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Workshop on Algorithms and Data Structures

WADS 1995: Algorithms and Data Structures pp 428–439Cite as

Faster enumeration of all spanning trees of a directed graph

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 955))

Abstract

We present an algorithm for enumerating all spanning trees of a directed graph with V vertices, E edges and N spanning trees. The algorithm takes O(log V) time per spanning tree; more precisely, it runs in O(Nlog V+V 2 α(V, V)+VE) time. It first outputs a single spanning tree and then a list of edge swaps; each spanning tree can be generated from the first spanning tree by applying a prefix of this sequence of edge swaps. The total output size is O(N) as against the O(NV) size of all spanning trees put together. The previous best known algorithm for this problem [KR91] took O(NV+V 3) time, even for generating the edge swap sequence.

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Author information

Authors and Affiliations

  1. Max-Planck Institut für Informatik, Saarbrücken, Germany

    Ramesh Hariharan

  2. Indian Institute of Technology, New Delhi, India

    Sanjiv Kapoor

  3. Northwestern University, Evanston, Illinois

    Vijay Kumar

Authors
  1. Ramesh Hariharan
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  2. Sanjiv Kapoor
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  3. Vijay Kumar
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Editor information

Selim G. Akl Frank Dehne Jörg-Rüdiger Sack Nicola Santoro

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© 1995 Springer-Verlag Berlin Heidelberg

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Hariharan, R., Kapoor, S., Kumar, V. (1995). Faster enumeration of all spanning trees of a directed graph. In: Akl, S.G., Dehne, F., Sack, JR., Santoro, N. (eds) Algorithms and Data Structures. WADS 1995. Lecture Notes in Computer Science, vol 955. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-60220-8_82

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  • DOI: https://doi.org/10.1007/3-540-60220-8_82

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-60220-0

  • Online ISBN: 978-3-540-44747-4

  • eBook Packages: Springer Book Archive

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