Beating (1-1/e)-Approximation for Weighted Stochastic Matching
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In the stochastic weighted matching problem, the goal is to find a large-weight matching of a graph when we are uncertain about the existence of its edges. In particular, each edge e has a known weight w_e but is realized independently with some probability p_e. The algorithm may query an edge to see whether it is realized. We consider the well-studied query commit version of the problem, in which any queried edge that happens to be realized must be included in the solution. Gamlath, Kale, and Svensson showed that when the input graph is bipartite, the problem admits a (1-1/e)-approximation. In this paper, we give an algorithm that for an absolute constant δ > 0.0014 obtains a (1-1/e+δ)-approximation, therefore breaking this prevalent bound.
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