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Attacking the Market Split Problem with Lattice Point Enumeration

Author

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  • Alfred Wassermann

    (Universität Bayreuth)

Abstract

The market split problem was proposed by Cornuéjols and Dawande as benchmark problem for algorithms solving linear systems with 0/1 variables. Here, we present an algorithm for the more general problem A · x = b with arbitrary lower and upper bound on the variables. The algorithm consists of exhaustive enumeration of all points of a suitable lattice which are contained in a given polyhedron. We present results for the feasibility version as well as for the integer programming version of the market split problem which indicate that the algorithm outperforms the previously published approaches to this problems considerably.

Suggested Citation

  • Alfred Wassermann, 2002. "Attacking the Market Split Problem with Lattice Point Enumeration," Journal of Combinatorial Optimization, Springer, vol. 6(1), pages 5-16, March.
    • Handle: RePEc:spr:jcomop:v:6:y:2002:i:1:d:10.1023_a:1013355015853
    DOI: 10.1023/A:1013355015853
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    Cited by:

    1. Karen Aardal, 2004. "Comments on the Paper: Attacking the Market Split Problem with Lattice Point Enumeration," Journal of Combinatorial Optimization, Springer, vol. 8(2), pages 147-149, June.
    2. Heiko Vogel, 2012. "Solving market split problems with heuristical lattice reduction," Annals of Operations Research, Springer, vol. 196(1), pages 581-590, July.
    3. Leonardo Lozano & David Bergman & J. Cole Smith, 2020. "On the Consistent Path Problem," Operations Research, INFORMS, vol. 68(6), pages 1913-1931, November.

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