Probability Theory of Classical Euclidean Optimization Problems This monograph describes the stochastic behavior of the solutions to the classic problems of Euclidean combinatorial optimization computational geometry and operations research. Using two sided additivity and isoperimetry it formulates general methods describing the total edge length of random graphs in Euclidean space. The approach furnishes strong laws of large numbers large deviations and rates of convergence for solutions to the random versions of various classic optimization problems including the traveling salesman minimal spanning tree minimal matching minimal triangulation two factor and k median problems. Essentially self contained this monograph may be read by probabilists combinatorialists graph theorists and theoretical computer scientists