On Approximation Methods for the Assignment Problem
Journal of the ACM (JACM)
Fast probabilistic algorithms for hamiltonian circuits and matchings
STOC '77 Proceedings of the ninth annual ACM symposium on Theory of computing
The analysis of double hashing(Extended Abstract)
STOC '76 Proceedings of the eighth annual ACM symposium on Theory of computing
STOC '80 Proceedings of the twelfth annual ACM symposium on Theory of computing
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we consider optimization problems on complete graphs with edge weights chosen from identical but independent normal distributions. We show some very general techniques for obtaining upper and lower bounds on the asymptotic behavior of these problems. Often, but not always, these bounds are equal, enabling us to state the asymptotic behavior of the maximum. Problems in which the bounds are tight include finding the optimum traveling salesman tour, finding a minimum cost spanning tree, and finding a heaviest clique on k vertices. We then discuss some greedy heuristic algorithms for these problems.