Random polymatroid flow problems
نویسندگان
چکیده
We generalize the so-called random assignment problem to a setting where we impose a polymatroid structure on the two vertex-sets of a complete bipartite graph, and ask for an edge set of prescribed size connecting independent sets. As an application, we show that under independent exponential edge-costs, the cost of the cheapest edge set covering all vertices of an n by n bipartite graph is asymptotically W (1)2 + 2W (1) ≈ 1.456, where W is the Lambert W -function. In particular it is essentially cheaper than the cheapest perfect matching, whose cost is asymptotically π2/6 ≈ 1.645.
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