On the metric distortion of nearest-neighbour graphs on random point sets
| dc.creator | Bagchi, Amitabha | |
| dc.creator | Bansal, Sohit | |
| dc.date | 2008-04-23 | |
| dc.date | 2008-07-18 | |
| dc.date.accessioned | 2026-07-07T09:50:50Z | |
| dc.date.available | 2026-07-07T09:50:50Z | |
| dc.description | We study the graph constructed on a Poisson point process in $d$ dimensions by connecting each point to the $k$ points nearest to it. This graph a.s. has an infinite cluster if $k > k_c(d)$ where $k_c(d)$, known as the critical value, depends only on the dimension $d$. This paper presents an improved upper bound of 188 on the value of $k_c(2)$. We also show that if $k \geq 188$ the infinite cluster of $\NN(2,k)$ has an infinite subset of points with the property that the distance along the edges of the graphs between these points is at most a constant multiplicative factor larger than their Euclidean distance. Finally we discuss in detail the relevance of our results to the study of multi-hop wireless sensor networks. | |
| dc.description | This work is now subsumed by arXiv:0805.4060v4 [cs.NI] | |
| dc.identifier | https://arxiv.org/abs/0804.3784 | |
| dc.identifier | http://arxiv.org/abs/0804.3784 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/165081 | |
| dc.subject | Networking and Internet Architecture | |
| dc.subject | Computational Geometry | |
| dc.title | On the metric distortion of nearest-neighbour graphs on random point sets | |
| dc.type | text |