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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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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.

Cite AsGet 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

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.

Subject Classification

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

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References

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