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STACS
2001
Springer

Approximation Algorithms for the Bottleneck Stretch Factor Problem

13 years 8 months ago
Approximation Algorithms for the Bottleneck Stretch Factor Problem
The stretch factor of a Euclidean graph is the maximum ratio of the distance in the graph between any two points and their Euclidean distance. Given a set S of n points in Rd, we show how to construct a data structure of size O(log n), such that for an arbitrary query value b > 0, we can in O(log log n) time compute an approximation of the stretch factor of the graph Gb, which is the threshold graph on S containing all edges of length at most b. Even though there could be up to n 2 different stretch factors, we show that this data structure can be constructed in subquadratic time. If we think of the points of S as being airports, then the stretch factor of Gb gives a measure of the maximum percentage increase in flight distance using flight segments of length at most b over the direct distance. Our algorithm uses techniques from computational geometry, such as well-separated pairs, minimum spanning trees, data structures for the nearest-neighbor problem, and algorithms for selec...
Giri Narasimhan, Michiel H. M. Smid
Added 30 Jul 2010
Updated 30 Jul 2010
Type Conference
Year 2001
Where STACS
Authors Giri Narasimhan, Michiel H. M. Smid
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