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arXiv · 2107.03795

An Efficient Reduction of a Gammoid to a Partition Matroid

Marilena Leichter·Benjamin Moseley·Kirk Pruhs
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Abstract

Our main contribution is a polynomial-time algorithm to reduce a $k$-colorable gammoid to a $(2k-2)$-colorable partition matroid. It is known that there are gammoids that can not be reduced to any $(2k-3)$-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.

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Marilena Leichter, Benjamin Moseley, Kirk Pruhs. 2021-07-08. An Efficient Reduction of a Gammoid to a Partition Matroid. https://arxiv.org/abs/2107.03795

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