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European Symposium on Algorithms

ESA 1995: Algorithms — ESA '95 pp 199–212Cite as

Fully Dynamic Transitive Closure in plane dags with one source and one sink

  • Session 3. Chair: Giuseppe Italiano
  • Conference paper
  • First Online:

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 979))

Abstract

We give an algorithm for the Dynamic Transitive Closure Problem for planar directed acyclic graphs with one source and one sink. The graph can be updated in logarithmic time under arbitrary edge insertions and deletions that preserve the embedding. Queries of the form ‘is there a directed path from u to v?’ for arbitrary vertices u and v can be answered in logarithmic time. The size of the data structure and the initialisation time are linear in the number of edges.

We also give a lower bound of Ω(log n/log log n) on the amortised complexity of the problem in the cell probe model with logarithmic word size.

A full version of this paper, including all proofs, can be found as RS-94-31 on the BRICS World Wide Web server at URL http://www.daimi.aau.dk/BRICS/. This work was partially supported by the ESPRIT II Basic Research Actions Program of the EC under contract no. 7141 (project ALCOM II). Part of this work was done while the author was at the Hebrew University of Jerusalem, Israel, supported by a grant from the Danish Research Academy.

Basic Research in Computer Science, Centre of the Danish National Research Foundation.

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Authors and Affiliations

  1. BRICS, Department of Computer Science, University of Aarhus, Ny Munkegade, DK-8000, Århus C, Denmark

    Thore Husfeldt

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  1. Thore Husfeldt
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Paul Spirakis

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© 1995 Springer-Verlag Berlin Heidelberg

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Husfeldt, T. (1995). Fully Dynamic Transitive Closure in plane dags with one source and one sink. In: Spirakis, P. (eds) Algorithms — ESA '95. ESA 1995. Lecture Notes in Computer Science, vol 979. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-60313-1_144

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  • DOI: https://doi.org/10.1007/3-540-60313-1_144

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-60313-9

  • Online ISBN: 978-3-540-44913-3

  • eBook Packages: Springer Book Archive

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