Improved distributed approximate matching

We present distributed network algorithms to compute weighted and unweighted matchings with improved approximation ratios and running times. The computational model is a network of processors exchanging O(log n)-bit messages (the CONGEST model). For unweighted graphs, we give an algorithm providing (1-ε)- approximation in O(log n) time for any constant > 0, improving on the classical 12-approximation in Olog n) time of Israeli and Itai [1986]. The time complexity of the algorithm depends on ¹ exponentially in the general case, and polynomially in bipartite graphs. For weighted graphs, we present another algorithm which provides (1 2-ε) approximation in general graphs in O(log ε ^-1 log n) time, improving on the previously known algorithms which attain (14-ε)-approximation in O(log n) time or 12-approximation in O(n) time. All our algorithms are randomized: the complexity bounds hold both with high probability and for the expected running time.