Abstract
We present an O((n+k) log(n+k)) time algorithm for computing the geodesic Voronoi diagram of k points in a simple polygon of n vertices improving upon the previously known results. The method introduces a new approach to the construction of geodesic Voronoi diagrams by combining a sweep of the polygon and the merging step of a usual divide-and-conquer strategy.
Supported in part by the National Science Foundation under the Grant CCR-9309743, and by the Office of Naval Research under the Grant No. N00014-93-1-0272.
This is a preview of subscription content, log in via an institution to check access.
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
B. Aronov. “On the geodesic Voronoi diagram of point sites in a simple polygon”, Algorithmica, 4 (1989), 109–140.
F. Aurenhammer, “Voronoi diagrams: A survey of a fundamental geometric data structure,” ACM Comput. Survey, 23 1991, 345–405.
Ta. Asano and Te. Asano, “Voronoi diagrams for points in a polygon,” in Discrete Algorithms & Complexity: Perspective in Computing, ed. D. S.Johnson, Academic Press, 1987, 51–64.
L. P. Chew, Constrained Delaunay triangulations, Algorithmica, 4 (1989), 97–108.
S. Fortune, A sweepline algorithm for Voronoi diagrams, Algorithmica, 2 (1987), 153–174.
L. J. Guibas, J. Hershberger, D. Leven, M. Sharir, and R.E. Tarjan, “Linear-time algorithms for visibility and shortest path problems inside triangulated simple polygons”, Algorithmica, 2 (1987), 209–233.
L. J. Guibas and R. Sedgewick, “A dichromatic framework for balanced trees”, Proc. 19th IEEE Symp. on Foundations of Computer Science, 1978, 8–21.
J. Hershberger and S. Suri, “Efficient Computation of Euclidean Shortest Paths in the Plane”, 34th Symp. on Foundations of Computer Science, 1993, 508–517.
D. Kirkpatrick, “Optimal Search in Planar Subdivisions” SIAM J. Computing, Vol. 12, No 1, 1983, 28–35.
D. T. Lee and A. K. Lin, “Generalized Delaunay triangulations for planar graphs”, Discrete Computational Geometry, 1 (1986),201–217.
D. T. Lee and F. P. Preparata, “Euclidean Shortest Paths in the Presence of Rectilinear Barriers”, Networks, 14 1984, 393–410.
J. S. B. Mitchell, “Shortest paths among obstacles in the plane”, Proc. 9th ACM Symp. on Comput. Geometry, May 1993, 308–317.
Preparata, F. P. and M. I. Shamos, Computational Geometry: an Introduction, Springer-Verlag, New York, NY 1985.
C. Wang and L. Schubert, “An optimal algorithm for constructing the Delaunay triangulation of a set of line segments”, Proc. 3rd ACM Symposium on Computational Geometry, 1987, 223–232.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1995 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Papadopoulou, E., Lee, D.T. (1995). Efficient computation of the geodesic Voronoi diagram of points in a simple polygon. 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_147
Download citation
DOI: https://doi.org/10.1007/3-540-60313-1_147
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-60313-9
Online ISBN: 978-3-540-44913-3
eBook Packages: Springer Book Archive