A matroid approach to finding edge connectivity and packing arborescences

We present an algorithm that finds the edge connectivity ? of a graph having n vectices and m edges. The running time is O(? m log(n2/m)) for directed graphs and slightly less for undirected graphs, O(m+?2n log(n/?)). This improves the previous best time bounds, O(min{mn, ?2n2}) for directed graphs and O(?n2) for undirected graphs. We present an algorithm that finds k edge-disjoint arborescences on a directed graph in time O((kn)2). This improves the previous best time bound, O(kmn + k3n2). Unlike previous work, our approach is based on two theorems of Edmonds that link these two problems and show how they can be solved.

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