An optimal algorithm for computing angle-constrained spanners

Let S be a set of n points in Rd and let t>1 be a real number. A graph G=(S,E) is called a t-spanner for S, if for any two points p and q in S, the shortest-path distance in G between p andq is at most t|pq|, where |pq| denotes the Euclidean distance between p and q. The graph G is called θ-angle...

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Bibliographic Details
Published in:Journal of computational geometry Vol. 3; no. 1
Main Authors: Paz Carmi, Michiel Smid
Format: Journal Article
Language:English
Published: Carleton University 01-11-2012
Online Access:Get full text
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Summary:Let S be a set of n points in Rd and let t>1 be a real number. A graph G=(S,E) is called a t-spanner for S, if for any two points p and q in S, the shortest-path distance in G between p andq is at most t|pq|, where |pq| denotes the Euclidean distance between p and q. The graph G is called θ-angle-constrained, if any two distinct edges sharing an endpoint make an angle of at least θ. It is shown that, for any θ with 0<θ<π/3, a θ-angle-constrained t-spanner can be computed in O(nlog n) time, where t depends only on θ. For values of θ approaching 0, we havet=1 + O(θ).
ISSN:1920-180X
DOI:10.20382/jocg.v3i1a10