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Efficient algorithms for graphic matroid intersection and parity

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Automata, Languages and Programming (ICALP 1985)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 194))

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Abstract

An algorithm for matroid intersection, based on the phase approach of Dinic for network flow and Hopcroft and Karp for matching, is presented. An implementation for graphic matroids uses time O(n 1/2 m) if m is Ω(n 3/2 lg n), and similar expressions otherwise. An implementation to find k edge-disjoint spanning trees on a graph uses time O(k 3/2 n 1/2 m) if m is Ω(n lg n) and a similar expression otherwise; when m is O(k 1/2 n 3/2) this improves the previous bound, O(k 2 n 2). Improved algorithms for other problems are obtained, including maintaining a minimum spanning tree on a planar graph subject to changing edge costs, and finding shortest pairs of disjoint paths in a network. An algorithm for graphic matroid parity is presented that runs in time O(n m lg 5 n). This improves the previous bound of O(n 2 m).

This work was supported in part by NSF Grant #MCS-8302648.

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Author information

Authors and Affiliations

  1. Department of Computer Science, University of Colorado, 80309, Boulder, CO, USA

    Harold N. Gabow

  2. Department of Computer Science, North Carolina State University, 27695-8206, Raleigh, NC, USA

    Matthias Stallmann

Authors
  1. Harold N. Gabow
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  2. Matthias Stallmann
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Wilfried Brauer

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© 1985 Springer-Verlag Berlin Heidelberg

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Gabow, H.N., Stallmann, M. (1985). Efficient algorithms for graphic matroid intersection and parity. In: Brauer, W. (eds) Automata, Languages and Programming. ICALP 1985. Lecture Notes in Computer Science, vol 194. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0015746

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  • DOI: https://doi.org/10.1007/BFb0015746

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-15650-5

  • Online ISBN: 978-3-540-39557-7

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