This monograph describes the stochastic habit of the suggestions to the vintage difficulties of Euclidean combinatorial optimization, computational geometry, and operations examine. utilizing two-sided additivity and isoperimetry, it formulates common equipment describing the full area size of random graphs in Euclidean house. The method furnishes powerful legislation of enormous numbers, huge deviations, and charges of convergence for suggestions to the random models of varied vintage optimization difficulties, together with the touring salesman, minimum spanning tree, minimum matching, minimum triangulation, two-factor, and k-median difficulties. primarily self-contained, this monograph will be learn by means of probabilists, combinatorialists, graph theorists, and theoretical desktop scientists.
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