Probabilistic analysis of algorithms for cost constrained minimum weighted combinatorial objects

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