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The maximization of submodular functions : old and new proofs for the correctness of the dichotomy algorithm


Author Info

  • Goldengorin, Boris
  • Tijssen, Gert A.
  • Tso, Michael

    (Groningen University)


The first purpose of this paper is to make an old (Russian) theoretical results about the structure of local and global maxima of submodular functions, Cherenin’s excluding rules and his Dichotomy Algorithm more accessible for Western community. The second purpose of this paper is to present our main result which can be stated as follows. For any pair of embedded subsets, the difference of their function values is a lower bound for the difference between the unknown(!) optimal values of the corresponding partition defined by these subsets. A simple justification of Cherenin’s rules, the Dichotomy Algorithmand its generalization with the new branching rules from our main result are presented. The usefulness of our new branching rules is illustrated by means of a numerical example.

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Paper provided by University of Groningen, Research Institute SOM (Systems, Organisations and Management) in its series Research Report with number 99A17.

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Date of creation: 1999
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Handle: RePEc:dgr:rugsom:99a17

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  1. Beasley, J. E., 1993. "Lagrangean heuristics for location problems," European Journal of Operational Research, Elsevier, Elsevier, vol. 65(3), pages 383-399, March.
  2. Boris Goldengorin & Gerard Sierksma & Gert A. Tijssen & Michael Tso, 1999. "The Data-Correcting Algorithm for the Minimization of Supermodular Functions," Management Science, INFORMS, INFORMS, vol. 45(11), pages 1539-1551, November.
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Cited by:
  1. Lones Smith & Hector Chade, 2004. "Simultaneous Search," 2004 Meeting Papers, Society for Economic Dynamics 25, Society for Economic Dynamics.


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