Abstract
This paper presents an O(n+k) time algorithm to compute the set of k non-crossing shortest paths between k source-destination pairs of points on the boundary of a simple polygon of n vertices. Paths are allowed to overlap but are not allowed to cross in the plane. A byproduct of this result is an O(n) time algorithm to compute a balanced geodesic triangulation which is easy to implement. The algorithm extends to a simple polygon with one hole where source destination pairs may appear on both the inner and outer boundary of the polygon. In the latter case, the goal is to compute a collection of non-crossing paths of minimum total cost.
This is a preview of subscription content, log in via an institution to check access.
Preview
Unable to display preview. Download preview PDF.
References
B. Chazelle, “A theorem on polygon cutting with applications”, Proc. 23rd Annu. IEEE Sympos. Found. Comput. Sci., 1982, pp. 339–349.
B. Chazelle, H. Eddelsbrunner, M. Grigni, L. Guibas, J. Hershberger, M. Sharir, and J. Snoeyink, “Ray shooting in polygons using geodesic triangualtions”, Algorithmica, 12, 1994, 54–68.
M. T. Goodrich and R. Tamassia, “Dynamic Ray Shooting and Shortest Paths via Balanced Geodesic Triangualtions”, In Proc. 9th Annu. ACM Sympos. Comput. Geom, 1993, 318–327.
L.J. Guibas and J. Hershberger, “Optimal shortest path queries in a simple polygon”, J. Comput. Syst. Sci., 39, 1989, 126–152.
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, 209–233, 1987.
J. Hershberger and J. Snoeyink, “Computing Minimum Length Paths of a given homotopy class”, Comput. Geometry: Theory and Applications, 4, 1994, 63–97.
D.T. Lee, “Non-crossing paths problems”, Manuscript, Dept. of EECS, Northwestern University, 1991.
D. T. Lee and F. P. Preparata, “Euclidean Shortest Paths in the Presence of Rectilinear Barriers”, Networks, 14 1984, 393–410.
F.P. Preparata and M. I. Shamos, Computational Geometry: an Introduction, Springer-Verlag, New York, NY 1985.
J. Takahashi, H. Suzuki, and T. Nishizeki, “Finding shortest non-crossing rectilinear paths in plane regions”, Proc. of ISAAC'93, Lect. Notes in Computer Science, Spinger-Verlag, 762, 1993, 98–107.
J. Takahashi, H. Suzuki, and T. Nishizeki, “Shortest non-crossing rectilinear paths in plane regions”, Algorithmica, to appear.
J. Takahashi, H. Suzuki, and T. Nishizeki, “Shortest non-crossing paths in plane graphs”, Algorithmica, to appear.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1996 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Papadopoulou, E. (1996). k-pairs non-crossing shortest paths in a simple polygon. In: Asano, T., Igarashi, Y., Nagamochi, H., Miyano, S., Suri, S. (eds) Algorithms and Computation. ISAAC 1996. Lecture Notes in Computer Science, vol 1178. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0009507
Download citation
DOI: https://doi.org/10.1007/BFb0009507
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-62048-8
Online ISBN: 978-3-540-49633-5
eBook Packages: Springer Book Archive