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New Approach for Speeding Up Enumeration Algorithms

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Algorithms and Computation (ISAAC 1998)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1533))

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Abstract

We propose a new approach for speeding up enumeration algorithms. The approach does not relies on data structures deeply, but utilizes some analysis of its computation time. The enumeration algorithms for directed spanning trees, matroid bases, and some bipartite matching problems are speeded up by this approach. For a given graph G = (V,E), the time complexity of the algorithm for directed spanning tree is O(log2 ¦V¦) per a directed spanning tree. For a given matroid ℳ, the algorithm for matroid bases runs in O(T/n) time per a base. Here n denotes the rank of ℳ, and T denotes the computation time to obtain elementary circuits. Enumeration algorithms for matching problems spend O(¦V¦) time per a matching.

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References

  1. H.N. Gabow and E.W. Myers, “Finding All Spanning Trees of Directed and Undi-rected graphs,” SIAM J. Comp. 7, pp. 280–287 (1978).

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  3. A. Shioura, A. Tamura and T. Uno, “An Optimal Algorithm for Scanning All Spanning Trees of Undirected graphs,” SIAM J. Comp. 26, pp. 678–692 (1997).

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  4. T. Uno, “An Algorithm for Enumerating All Directed Spanning Trees in a Directed graph,” LNCS 1178, Springer-Verlag, pp. 166–173 (1996).

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  5. T. Uno, “Algorithms for Enumerating All Perfect, Maximum and Maximal Matchings in Bipartite Graphs,” LNCS 1350, Springer-Verlag, pp. 92–101 (1997).

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Author information

Authors and Affiliations

  1. Dept. Industrial Engineering and Management, Tokyo Institute of Technology, 2-12-1 Oh-okayama, Meguro-ku, Tokyo, 152, Japan

    Takeaki Uno

Authors
  1. Takeaki Uno
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Editor information

Editors and Affiliations

  1. Department of Computer Science, Korea Advanced Institute of Science and Technology, 373-1, Kusong-dong, Yusong-gu, Taejon, 305-701, Korea

    Kyung-Yong Chwa

  2. Department of Computer Science, University of California, Santa Barbara, CA, 93106, USA

    Oscar H. Ibarra

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© 1998 Springer-Verlag Berlin Heidelberg

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Uno, T. (1998). New Approach for Speeding Up Enumeration Algorithms. In: Chwa, KY., Ibarra, O.H. (eds) Algorithms and Computation. ISAAC 1998. Lecture Notes in Computer Science, vol 1533. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-49381-6_31

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  • DOI: https://doi.org/10.1007/3-540-49381-6_31

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-65385-1

  • Online ISBN: 978-3-540-49381-5

  • eBook Packages: Springer Book Archive

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