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Computing an Upper Bound for the Longest Edge in an Optimal TSP-Solution

In: Operations Research Proceedings 2013

Author

Listed:
  • Hans Achatz

    (University of Passau)

  • Peter Kleinschmidt

    (University of Passau)

Abstract

A solution of the traveling salesman problem (TSP) with n nodes consists of n edges which form a shortest tour. In our approach we compute an upper bound u for the longest edge which could be in an optimal solution. This means that every edge longer than this bound cannot be in an optimal solution. The quantity u can be computed in polynomial time. We have applied our approach to different problems of the TSPLIB (library of sample instances for the TSP). Our bound does not necessarily improve the fastest TSP-algorithms. However, the reduction of the number of edges might be useful for certain instances.

Suggested Citation

  • Hans Achatz & Peter Kleinschmidt, 2014. "Computing an Upper Bound for the Longest Edge in an Optimal TSP-Solution," Operations Research Proceedings, in: Dennis Huisman & Ilse Louwerse & Albert P.M. Wagelmans (ed.), Operations Research Proceedings 2013, edition 127, pages 1-6, Springer.
    • Handle: RePEc:spr:oprchp:978-3-319-07001-8_1
    DOI: 10.1007/978-3-319-07001-8_1
    as

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