On a Family of Strong Geometric Spanners That Admit Local Routing Strategies

We introduce a family of directed geometric graphs, denoted Gθ λ, that depend on two parameters λ and θ. For 0 ≤ θ < π 2 and 1 2 < λ < 1, the Gθ λ graph is a strong t-spanner, with t = 1 (1−λ) cos θ . The out-degree of a node in the Gθ λ graph is at most 2π/ min(θ, arccos 1 2λ ) . Moreover, we show that routing can be achieved locally on Gθ λ. 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 Gθ λ is better than the proven theoretical bounds.

• Type: Conference
• Year: 2007
• Where: WADS
• Authors: Prosenjit Bose, Paz Carmi, Mathieu Couture, Michiel H. M. Smid, Daming Xu
• Keywords: Algorithms, Geometric Graphs, Strong T-spanners, Unit Disk Graph, WADS 2007