Fast algorithms for transversal matroid intersection problems

Abstract

Algorithms for the maximum weight transversal matroid intersection problems are presented. Efficient implementations are given for various special cases. For the convex transversal matroid intersection, our strongly-polynomial algorithm and scaling algorithm run in time O(nm log n) and O(√n(m + n log* n) log(nN)), respectively, where n and m are the rank and the cardinality of the matroid, respectively, and N is the largest magnitude of a weight assuming all the weights are integral.