TY - JOUR
T1 - On a family of strong geometric spanners that admit local routing strategies
AU - Bose, Prosenjit
AU - Carmi, Paz
AU - Couture, Mathieu
AU - Smid, Michiel
AU - Xu, Daming
N1 - Funding Information:
✩ An extended abstract of this paper appeared in the Proceedings of the 10th Workshop on Algorithms and Data Structures, 2007. This research was supported in part by NSERC, MITACS, MRI, and HPCVL. * Corresponding author. E-mail address: michiel@scs.carleton.ca (M. Smid).
PY - 2011/8/1
Y1 - 2011/8/1
N2 - We introduce a family of directed geometric graphs, whose vertices are points in Rd. The graphs Gλθ in this family depend on two real parameters λ and θ. For 12<λ<1 and π3<θ<π2, the graph Gλθ is a strong t-spanner for t=1(1-λ)cosθ. That is, for any two vertices p and q, Gλθ contains a path from p to q of length at most t times the Euclidean distance |pq|, and all edges on this path have length at most |pq|. The out-degree of any node in the graph Gλθ is O(1/πd- 1), where π=min(θ,arccos12λ). We show that routing on Gλθ can be achieved locally. Finally, we show that all strong t-spanners are also t-spanners of the unit-disk graph.
AB - We introduce a family of directed geometric graphs, whose vertices are points in Rd. The graphs Gλθ in this family depend on two real parameters λ and θ. For 12<λ<1 and π3<θ<π2, the graph Gλθ is a strong t-spanner for t=1(1-λ)cosθ. That is, for any two vertices p and q, Gλθ contains a path from p to q of length at most t times the Euclidean distance |pq|, and all edges on this path have length at most |pq|. The out-degree of any node in the graph Gλθ is O(1/πd- 1), where π=min(θ,arccos12λ). We show that routing on Gλθ can be achieved locally. Finally, we show that all strong t-spanners are also t-spanners of the unit-disk graph.
KW - Geometric spanner
KW - Local routing algorithms
KW - Yao graph
UR - http://www.scopus.com/inward/record.url?scp=79851516649&partnerID=8YFLogxK
U2 - 10.1016/j.comgeo.2011.01.002
DO - 10.1016/j.comgeo.2011.01.002
M3 - Article
AN - SCOPUS:79851516649
SN - 0925-7721
VL - 44
SP - 319
EP - 328
JO - Computational Geometry: Theory and Applications
JF - Computational Geometry: Theory and Applications
IS - 6-7
ER -