Skip to main content
SpringerLink
Log in
Book cover

International Symposium on Fundamentals of Computation Theory

FCT 1995: Fundamentals of Computation Theory pp 191–200Cite as

Fast algorithms for maintaining shortest paths in outerplanar and planar digraphs

  • Communications
  • Conference paper
  • First Online:

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 965))

Abstract

We present algorithms for maintaining shortest path information in dynamic outerplanar digraphs with sublogarithmic query time. By choosing appropriate parameters we achieve continuous trade-offs between the preprocessing, query, and update times. Our data structure is based on a recursive separator decomposition of the graph and it encodes the shortest paths between the members of a properly chosen subset of vertices. We apply this result to construct improved shortest path algorithms for dynamic planar digraphs.

This work was partially supported by the EU ESPRIT BRA No. 7141 (ALCOM II), by the EU Cooperative Action IC-1000 (ALTEC) and by the NSF grant No. CCR-9409191.

This is a preview of subscription content, log in via an institution.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. H. Bondlaender, “Dynamic Algorithms for Graphs with Treewidth 2”, Proc. 19th WG'93, LNCS 790, pp.112–124, Springer-Verlag, 1994.

    Google Scholar 

  2. S. Chaudhuri and C. Zaroliagis, “Shortest Path Queries in Digraphs of Small Treewidth”, Proc. 22nd ICALP, LNCS, Springer-Verlag, 1995, to appear.

    Google Scholar 

  3. H. Djidjev, G. Pantziou and C. Zaroliagis, “On-line and Dynamic Algorithms for Shortest Path Problems”, Proc. 12th STACS, LNCS 900, pp.193–204, Springer-Verlag, 1995.

    Google Scholar 

  4. E. Feuerstein and A.M. Spaccamela, “Dynamic Algorithms for Shortest Paths in Planar Graphs”, Theor. Computer Science, 116 (1993), pp.359–371.

    Google Scholar 

  5. G.N. Frederickson, “Using Cellular Graph Embeddings in Solving All Pairs Shortest Path Problems”, Proc. 30th Annual IEEE Symp. on FOCS, 1989.

    Google Scholar 

  6. G.N. Frederickson, “Planar Graph Decomposition and All Pairs Shortest Paths”, J. ACM, Vol.38, No.1, January 1991, pp.162–204.

    Article  Google Scholar 

  7. R. Hassin, “Maximum flow in (s,t)-planar networks”, Inform. Proc. Lett., 13(1981), p.107.

    Google Scholar 

  8. G. Miller and J. Naor, “Flows in planar graphs with multiple sources and sinks”, Proc. 30th IEEE Symp. on FOCS, 1989, pp.112–117.

    Google Scholar 

  9. B. Schieber and U. Vishkin, “On Finding Lowest Common Ancestors: Simplification and Parallelization”, SIAM J. Computing, 17(6), pp.1253–1262, 1988.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Computer Science Dept, Rice University, P.O. Box 1892, 77251, Houston, TX, USA

    Hristo N. Djidjev

  2. Computer Science Dept, University of Central Florida, 82816, Orlando, FL, USA

    Grammati E. Pantziou

  3. Max-Planck Institut für Informatik, Im Stadtwald, 66123, Saarbrücken, Germany

    Christos D. Zaroliagis

Authors
  1. Hristo N. Djidjev
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Grammati E. Pantziou
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Christos D. Zaroliagis
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Horst Reichel

Rights and permissions

Reprints and permissions

Copyright information

© 1995 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Djidjev, H.N., Pantziou, G.E., Zaroliagis, C.D. (1995). Fast algorithms for maintaining shortest paths in outerplanar and planar digraphs. In: Reichel, H. (eds) Fundamentals of Computation Theory. FCT 1995. Lecture Notes in Computer Science, vol 965. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-60249-6_51

Download citation

  • DOI: https://doi.org/10.1007/3-540-60249-6_51

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-60249-1

  • Online ISBN: 978-3-540-44770-2

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation