Technical Reports on Mathematical and Computing Sciences : TR - C 209 title : Hausdorff Dimension and the Stochastic Traveling Salesman Problem
نویسنده
چکیده
The traveling salesman problem is a problem of finding the shortest tour through given points. In 1959, Beardwood, Halton, and Hammersley studied asymptotic length of the shortest tour through points on Euclidean space. In particular they described the optimal tour length with Euclidean dimension for the case that points are distributed with respect to Lebesgue absolutely continuous measure. In this paper we reinterpret and generalize their results in terms of fractal geometry. We give the asymptotic order of the optimal tour length in terms of Hausdorff dimension. key words: TSP, BHH theorem, Hausdorff dimension, fractal geometry.
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