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A strongly polynomial-time algorithm for minimizing submodular functions

Author

Listed:
  • IWATA, Satoru

    (Division of Systems Science, Graduate School of Engineering Science, Osaka University, Toyonaka, Osaka 560-8531, Japan)

  • FLEISCHER, Lisa

    (Department of Industrial Engineering and Operations Research, Columbia University, New York, NY 10027, USA)

  • FUJISHIGE, Satoru

    (Division of Systems Science, Graduate School of Engineering Science, Osaka University, Toyonaka, Osaka 560-8531, Japan)

Abstract

This paper presents a combinatorial polynomial-time algorithm for minimizing submolular set functions. The algorithm employs a scaling scheme that uses a flow in the complete directed graph on the underlying set with each arc capacity equal to thescaled parameter. The resulting algorithm runs in time bounded by a polynomial in the size of the underlying set and the largest length of the function value. The paper also presents a strongly polynomial-time version that runs in time bounded by a polynomial in the size of the underlying set independent of the function value. These are the first combinatorial algorithms for submodular function minimization that run in (strongly) polynomial time.

Suggested Citation

  • IWATA, Satoru & FLEISCHER, Lisa & FUJISHIGE, Satoru, 1999. "A strongly polynomial-time algorithm for minimizing submodular functions," LIDAM Discussion Papers CORE 1999048, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    • Handle: RePEc:cor:louvco:1999048
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    File URL: https://sites.uclouvain.be/core/publications/coredp/coredp1999.html
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    Cited by:

    1. FLEISCHER, Lisa & IWATA, Satoru & McCORMICK, Thomas, 1999. "A faster capacity scaling algorithm for minimum cost submodular flow," LIDAM Discussion Papers CORE 1999047, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).

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