Sphericity sph(G): minimum d for G = intersection of d-balls (Euclidean). Different from boxicity (L∞ metric). Unit disk graphs: sph ≤ 2. Every graph: sph ≤ n-1. Captures Euclidean intersection structure.
How to Use
Select graph:
- sph: Sphericity
- vs box: Compare L₂ vs L∞
- Metric: Euclidean
L₂ vs L∞
Boxicity uses L∞ (max coordinate). Sphericity uses L₂ (Euclidean). Different norms give different intersection graphs! Neither dominates: some graphs have box < sph, others sph < box.
Applications
Sensor networks: spherical coverage regions. Molecular modeling: atom van der Waals radii. Geography: circular service areas. Any domain with Euclidean proximity relationships.
Step-by-Step Instructions
- 1Select graph.
- 2Compute sphericity.
- 3Compare with boxicity.
- 4Euclidean embedding.
- 5Apply bounds.