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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Published in: | Journal of computational geometry Vol. 3; no. 1 |
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Main Authors: | , |
Format: | Journal Article |
Language: | English |
Published: |
Carleton University
01-11-2012
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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). |
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ISSN: | 1920-180X |
DOI: | 10.20382/jocg.v3i1a10 |