Abstract
In a geometric bottleneck shortest path problem, we are given a set S of n points in the plane, and want to answer queries of the following type: Given two points p and q of S and a real number L, compute (or approximate) a shortest path in the subgraph of the complete graph on S consisting of all edges whose length is less than or equal to L. We present efficient algorithms for answering several query problems of this type. Our solutions are based on minimum spanning trees, spanners, the Delaunay triangulation, and planar separators.
Bose, Maheshwari, and Smid were supported by NSERC.
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References
M. A. Bender and M. Farach-Colton. The LCA problem revisited. Proc. 4th LATIN, LNCS, 1776, pp. 88–94, 2000.
M. S. Chang, N.-F. Huang, and C.-Y. Tang. An optimal algorithm for constructing oriented Voronoi diagrams and geographic neighborhood graphs. Information Processing Letters, 35:255–260, 1990.
H. N. Djidjev. Efficient algorithms for shortest path queries in planar digraphs. Proc. 22nd WG, LNCS, 1197, pp. 151–165, 1996.
D. Eppstein. Spanning trees and spanners. In Handbook of Computational Geometry, pages 425–461. Elsevier, 2000.
J. M. Keil and C. A. Gutwin. Classes of graphs which approximate the complete Euclidean graph. Discrete & Computational Geometry, 7:13–28, 1992.
G. Narasimhan and M. Smid. Approximation algorithms for the bottleneck stretch factor problem. Nordic Journal of Computing, 9:13–31, 2002.
A. C. Yao. On constructing minimum spanning trees in k-dimensional spaces and related problems. SIAM Journal on Computing, 11:721–736, 1982.
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© 2003 Springer-Verlag Berlin Heidelberg
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Bose, P., Maheshwari, 1., Narasimhan, G., Smid, M., Zeh, N. (2003). Approximating Geometric Bottleneck Shortest Paths. In: Alt, H., Habib, M. (eds) STACS 2003. STACS 2003. Lecture Notes in Computer Science, vol 2607. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-36494-3_5
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DOI: https://doi.org/10.1007/3-540-36494-3_5
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