Improved approximation guarantees for weighted matching in the semi-streaming model

We study the maximum weight matching problem in the semi-streaming model, and improve on the currently best one-pass algorithm due to Zelke [Proceedings of the 25th Annual Symposium on Theoretical Aspects of Computer Science, 2008, pp. 669-680] by devising a deterministic approach whose performance guarantee is 4.91 + ε. In addition, we study preemptive online algorithms, a class of algorithms related to one-pass semi-streaming algorithms, where we are allowed to maintain only a feasible matching in memory at any point in time. We provide a lower bound of 4.967 on the competitive ratio of any such deterministic algorithm, and hence show that future improvements will have to store in memory a set of edges that is not necessarily a feasible matching. We conclude by presenting an empirical study, conducted in order to compare the practical performance of our approach to that of previously suggested algorithms.