Traveling salesman problem of segments
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 epsilon-separated segments in two dimensional space. Our results are based on an interesting combinatorial result which bounds the total number of entry points in an optimal TSP tour and a generalization of Arora's technique(5) for Euclidean TSP (of a set of points). The randomized version of our algorithm takes O(n(2)(log n)(O(1/e2))) time to compute a (1 + epsilon)-approximation with probability greater than or equal to 1/2, and can be derandomized with an additional factor of O(n(2)).
traveling salesman problem polynomial time approximation scheme algorithm