An Efficient Reduction of a Gammoid to a Partition Matroid
arXiv:2107.03795
Abstract
Our main contribution is a polynomial-time algorithm to reduce a -colorable gammoid to a -colorable partition matroid. It is known that there are gammoids that can not be reduced to any -colorable partition matroid, so this result is tight. We then discuss how such a reduction can be used to obtain polynomial-time algorithms with better approximation ratios for various natural problems related to coloring and list coloring the intersection of matroids.
Full version of a paper accepted at ESA 2021