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arXiv · 1207.4694

A New Upper Bound for the Traveling Salesman Problem in Cubic Graphs

Maciej Liskiewicz·Martin R. Schuster
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Abstract

We provide a new upper bound for traveling salesman problem (TSP) in cubic graphs, i.e. graphs with maximum vertex degree three, and prove that the problem for an $n$-vertex graph can be solved in $O(1.2553^n)$ time and in linear space. We show that the exact TSP algorithm of Eppstein, with some minor modifications, yields the stated result. The previous best known upper bound $O(1.251^n)$ was claimed by Iwama and Nakashima [Proc. COCOON 2007]. Unfortunately, their analysis contains several mistakes that render the proof for the upper bound invalid.

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Maciej Liskiewicz, Martin R. Schuster. 2012-07-19. A New Upper Bound for the Traveling Salesman Problem in Cubic Graphs. https://arxiv.org/abs/1207.4694

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