Abstract
Consider the shortest tour throughn pointsX 1,...,X n independently uniformly distributed over [0,1]2. Then we show that for some universal constantK, the number of edges of length at leastun −1/2 is at mostKnxp(−u)2/K)with overwhelmingprobability.
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This research is in part supported by an NSF grant.
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Rhee, W.T., Talagrand, M. On the long edges in the shortest tour throughN random points. Combinatorica 12, 323–330 (1992). https://doi.org/10.1007/BF01285821
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DOI: https://doi.org/10.1007/BF01285821