Abstract
The minimum traveling salesman problem with distances one and two is the following problem: Given a complete undirected graph G=(V,E) with a cost function w: E→ {1, 2}, find a Hamiltonian tour of minimum cost. In this paper, we provide an approximation algorithm for this problem achieving a performance guarantee of \(\frac{315}{271}\). This algorithm can be further improved obtaining a performance guarantee of \(\frac{65}{56}\). This is better than the one achieved by Papadimitriou and Yannakakis [8], with a ratio \(\frac{7}{6}\), more than a decade ago. We enhance their algorithm by an involved procedure and find an improved lower bound for the cost of an optimal Hamiltonian tour.
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Bläser, M., Ram, L.S. (2005). An Improved Approximation Algorithm for TSP with Distances One and Two. In: Liśkiewicz, M., Reischuk, R. (eds) Fundamentals of Computation Theory. FCT 2005. Lecture Notes in Computer Science, vol 3623. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11537311_44
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DOI: https://doi.org/10.1007/11537311_44
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-28193-1
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