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On the Relation Between the Traveling-Salesman and the Longest-Path Problems

Author

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  • William W. Hardgrave

    (Bell Telephone Laboratories, Inc., Holmdel, New Jersey)

  • George L. Nemhauser

    (The Johns Hopkins University, Baltimore, Maryland)

Abstract

The main result of this paper is that the traveling-salesman problem is a special case of the longest-path problem. Two formulations of the traveling-salesman problem are considered, the version in which the salesman visits each city exactly once and the more general formulation in which each city may be visited more than once. Both cases are reduced to the problem of finding the longest path between two nodes in a finite, connected graph. The remainder of the paper is then devoted to possible algorithms for the longest-path problem, since none presently exist.

Suggested Citation

  • William W. Hardgrave & George L. Nemhauser, 1962. "On the Relation Between the Traveling-Salesman and the Longest-Path Problems," Operations Research, INFORMS, vol. 10(5), pages 647-657, October.
    • Handle: RePEc:inm:oropre:v:10:y:1962:i:5:p:647-657
    DOI: 10.1287/opre.10.5.647
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    Cited by:

    1. Rodríguez-Pereira, Jessica & Fernández, Elena & Laporte, Gilbert & Benavent, Enrique & Martínez-Sykora, Antonio, 2019. "The Steiner Traveling Salesman Problem and its extensions," European Journal of Operational Research, Elsevier, vol. 278(2), pages 615-628.
    2. Letchford, Adam N. & Nasiri, Saeideh D. & Theis, Dirk Oliver, 2013. "Compact formulations of the Steiner Traveling Salesman Problem and related problems," European Journal of Operational Research, Elsevier, vol. 228(1), pages 83-92.

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