Traveling salesman problem of segments

Authors:
Jinhui Xu;Yang Yang;Zhiyong Lin
Affiliations:
Department of Computer Science and Engineering, State University of New York at Buffalo, Buffalo, NY;Department of Computer Science and Engineering, State University of New York at Buffalo, Buffalo, NY;Department of Computer Science and Engineering, State University of New York at Buffalo, Buffalo, NY
Venue:
COCOON'03 Proceedings of the 9th annual international conference on Computing and combinatorics
Year:
2003

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Abstract

In this paper, we present a polynomial time approximation scheme (PTAS) for a variant of the traveling salesman problem (called segment TSP) in which a traveling salesman tour is sought to traverse a set of n Ɛ-separated segments in two dimensional space. Our results are based on a number of geometric observations and an interesting generalization of Arora's technique [5] for Euclidean TSP (of a set of points). The randomized version of our algorithm takes O(n2(log n)O(1/Ɛ4)) time to compute a (1 + Ɛ)-approximation with probability ≥ 1/2, and can be derandomized with an additional factor of O(n2). Our technique is likely applicable to TSP problems of certain Jordan arcs and related problems.