Probabilistic and Worst Case Analyses of Classical Problems of Combinatorial Optimization in Euclidean Space

Abstract

The classical problems reviewed are the traveling salesman problem, minimal spanning tree, minimal matching, greedy matching, minimal triangulation, and others. Each optimization problem is considered for finite sets of points in ℝd, and the feature of principal interest is the value of the associated objective function. Special attention is given to the asymptotic behavior of this value under probabilistic assumptions, but both probabilistic and worst case analyses are surveyed.