Dynamic maintenance of shortest path trees in simple polygons

  • Sanjiv Kapoor
  • Tripurari Singh
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1180)

Abstract

We present a scheme to dynamically maintain a tooted shortest path tree in a simple polygon. Both insertion and deletion of vertices of the simple polygon are supported. Both operations require O(k log(n/k)) time where k is the number of changes in the shortest path tree. Only simple balanced binary trees are used in the data structure. O(n) space is required.

References

  1. [1]
    [CT] “Dynamic algorithms in computational geometry” by Y.J. Chiang and R. Tamassia, Proc. IEEE, 80(9):1412–1434Google Scholar
  2. [2]
    [GH] “Optimal Shortest Path Queries in a Simple Polygon”, L.J. Guibas and J.Hershberger. Proceedings of the 3rd ACM Symposium on computational Geometry, Waterloo, Canada (1987), pp 50–63.Google Scholar
  3. [3]
    [GHLST) “Linear time algorithms for visibility and shortest path problems inside simple polygons” by L.Guibas, J.Hershberger, D.Leven, M.Sharir and R.Tarjan, Proc. of the 3rd ACM Symposium on Computational Geometry, June 1987.Google Scholar
  4. [4]
    [GT] “Dynamic trees and dynamic point location”, by M. Goodrich and R. Tamassia,Proceedings of the 23rd Annu. ACM Sympos. Theory Comput., pp 523–533, 1991.Google Scholar
  5. [5]
    [LP] “Euclidean Shortest Paths in the Presence of Rectilinear Barriers”, D.T. Lee and F.P. Preparata., Networks, vol.14 (1984), pp.393–410.Google Scholar
  6. [6]
    [ST) “A Data Structure for Dynamic Trees”, D.D.Sleator and R.E. Tarjan, Jour. of Computer and System Sciences, 26, 362–391 (1983).Google Scholar
  7. [7]
    [V] “Dynamically maintaining the visibility graph”, G. Vegter, WADS, 1991, pp 425–436.Google Scholar

Copyright information

© Springer-Verlag 1996

Authors and Affiliations

  • Sanjiv Kapoor
    • 1
  • Tripurari Singh
    • 1
  1. 1.Dept. of Computer Science and EngineeringIndian Institute of TechnologyNew Delhi

Personalised recommendations