Cone-Based Graphs

Requires a Wolfram Notebook System
Interact on desktop, mobile and cloud with the free Wolfram Player or other Wolfram Language products.
In graph theory, a spanner graph has the property that the length of a shortest path between vertices is no greater than a constant times the spatial distance between the vertices. Cone-based graphs are geometric graphs defined for points in the plane. The space around each point is partitioned into a fixed number of equiangular cones, and a nearest neighbor is selected in each cone. These graphs are known to be spanners for certain values of
. Various types of cone-based graphs differ in the way the nearest neighbor is defined.
Contributed by: Mirela Damian, Kelly Gremban, and Naresh Nelavalli (May 2015)
Supported by NSF grant CCF-1218814.
Open content licensed under CC BY-NC-SA
Snapshots
Details
Reference
[1] M. Damian and D. Voicu, "Spanning Properties of Theta-Theta Graphs," in Combinatorial Optimization and Applications, 8th International Conference (Z. Zhang, L. Wu, W. Xu, D. Du, eds.), Springer Science+Business Media, 2014, pp. 216–230.
Permanent Citation
"Cone-Based Graphs"
http://demonstrations.wolfram.com/ConeBasedGraphs/
Wolfram Demonstrations Project
Published: May 26 2015