Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
6868553 | Computational Geometry | 2018 | 11 Pages |
Abstract
We study the spanning ratio of cY(θ) for different values of θ. Using a new algebraic technique, we show that cY(θ) is a spanner when θ⩽2Ï/3. We believe that this technique may be of independent interest. We also show that cY(Ï) is not a spanner, and that cY(θ) may be disconnected for θ>Ï, but on the other hand is always connected for θ⩽Ï. Furthermore, we show that cY(θ) is a region-fault-tolerant geometric spanner for convex fault regions when θ<Ï/3. For half-plane faults, cY(θ) remains connected if θ⩽Ï. Finally, we show that cY(θ) is not always self-approaching for any value of θ.
Keywords
Related Topics
Physical Sciences and Engineering
Computer Science
Computational Theory and Mathematics
Authors
Davood Bakhshesh, Luis Barba, Prosenjit Bose, Jean-Lou De Carufel, Mirela Damian, Rolf Fagerberg, Mohammad Farshi, André van Renssen, Perouz Taslakian, Sander Verdonschot,