### abstract

- 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-e)-approximation in O (log n ) time for any constant e>0, improving on the classical ½-approximation in O log n ) time of Israeli and Itai [1986]. The time complexity of the algorithm depends on 1he exponentially in the general case, and polynomially in bipartite graphs. For weighted graphs, we present another algorithm which provides (½-e) approximation in general graphs in O (loge -1 log n ) time, improving on the previously known algorithms which attain (¼-e)-approximation in O (log n ) time or ½-approximation in O ( n ) time. All our algorithms are randomized: the complexity bounds hold both with high probability and for the expected running time.