Derandomizing the Isolation Lemma and Lower Bounds for Circuit Size
APPROX '08 / RANDOM '08 Proceedings of the 11th international workshop, APPROX 2008, and 12th international workshop, RANDOM 2008 on Approximation, Randomization and Combinatorial Optimization: Algorithms and Techniques
Matroid matching: the power of local search
Proceedings of the forty-second ACM symposium on Theory of computing
Algebraic algorithms for linear matroid parity problems
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
A simple PTAS for weighted matroid matching on strongly base orderable matroids
Discrete Applied Mathematics
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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 arboresence and a maximum cardinality set of edge-disjoint spanning trees in a graph are obtained. The key tools used are linear algebra and randomization.