI: https://doi.org/10.1007/3-540-45535-3_13

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-42225-9

  • Online ISBN: 978-3-540-45535-6

  • eBook Packages: Springer Book Archive

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