Random Pseudo-Polynomial Algorithms for Exact Matroid Problems

Abstract In this work we present a random pseudo-polynomial algorithm for the problem of finding a base of specified value in a weighted represented matroid, subject to parity conditions. We also describe a specialized version of the algorithm suitable for finding a base of specified value in the intersection of two matroids. This result generalizes an existing pseudo-polynomial algorithm for computing exact arborescences in weighted graphs. Another (simpler) specialized version of our algorithms is also presented for computing perfect matchings of specified value in weighted graphs.

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