Maximum Matchings in Planar Graphs via Gaussian Elimination 1

We present a randomized algorithm for finding maximum matchings in planar graphs in time O(n'~ where co is the exponent of the best known matrix multiplication algorithm. Since co < 2.38, this algorithm breaks through the O (n J.5) barrier for the matching problem. This is the first result of this kind for general planar graphs. We also present an algorithm… CONTINUE READING