Many Random Walks Are Faster Than One
| dc.creator | Alon, Noga | |
| dc.creator | Avin, Chen | |
| dc.creator | Koucky, Michal | |
| dc.creator | Kozma, Gady | |
| dc.creator | Lotker, Zvi | |
| dc.creator | Tuttle, Mark R. | |
| dc.date | 2007-05-03 | |
| dc.date | 2007-11-20 | |
| dc.date.accessioned | 2026-07-07T08:43:31Z | |
| dc.date.available | 2026-07-07T08:43:31Z | |
| dc.description | We pose a new and intriguing question motivated by distributed computing regarding random walks on graphs: How long does it take for several independent random walks, starting from the same vertex, to cover an entire graph? We study the cover time - the expected time required to visit every node in a graph at least once - and we show that for a large collection of interesting graphs, running many random walks in parallel yields a speed-up in the cover time that is linear in the number of parallel walks. We demonstrate that an exponential speed-up is sometimes possible, but that some natural graphs allow only a logarithmic speed-up. A problem related to ours (in which the walks start from some probabilistic distribution on vertices) was previously studied in the context of space efficient algorithms for undirected s-t connectivity and our results yield, in certain cases, an improvement upon some of the earlier bounds. | |
| dc.description | 15 pages | |
| dc.identifier | https://arxiv.org/abs/0705.0467 | |
| dc.identifier | http://arxiv.org/abs/0705.0467 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/142342 | |
| dc.subject | Probability | |
| dc.title | Many Random Walks Are Faster Than One | |
| dc.type | text |