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An Efficient Reduction of a Gammoid to a Partition Matroid

Authors Marilena Leichter, Benjamin Moseley, Kirk Pruhs

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Subject Classification

ACM Subject Classification
  • Theory of computation → Network optimization
Keywords
  • Matroid
  • Gammoid
  • Reduction
  • Algorithms

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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.

Cite As Get BibTex

Marilena Leichter, Benjamin Moseley, and Kirk Pruhs. An Efficient Reduction of a Gammoid to a Partition Matroid. In 29th Annual European Symposium on Algorithms (ESA 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 204, pp. 62:1-62:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021) https://doi.org/10.4230/LIPIcs.ESA.2021.62

Author Details

Marilena Leichter
  • Department of Mathematics, Technische Universität München, Germany
Benjamin Moseley
  • Tepper School of Business, Carnegie Mellon University, Pittsburgh, PA, USA
Kirk Pruhs
  • Computer Science Department, University of Pittsburgh, PA, USA

Funding

  • Leichter, Marilena: Supported in part by the Alexander von Humboldt Foundation with funds from the German Federal Ministry of Education and Research (BMBF) and by the Deutsche Forschungsgemeinschaft (DFG), GRK 2201.
  • Moseley, Benjamin: Supported in part by a Google Research Award, an Infor Research Award, a Carnegie Bosch Junior Faculty Chair and NSF grants CCF-1824303, CCF-1845146, CCF-1733873 and CMMI-1938909.
  • Pruhs, Kirk: Supported in part by NSF grants CCF-1535755, CCF-1907673, CCF-2036077 and an IBM Faculty Award.

References

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