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Worst-Case Analysis of a New Heuristic for the Travelling Salesman Problem

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  • Nicos Christofides

    (Carnegie-Mellon University)

Abstract

An O(n3) heuristic algorithm is described for solving d-city travelling salesman problems (TSP) whose cost matrix satisfies the triangularity condition. The algorithm involves as substeps the computation of a shortest spanning tree of the graph G defining the TSP and the finding of a minimum cost perfect matching of a certain induced subgraph of G. A worst-case analysis of this heuristic shows that the ratio of the answer obtained to the optimum TSP solution is strictly less than 3/2. This represents a 50% reduction over the value 2 which was the previously best known such ratio for the performance of other polynomial growth algorithms for the TSP.

Suggested Citation

  • Nicos Christofides, 2022. "Worst-Case Analysis of a New Heuristic for the Travelling Salesman Problem," SN Operations Research Forum, Springer, vol. 3(1), pages 1-4, March.
    • Handle: RePEc:spr:snopef:v:3:y:2022:i:1:d:10.1007_s43069-021-00101-z
    DOI: 10.1007/s43069-021-00101-z
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    References listed on IDEAS

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    1. Samuel Eilon & Nicos Christofides, 1971. "The Loading Problem," Management Science, INFORMS, vol. 17(5), pages 259-268, January.
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