We present a new scaling algorithm for maximum (or minimum) weight perfectmatching on general, edge weighted graphs. Our algorithm runs in$O(m\sqrt{n}\log(nN))$ time, $O(m\sqrt{n})$ per scale, which matches therunning time of the best cardinality matching algorithms on sparse graphs. Here$m,n,$ and $N$ bound the number of edges, vertices, and magnitude of any edgeweight. Our result improves on a 25-year old algorithm of Gabow and Tarjan,which runs in $O(m\sqrt{n\log n\alpha(m,n)} \log(nN))$ time.
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