Computing the Maximum Detour and Spanning Ratio of Planar Paths, Trees, and Cycles
نویسندگان
چکیده
The maximum detour and spanning ratio of an embedded graph G are values that measure how well G approximates Euclidean space and the complete Euclidean graph, respectively. In this paper we describe O(n logn) time algorithms for computing the maximum detour and spanning ratio of a planar polygonal path. These algorithms solve open problems posed in at least two previous works [5,10]. We also generalize these algorithms to obtain O(n log n) time algorithms for computing the maximum detour and spanning ratio of planar trees and cycles.
منابع مشابه
Computing the Detour and Spanning Ratio of Paths, Trees, and Cycles in 2D and 3D
The detour and spanning ratio of a graph embedded in measure how well approximates Euclidean space and the complete Euclidean graph, respectively. In this paper we describe time algorithms for computing the detour and spanning ratio of a planar polygonal path. By generalizing these algorithms, we obtain -time algorithms for computing the detour or spanning ratio of planar trees and cycles. Fina...
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