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 lor generating perfect matchings in planar graphs uniformly at random using O (n ~ arithmetic operations. Our algorithms are based on the Gaussian elimination approach to maximum matchings introduced in [ 16] .
This allowed Mucha and Sankowski REF to find maximum matchings via Gaussian elimination in planar graphs in O(n ω /2 ) time, where ω < 2.38 is the exponent of the best known matrix multiplication algorithm.
Maximum matchings in planar graphs via gaussian elimination
Algorithmica
Algorithmica
Mathematics Computer Science