Online Routing in Convex Subdivisions

  • Prosenjit Bose
  • Andrej Brodnik
  • Svante Carlsson
  • Erik D. Demaine
  • Rudolf Fleischer
  • Alejandro López-Ortiz
  • Pat Morin
  • J.Ian Munro
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1969)

Abstract

We consider online routing algorithms for finding paths between the vertices of plane graphs. We show (1) there exists a routing algorithm for arbitrary triangulations that has no memory and uses no randomization, (2) no equivalent result is possible for convex subdivisions, (3) there is no competitive online routing algorithm under the Euclidean distance metric in arbitrary triangulations, and (4) there is no competitive online routing algorithm under the link distance metric even when the input graph is restricted to be a Delaunay, greedy, or minimum-weight triangulation.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    O. Aichholzer, F. Aurenhammer, S.-W. Cheng, N. Katoh, G. Rote, M. Taschwer, and Y.-F. Xu. Triangulations intersect nicely. Discrete and Computational Geometry, 16(4):339–359, 1996.MATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    A. Borodin and R. El-Yaniv. Online Computation and Competitive Analysis. Cambridge University Press, 1998.Google Scholar
  3. 3.
    P. Bose and P. Morin. Online routing in triangulations. In Proceedings of the Tenth International Symposium on Algorithms and Computation (ISAAC’99), volume 1741 of Springer LNCS, pages 113–122, 1999.Google Scholar
  4. 4.
    P. Bose and P. Morin. Competitive routing algorithms for greedy and minimum-weight triangulations. Manuscript, 2000.Google Scholar
  5. 5.
    P. Cucka, N. S. Netanyahu, and A. Rosenfeld. Learning in navigation: Goal finding in graphs. International Journal of Pattern Recognition and Artificial Intelligence, 10(5):429–446, 1996.CrossRefGoogle Scholar
  6. 6.
    R. L. Graham. An efficient algorithm for determining the convex hull of a finite planar set. Information Processing Letters, 1:132–133, 1972.MATHCrossRefGoogle Scholar
  7. 7.
    B. Kalyanasundaram and K. R. Pruhs. Constructing competitive tours from local information. Theoretical Computer Science, 130:125–138, 1994.MATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    E. Kranakis, H. Singh, and J. Urrutia. Compass routing on geometric networks. In Proceedings of the 11th Canadian Conference on Computational Geometry (CCCG’99), 1999.Google Scholar
  9. 9.
    C. H. Papadimitriou and M. Yannakakis. Shortest paths without a map. Theoretical Computer Science, 84:127–150, 1991.MATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    F. P. Preparata and M. I. Shamos. Computational Geometry. Springer-Verlag, New York, 1985.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Prosenjit Bose
    • 1
  • Andrej Brodnik
    • 2
  • Svante Carlsson
    • 3
  • Erik D. Demaine
    • 4
  • Rudolf Fleischer
    • 4
  • Alejandro López-Ortiz
    • 5
  • Pat Morin
    • 1
  • J.Ian Munro
    • 4
  1. 1.School of Computer ScienceCarleton UniversityOttawaCanada
  2. 2.IMFMUniversity of LjubljanaLjubljanaSlovenia
  3. 3.University of Karlskona/RonnebyKARLSKRONASweden
  4. 4.Department of Computer ScienceUniversity of WaterlooWaterlooCanada
  5. 5.Faculty of Computer ScienceUniversity of New BrunswickFrederictonCanada

Personalised recommendations