Improved distributed approximate matching

Authors:
Zvi Lotker;Boaz Patt-Shamir;Seth Pettie
Affiliations:
Ben Gurion University, Beer Sheva, Israel;Tel Aviv University, Tel Aviv, Israel;University of Michigan, Ann Arbor, MI, USA
Venue:
Proceedings of the twentieth annual symposium on Parallelism in algorithms and architectures
Year:
2008

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Abstract

We present improved algorithms for finding approximately optimal matchings in both weighted and unweighted graphs. For unweighted graphs, we give an algorithm providing (1-ε-approximation in O(log n) time for any constant ε 0. This result improves on the classical 1 over 2-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 (1 over 2-ε) approximation in general graphs in O(log n)time. The latter result improves on the known (1 over 4-ε-approximation in O(log n)time.