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An Analysis of Approximations for Finding a Maximum Weight Hamiltonian Circuit

Author

Listed:
  • M. L. Fisher

    (University of Pennsylvania, Philadelphia, Pennsylvania)

  • G. L. Nemhauser

    (Cornell University, Ithaca, New York)

  • L. A. Wolsey

    (University of Louvain, Louvain-La-Neuve, Belgium)

Abstract

We give bounds on heuristics and relaxations for the problem of determining a maximum weight hamiltonian circuit in a complete, undirected graph with non-negative edge weights. Three well-known heuristics are shown to produce a tour whose weight is at least half of the weight of an optimal tour. Another heuristic, based on perfect two-matchings, is shown to produce a tour whose weight is at least two-thirds of the weight of an optimal tour. Assignment and perfect two-matching relaxations are shown to produce upper bounds that are, respectively, at most 2 and 3/2 times the optimal value. By defining a more general measure of performance, we extend the results to arbitrary edge weights and minimization problems. We also present analogous results for directed graphs.

Suggested Citation

  • M. L. Fisher & G. L. Nemhauser & L. A. Wolsey, 1979. "An Analysis of Approximations for Finding a Maximum Weight Hamiltonian Circuit," Operations Research, INFORMS, vol. 27(4), pages 799-809, August.
    • Handle: RePEc:inm:oropre:v:27:y:1979:i:4:p:799-809
    DOI: 10.1287/opre.27.4.799
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    Cited by:

    1. Marshall L. Fisher, 2004. "The Lagrangian Relaxation Method for Solving Integer Programming Problems," Management Science, INFORMS, vol. 50(12_supple), pages 1861-1871, December.
    2. Paul Dütting & Thomas Kesselheim & Éva Tardos, 2021. "Algorithms as Mechanisms: The Price of Anarchy of Relax and Round," Mathematics of Operations Research, INFORMS, vol. 46(1), pages 317-335, February.
    3. Monnot, Jerome, 2005. "Approximation algorithms for the maximum Hamiltonian path problem with specified endpoint(s)," European Journal of Operational Research, Elsevier, vol. 161(3), pages 721-735, March.

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