An Efficient Reduction of a Gammoid to a Partition Matroid

Marilena Leichter; Benjamin Moseley; Kirk Pruhs

An Efficient Reduction of a Gammoid to a Partition Matroid

Data Structures and Algorithms 2021-07-09 v1 Combinatorics

Authors: Marilena Leichter , Benjamin Moseley , Kirk Pruhs

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.

Keywords

gammoid partition matroid polynomial-time reduction matroid coloring list coloring approximation algorithm

Cite

@article{arxiv.2107.03795,
  title  = {An Efficient Reduction of a Gammoid to a Partition Matroid},
  author = {Marilena Leichter and Benjamin Moseley and Kirk Pruhs},
  journal= {arXiv preprint arXiv:2107.03795},
  year   = {2021}
}

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Full version of a paper accepted at ESA 2021

An Efficient Reduction of a Gammoid to a Partition Matroid

Abstract

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