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An algorithm for enumerating all directed spanning trees in a directed graph

  • Takeaki Uno
Session 5a: Invited Presentation
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1178)

Abstract

A directed spanning tree in a directed graph G=(V, A) is a spanning tree such that no two arcs share their tails. In this paper, we propose an algorithm for listing all directed spanning trees of G. Its time and space complexities are O(¦A¦+ND(¦V¦, ¦A¦)) and OA¦+DS(¦V¦, ¦A¦)), where DV¦, ¦A¦) and DS(¦V¦, ¦A¦) are the time and space complexities of the data structure for updating the minimum spanning tree in an undirected graph with ¦V¦ vertices and ¦A¦ edges. Here N denotes the number of directed spanning trees in G.

Keywords

directed spanning tree listing enumerating algorithm 

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References

  1. [1]
    H. N. Gabow, E. W. Myers, “Finding All Spanning Trees of Directed and Undirected Graphs”, SIAM J. Comp., 7, 280–287, 1978.CrossRefGoogle Scholar
  2. [2]
    H. N. Kapoor and H. Ramesh, “Algorithms for Generating All Spanning Trees of Undirected, Directed and Weighted Graphs”, Lecture Notes in Computer Science, Springer-Verlag, 461–472, 1992.Google Scholar
  3. [3]
    A. Shioura, A. Tamura and T. Uno, “An Optimal Algorithm for Scanning All Spanning Trees of Undirected Graphs”, SIAM J. Comp., to be appeared.Google Scholar
  4. [4]
    D. Eppstein, Z. Galil, G. F. Italiano and A. Nissenzweig, “Sparsification — A Technique for Speeding up Dynamic Graph Algorithms”, FOCS 33, 60–69, 1992.Google Scholar
  5. [5]
    G. N. Fredrickson, “Data Structure for On-line Updating of Minimum Spanning Trees, with Applications”, SIAM J. Comp., 14, No 4, 781–798, 1985.CrossRefGoogle Scholar
  6. [6]
    D. D. Sleator and R. E. Tarjan, “A Data Structure for Dynamic Trees”, J. Comp. Sys. Sci. 26, 362–391, 1983.CrossRefGoogle Scholar
  7. [7]
    R. E. Tarjan, “Depth-First Search and Linear Graph Algorithm”, SIAM J. Comp. 1, 146–169, 1972.CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1996

Authors and Affiliations

  • Takeaki Uno
    • 1
  1. 1.Department of Systems ScienceTokyo Institute of TechnologyTokyoJapan

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