On a family of strong geometric spanners that admit local routing strategies

Authors:
Prosenjit Bose;Paz Carmi;Mathieu Couture;Michiel Smid;Daming Xu
Affiliations:
School of Computer Science, Carleton University, Ottawa, Ontario, Canada;School of Computer Science, Carleton University, Ottawa, Ontario, Canada;School of Computer Science, Carleton University, Ottawa, Ontario, Canada;School of Computer Science, Carleton University, Ottawa, Ontario, Canada;School of Computer Science, Carleton University, Ottawa, Ontario, Canada
Venue:
WADS'07 Proceedings of the 10th international conference on Algorithms and Data Structures
Year:
2007

Citing 5
Cited 1

Classes of graphs which approximate the complete Euclidean graph

Discrete & Computational Geometry
Approximating geometric bottleneck shortest paths

Computational Geometry: Theory and Applications
On the Spanning Ratio of Gabriel Graphs and beta-Skeletons

SIAM Journal on Discrete Mathematics
Geometric Spanner Networks

Geometric Spanner Networks
Half-space proximal: a new local test for extracting a bounded dilation spanner of a unit disk graph

OPODIS'05 Proceedings of the 9th international conference on Principles of Distributed Systems

A set of topological graphs for 2-D sensor ad hoc networks

ICC'09 Proceedings of the 2009 IEEE international conference on Communications

Quantified Score

Hi-index	0.00

Visualization

Abstract

We introduce a family of directed geometric graphs, denoted GΛθ, that depend on two parameters λ and θ. For 0 ≤ θ GΛθ graph is a strong t-spanner, with t = 1/(1-λ) cos θ. The out-degree of a node in the GΛθ graph is at most ⌊2π/ min(θ, arccos 1/2λ)⌋. Moreover, we show that routing can be achieved locally on GΛθ. Next, we show that all strong t-spanners are also t-spanners of the unit disk graph. Simulations for various values of the parameters λ and θ indicate that for random point sets, the spanning ratio of GΛθ is better than the proven theoretical bounds.