Maximum Scatter TSP in Doubling Metrics
نویسندگان
چکیده
We study the problem of finding a tour of n points in which every edge is long. More precisely, we wish to find a tour that visits every point exactly once, maximizing the length of the shortest edge in the tour. The problem is known as Maximum Scatter TSP, and was introduced by Arkin et al. (SODA 1997), motivated by applications in manufacturing and medical imaging. Arkin et al. gave a 0.5 -approximation for the metric version of the problem and showed that this is the best possible ratio achievable in polynomial time (assuming P 6= NP). Arkin et al. raised the question of whether a better approximation ratio can be obtained in the Euclidean plane.
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