Abstract

We present a randomized algorithm for finding maximum matchings in planar graphs in time O(n ω/2), where ω is the exponent of the best known matrix multiplication algorithm. Since ω< 2.38, this algorithm breaks through the O(n 1.5) barrier for the matching problem. This is the first result of this kind for general planar graphs. Our algorithm is based on the Gaussian elimination approach to maximum matchings introduced in [1].

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