We consider the undirected minimum spanning tree problem in a stochastic optimization setting. For the two-stage stochastic optimization formulation with finite scenarios, a simple iterative randomized rounding method on a natural LP formulation of the problem yields a nearly best-possible approximation algorithm.<\/p>\n
We then consider the Stochastic minimum spanning tree problem in a more general black-box model and show that even under the assumptions of bounded inflation the problem remains log n<\/em>-hard to approximate unless P<\/em> = NP<\/em>; where n<\/em> is the size of graph. We also give approximation algorithm matching the lower bound up to a constant factor.<\/p>\n Finally, we consider a slightly different cost model where the second stage costs are independent random variables uniformly distributed between [0,1].<\/p>\n [See attachment or URL for further mathematical equations that cannot be displayed here.]<\/p>\n","protected":false},"excerpt":{"rendered":" We consider the undirected minimum spanning tree problem in a stochastic optimization setting. For the two-stage stochastic optimization formulation with finite scenarios, a simple iterative randomized rounding method on a natural LP formulation of the problem yields a nearly best-possible approximation algorithm. 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