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A solvable case of the traveling salesman problem

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Abstract

LetD = ‖d ij ‖ be the distance matrix defining a traveling salesman problem. IfD is upper triangular, i.e.d ij = 0, fori ≥ j, then the traveling salesman problem can be solved with an amount of computation approximately equal to that required for an assignment problem of the same dimension.

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References

  1. A.J. Hoffman and H.M. Markovitz, “A note on shortest path, assignment, and transportation problems,”Naval Research Logistics Quarterly 10 (1963) 375–380.

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  2. P.C. Gilmore and R.E. Gomory, “Sequencing a one state-variable machine: A solvable case of the traveling salesman problem,”Operations Research 12 (1964) 655–679.

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Authors and Affiliations

  1. University of California, Berkeley, California, USA

    Eugene L. Lawler

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  1. Eugene L. Lawler
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Lawler, E.L. A solvable case of the traveling salesman problem. Mathematical Programming 1, 267–269 (1971). https://doi.org/10.1007/BF01584089

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  • DOI: https://doi.org/10.1007/BF01584089

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