Online stochastic matching, poisson arrivals, and the natural linear program
Zhiyi Huang, Xinkai Shu
Abstract
We study the online stochastic matching problem. Consider a bipartite graph with offline vertices on one side, and with i.i.d.online vertices on the other side. The offline vertices and the distribution of online vertices are known to the algorithm beforehand. The realization of the online vertices, however, is revealed one at a time, upon which the algorithm immediately decides how to match it. For maximizing the cardinality of the matching, we give a 0.711-competitive online algorithm, which improves the best previous ratio of 0.706. When the offline vertices are weighted, we introduce a 0.7009-competitive online algorithm for maximizing the total weight of the matched offline vertices, which improves the best previous ratio of 0.662.