A Subquadratic-Time Distributed Algorithm for Exact Maximum Matching

For a graph G=(V,E), finding set of disjoint edges that do not share any vertices is called matching problem, and the maximum fundamental problem in theory distributed algorithms. Although local algorithms for approximate have been widely studied, exact has much studied. In fact, no algorithm faster than trivial upper bound O(n^2) rounds known general instance. this paper, we propose randomized O(s_{max}^{3/2}+log n)-round CONGEST model, where s_{\max} size matching. This first o(n^2) instances model. The key technical ingredient our result an augmenting path O(s_{\max}) rounds, which based on novel technique constructing sparse certificate paths, subgraph input preserving at least one path. To establish highly parallel construction certificates, also new characterization might be independent interest.