A Lower Bound on the Area of a 3-Coloured Disk Packing
| dc.creator | Brass, Peter | |
| dc.creator | Hurtado, Ferran | |
| dc.creator | Lafreniere, Benjamin | |
| dc.creator | Lubiw, Anna | |
| dc.date | 2008-04-08 | |
| dc.date.accessioned | 2026-07-07T09:31:00Z | |
| dc.date.available | 2026-07-07T09:31:00Z | |
| dc.description | Given a set of unit-disks in the plane with union area $A$, what fraction of $A$ can be covered by selecting a pairwise disjoint subset of the disks? Rado conjectured 1/4 and proved $1/4.41$. Motivated by the problem of channel-assignment for wireless access points, in which use of 3 channels is a standard practice, we consider a variant where the selected subset of disks must be 3-colourable with disks of the same colour pairwise-disjoint. For this variant of the problem, we conjecture that it is always possible to cover at least $1/1.41$ of the union area and prove $1/2.09$. We also provide an $O(n^2)$ algorithm to select a subset achieving a $1/2.77$ bound. | |
| dc.description | 15 pages (11 pages + 4 page appendix), 12 figures | |
| dc.identifier | https://arxiv.org/abs/0804.1173 | |
| dc.identifier | http://arxiv.org/abs/0804.1173 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/158309 | |
| dc.subject | Computational Geometry | |
| dc.subject | Discrete Mathematics | |
| dc.subject | F.2.2 | |
| dc.title | A Lower Bound on the Area of a 3-Coloured Disk Packing | |
| dc.type | text |