Abstract
Assume that we are given the coordinates of n airports. Given an airplane that can fly a distance of b miles without refueling, a typical query is to determine the smallest value of t such that the airplane can travel between any pair of airports using flight segments of length at most b miles, such that the sum of the lengths of the flight segments is not longer than t times the direct “as-the-crow-flies” distance between the airports. This problem falls under the general category of bottleneck problems. In our case, the stretch factor, i.e., the value of t, is a measure of the maximum increase in fuel costs caused by choosing a path other than the direct path between any source and any destination. (Clearly, this direct path cannot be taken if its length is larger than b miles.)
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References
P. K. Agarwal and J. Matoušek. Ray shooting and parametric search. SIAM J. Comput., 22:794–806, 1993.
S. Arya, G. Das, D. M. Mount, J. S. Salowe, and M. Smid. Euclidean spanners: short, thin, and lanky. In Proc. 27th Annu. ACM Sympos. Theory Comput., pages 489–498, 1995.
J. L. Bentley. Decomposable searching problems. Inform. Process. Lett., 8:244–251, 1979.
J. L. Bentley and J. B. Saxe. Decomposable searching problems I: Static-to-dynamic transformations. J. Algorithms, 1:301–358, 1980.
P. B. Callahan. Dealing with higher dimensions: the well-separated pair decomposition and its applications. Ph.D. thesis, Dept. Comput. Sci., Johns Hopkins University, Baltimore, Maryland, 1995.
P. B. Callahan and S. R. Kosaraju. Faster algorithms for some geometric graph problems in higher dimensions. In Proc. 4th ACM-SIAM Sympos. Discrete Algorithms, pages 291–300, 1993.
P. B. Callahan and S. R. Kosaraju. A decomposition of multidimensional point sets with applications to k-nearest-neighbors and n-body potential fields. J. ACM, 42:67–90, 1995.
T. M. Chan. On enumerating and selecting distances. In Proc. 14th Annu. ACM Sympos. Comput. Geom., pages 279–286, 1998.
T. H. Cormen, C. E. Leiserson, and R. L. Rivest. Introduction to Algorithms. MIT Press, Cambridge, MA, 1990.
M. T. Dickerson and D. Eppstein. Algorithms for proximity problems in higher dimensions. Comput. Geom. Theory Appl., 5:277–291, 1996.
D. Eppstein. Spanning trees and spanners. In J.-R. Sack and J. Urrutia, editors, Handbook of Computational Geometry, pages 425–461. Elsevier Science, Amsterdam, 1999.
J. Matoušek and O. Schwarzkopf. On ray shooting in convex polytopes. Discrete Comput. Geom., 10:215–232, 1993.
G. Narasimhan and M. Smid. Approximating the stretch factor of Euclidean graphs. SIAM J. Comput., 30:978–989, 2000.
F. P. Preparata and M. I. Shamos. Computational Geometry: An Introduction. Springer-Verlag, Berlin, 1988.
M. Smid. Closest-point problems in computational geometry. In J.-R. Sack and J. Urrutia, editors, Handbook of Computational Geometry, pages 877–935. Elsevier Science, Amsterdam, 1999.
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Narasimhan, G., Smid, M. (2001). Approximation Algorithms for the Bottleneck Stretch Factor Problem. In: Ferreira, A., Reichel, H. (eds) STACS 2001. STACS 2001. Lecture Notes in Computer Science, vol 2010. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44693-1_44
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DOI: https://doi.org/10.1007/3-540-44693-1_44
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