On a family of strong geometric spanners that admit local routing strategies
- Bose, Prosenjit
- Carmi, Paz
- Couture, Mathieu
- Smid, Michiel
- Xu, Daming
DOIAbstract
AbstractWe 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/ϕd−1), where ϕ=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
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