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On Integer Programming, Discrepancy, and Convolution

Author

Listed:
  • Klaus Jansen

    (University of Kiel, 24118 Kiel, Germany)

  • Lars Rohwedder

    (Maastricht University, 6211 LK Maastricht, Netherlands)

Abstract

Integer programs with a fixed number of constraints are solvable in pseudo-polynomial time in the largest coefficient of any constraint. We give a new algorithm which improves the running time of the state of the art. Moreover, we show that improving on our algorithm for any number of constraints is equivalent to improving over the quadratic time algorithm for (min, +)-convolution. This is strong evidence that our algorithm’s running time is the best possible. We also present a specialized algorithm for testing the feasibility of an integer program and give a tight lower bound, which is based on the strong exponential time hypothesis in this case.

Suggested Citation

  • Klaus Jansen & Lars Rohwedder, 2023. "On Integer Programming, Discrepancy, and Convolution," Mathematics of Operations Research, INFORMS, vol. 48(3), pages 1481-1495, August.
    • Handle: RePEc:inm:ormoor:v:48:y:2023:i:3:p:1481-1495
    DOI: 10.1287/moor.2022.1308
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    References listed on IDEAS

    as
    1. Ravi Kannan, 1987. "Minkowski's Convex Body Theorem and Integer Programming," Mathematics of Operations Research, INFORMS, vol. 12(3), pages 415-440, August.
    2. H. W. Lenstra, 1983. "Integer Programming with a Fixed Number of Variables," Mathematics of Operations Research, INFORMS, vol. 8(4), pages 538-548, November.
    3. Klaus Jansen & Kim-Manuel Klein & José Verschae, 2020. "Closing the Gap for Makespan Scheduling via Sparsification Techniques," Mathematics of Operations Research, INFORMS, vol. 45(4), pages 1371-1392, November.
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    Cited by:

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