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The Data-Correcting Algorithm for the Minimization of Supermodular Functions

  • Boris Goldengorin

    (Department of Econometrics and Operations Research, University of Groningen, P.O. Box 800, 9700 AV Groningen, The Netherlands)

  • Gerard Sierksma

    (Department of Econometrics and Operations Research, University of Groningen, P.O. Box 800, 9700 AV Groningen, The Netherlands)

  • Gert A. Tijssen

    (Department of Econometrics and Operations Research, University of Groningen, P.O. Box 800, 9700 AV Groningen, The Netherlands)

  • Michael Tso

    (Department of Mathematics, University of Manchester, Institute of Science and Technology, UMIST, Manchester, United Kingdom)

The Data-Correcting (DC) Algorithm is a recursive branch-and-bound type algorithm, in which the data of a given problem instance are "heuristically corrected" at each branching in such a way that the new instance will be as close as possible to polynomially solvable and the result satisfies a prescribed accuracy (the difference between optimal and current solution). In this paper the DC algorithm is applied to determining exact or approximate global minima of supermodular functions. The working of the algorithm is illustrated by an instance of the Simple Plant Location (SPL) Problem. Computational results, obtained for the Quadratic Cost Partition Problem (QCP), show that the DC algorithm outperforms a branch-and-cut algorithm, not only for sparse graphs but also for nonsparse graphs (with density more than 40%), often with speeds 100 times faster.

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Article provided by INFORMS in its journal Management Science.

Volume (Year): 45 (1999)
Issue (Month): 11 (November)
Pages: 1539-1551

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Handle: RePEc:inm:ormnsc:v:45:y:1999:i:11:p:1539-1551
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