Spanning Ratio and Maximum Detour of Rectilinear Paths in the L1 Plane

The spanning ratio and maximum detour of a graph G embedded in a metric space measure how well G approximates the minimum complete graph containing G and metric space, respectively. In this paper we show that computing the spanning ratio of a rectilinear path P in L1 space has a lower bound of Ω(n l...

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Published inAlgorithms and Computation pp. 121 - 131
Main Authors Grüne, Ansgar, Lin, Tien-Ching, Yu, Teng-Kai, Klein, Rolf, Langetepe, Elmar, Lee, D. T., Poon, Sheung-Hung
Format Book Chapter
LanguageEnglish
Published Berlin, Heidelberg Springer Berlin Heidelberg
SeriesLecture Notes in Computer Science
Subjects
dilation
Manhattan plane
maximum detour
metric
rectilinear path
spanning ratio
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Abstract The spanning ratio and maximum detour of a graph G embedded in a metric space measure how well G approximates the minimum complete graph containing G and metric space, respectively. In this paper we show that computing the spanning ratio of a rectilinear path P in L1 space has a lower bound of Ω(n logn) in the algebraic computation tree model and describe a deterministic O(n log2n) time algorithm. On the other hand, we give a deterministic O(n log2n) time algorithm for computing the maximum detour of a rectilinear path P in L1 space and obtain an O(n) time algorithm when P is a monotone rectilinear path.
AbstractList The spanning ratio and maximum detour of a graph G embedded in a metric space measure how well G approximates the minimum complete graph containing G and metric space, respectively. In this paper we show that computing the spanning ratio of a rectilinear path P in L1 space has a lower bound of Ω(n logn) in the algebraic computation tree model and describe a deterministic O(n log2n) time algorithm. On the other hand, we give a deterministic O(n log2n) time algorithm for computing the maximum detour of a rectilinear path P in L1 space and obtain an O(n) time algorithm when P is a monotone rectilinear path.
Author Lin, Tien-Ching
Yu, Teng-Kai
Poon, Sheung-Hung
Grüne, Ansgar
Lee, D. T.
Klein, Rolf
Langetepe, Elmar
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Snippet The spanning ratio and maximum detour of a graph G embedded in a metric space measure how well G approximates the minimum complete graph containing G and...
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StartPage 121
SubjectTerms dilation
Manhattan plane
maximum detour
metric
rectilinear path
spanning ratio
Title Spanning Ratio and Maximum Detour of Rectilinear Paths in the L1 Plane
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