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A Fast Algorithm for Enumerating Bipartite Perfect Matchings

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Algorithms and Computation (ISAAC 2001)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2223))

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Abstract

In this paper, we propose an algorithm for enumerating all the perfect matchings included in a given bipartite graph G = (V,E). The algorithm is improved by the approach which we proposed at ISAAC98. Our algorithm takes O(log ∣V ∣) time per perfect matching while the current fastest algorithm takes O(∣V ∣) time per perfect matching.

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References

  1. K. Fukuda and T. Matsui, “Finding All the Perfect Matchings in Bipartite Graphs,” Appl. Math. Lett. 7, No. 1, 15–18 (1994).

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  2. J. E. Hopcroft and R. M. Karp, “An n 5/2 Algorithm for Maximum Matching in Bipartite Graphs,” SIAM J. Comp. 2, 225–231 (1973).

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  3. T. Uno, “Algorithms for Enumerating All Perfect, Maximum and Maximal Matchings in Bipartite Graphs,” Lecture Note in Computer Science 1350, Springer-Verlag, Algorithms and Computation, 92–101 (1997).

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  4. T. Uno, “A New Approach for Speeding Up Enumeration Algorithms,” Lecture Note in Computer Science 1533, Springer-Verlag, Algorithms and Computation, 287–296 (1998).

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  5. T. Uno, “A New Approach for Speeding Up Enumeration Algorithms and Its Application for Matroid Bases,” Lecture Note in Computer Science 1627, Springer-Verlag, Computing and Combinatorics (Proceeding of COCOON99), 349–359, (1999)

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Author information

Authors and Affiliations

  1. Foundations of Informatics Research Division, National Institute of Informatics, 2-1-2 Hitotsubashi, Chiyoda-ku, 101-8430, Tokyo, Japan

    Takeaki Uno

Authors
  1. Takeaki Uno
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Editor information

Editors and Affiliations

  1. Basser Department of Computer Science, University of Sydney, Madsen Building F09, 2006, Sydney, NSW, Australia

    Peter Eades

  2. Department of Computer Science, University of Canterbury, Private Bag 4800, Christchurch, New Zealand

    Tadao Takaoka

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© 2001 Springer-Verlag Berlin Heidelberg

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Cite this paper

Uno, T. (2001). A Fast Algorithm for Enumerating Bipartite Perfect Matchings. In: Eades, P., Takaoka, T. (eds) Algorithms and Computation. ISAAC 2001. Lecture Notes in Computer Science, vol 2223. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45678-3_32

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  • DOI: https://doi.org/10.1007/3-540-45678-3_32

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-42985-2

  • Online ISBN: 978-3-540-45678-0

  • eBook Packages: Springer Book Archive

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