Abstract
In 1975, Kalmanson proved that in case the distance matrix in the Travelling Salesman Problem (TSP) fulfills certain combinatorial conditions (nowadays called the Kalmanson conditions) then the TSP is solvable in polynomial time.
We deal with the problem of deciding for a given instance of the TSP, whether there is a renumbering of the cities such that the corresponding renumbered distance matrix fulfills the Kalmanson conditions. Two results are derived: First, it is shown that such a renumbering can be found in polynomial time (in case it exists). Secondly, it is proved that such a renumbering exists if and only if the instance possesses the so-called master tour property. Thereby a recently posed question by Papadimitriou is answered in the negative.
This research has been supported by the Spezialforschungsbereich F 003 “Optimierung und Kontrolle”, Projektbereich Diskrete Optimierung.
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© 1995 Springer-Verlag Berlin Heidelberg
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Deineko, V.G., Rudolf, R., Woeginger, G.J. (1995). Sometimes travelling is easy: The master tour problem. In: Spirakis, P. (eds) Algorithms — ESA '95. ESA 1995. Lecture Notes in Computer Science, vol 979. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-60313-1_139
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DOI: https://doi.org/10.1007/3-540-60313-1_139
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