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

Hans Achatz () and Peter Kleinschmidt ()
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Hans Achatz: University of Passau
Peter Kleinschmidt: University of Passau

A chapter in Operations Research Proceedings 2013, 2014, pp 1-6 from Springer

Abstract: 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.

Keywords: Assignment Problem; Travel Salesman Problem; Travel Salesman Problem; Cost Matrix; Adjacent Edge (search for similar items in EconPapers)
Date: 2014
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Persistent link: https://EconPapers.repec.org/RePEc:spr:oprchp:978-3-319-07001-8_1

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DOI: 10.1007/978-3-319-07001-8_1

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