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

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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)


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
  • Matroid
  • Gammoid
  • Reduction
  • Algorithms


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  1. Ron Aharoni and Eli Berger. The intersection of a matroid and a simplicial complex. Transactions of the American Math Society, 2006. Google Scholar
  2. Ravindra K Ahuja, Thomas L Magnanti, and James B Orlin. Network Flows: Theory, Algorithms, and Applications. Prentice hall, 1993. Google Scholar
  3. Kristóf Bérczi, Tamás Schwarcz, and Yutaro Yamaguchi. List colouring of two matroids through reduction to partition matroids. arXiv preprint arXiv:1911.10485, 2019. Google Scholar
  4. Jack Edmonds. Minimum partition of a matroid into independent subsets. Journal of Research of the National Bureau of Standards, 69B:67–72, 1965. Google Scholar
  5. Sungjin Im, Benjamin Moseley, and Kirk Pruhs. The matroid intersection cover problem. Operations Research Letters, 49(1):17-22, 2020. Google Scholar
  6. Jon M. Kleinberg. Single-source unsplittable flow. In Symposium on Foundations of Computer Science, pages 68-77, 1996. Google Scholar
  7. Nabil Hassan Mustafa and Saurabh Ray. PTAS for geometric hitting set problems via local search. In Proceedings of the twenty-fifth annual symposium on Computational geometry, pages 17-22, 2009. Google Scholar
  8. James Oxley. Matroid Theory. Oxford graduate texts in mathematics. Oxford University Press, 2006. Google Scholar
  9. Paul D Seymour. A note on list arboricity. Journal of Combinatorial Theory, Series B, 72(1):150-151, 1998. Google Scholar
  10. Vijay Vazirani. Approximation Algorithms. Springer-Verlag, 2001. Google Scholar
  11. David P. Williamson and David B. Shmoys. The Design of Approximation Algorithms. Cambridge University Press, 2011. Google Scholar
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