Probabilistic analysis of algorithms for cost constrained minimum weighted combinatorial objects

We consider cost constrained versions of the minimum spanning tree problem and the assignment problem. We assume edge weights are independent copies of a continuous random variable Z that satisfies F(x) = P(Z <= x) approximate to x(alpha) as x -> 0, where alpha >= 1. Also, there are r = O(1) budget constraints with edge costs chosen from the same distribution. We use Lagrangean duality to construct polynomial time algorithms that produce asymptotically optimal solutions. For the spanning tree problem, we allow r > 1, but for the assignment problem we can only analyse the case r = 1. (C) 2021 Elsevier B.V. All rights reserved.