We present improved algorithms for finding approximately optimal matchings in both weighted and unweighted graphs. For unweighted graphs, we give an algorithm providing (1 − )-approximation in O(log n) time for any constant > 0. This result improves on the classical -approximation due to Israeli and Itai. As a by-product, we also provide an improved algorithm for unweighted matchings in bipartite graphs. In the context of weighted graphs, we give another algorithm which provides ( − )-approximation in O(log n) time.
This was later improved in REF to achieve a (2+ϵ)-approximation in O(log ϵ −1 log n) rounds.
Improved distributed approximate matching
SPAA '08
Mathematics Computer Science