Distance-preserving approximations of polygonal paths

Given a polygonal path P with vertices p 1 , p 2 , … , p n ∈ R d and a real number t ⩾ 1 , a path Q = ( p i 1 , p i 2 , … , p i k ) is a t-distance-preserving approximation of P if 1 = i 1 < i 2 < ⋯ < i k = n and each straight-line edge ( p i j , p i j + 1 ) of Q approximates the distance b...

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Bibliographic Details
Published in:Computational geometry : theory and applications Vol. 36; no. 3; pp. 183 - 196
Main Authors: Gudmundsson, Joachim, Narasimhan, Giri, Smid, Michiel
Format: Journal Article
Language:English
Published: Elsevier B.V 01.04.2007
Subjects:
Experimental algorithms
Path simplification
t-spanners
Well-separated pair decomposition
Path simplification
t-spanners
Experimental algorithms
Well-separated pair decomposition
ISSN:0925-7721
Online Access:Get full text
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Summary:Given a polygonal path P with vertices p 1 , p 2 , … , p n ∈ R d and a real number t ⩾ 1 , a path Q = ( p i 1 , p i 2 , … , p i k ) is a t-distance-preserving approximation of P if 1 = i 1 < i 2 < ⋯ < i k = n and each straight-line edge ( p i j , p i j + 1 ) of Q approximates the distance between p i j and p i j + 1 along the path P within a factor of t. We present exact and approximation algorithms that compute such a path Q that minimizes k (when given t) or t (when given k). We also present some experimental results.
ISSN:0925-7721
DOI:10.1016/j.comgeo.2006.05.002