Randomized parallel algorithms for matroid union and intersection, with applications to arboresences and edge-disjoint spanning trees

The strong link between matroids and matching is used to extend the ideas that resulted in the design of random NC (RNC) algorithms for matching to obtain RNC algorithms for the matroid union, intersection, and matching problems, and for linearly representable matroids. As a consequence, RNC algorithms for the well-known problems of finding an arborescence and a maximum cardinality set of edge-disjoint spanning trees in a graph are obtained. The key tools used are linear algebra and randomization.