A factor ½ approximation algorithm for two-stage stochastic matching problems

We introduce the two-stage stochastic maximum-weight matching problem and demonstrate that this problem is NP-complete. We give a factor ½ approximation algorithm and prove its correctness. We also provide a tight example to show the bound given by the algorithm is exactly ½. Computational results on some two-stage stochastic bipartite matching instances indicate that the performance of the approximation algorithm appears to be substantially better than its worst-case performance.