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...

• Type: Conference
• Year: 2001
• Where: STACS
• Authors: Giri Narasimhan, Michiel H. M. Smid
• Keywords: Data Structures, Euclidean Graph, STACS 2001, Stretch Factor, Theoretical Computer Science