@inproceedings{eafa3a346dc84ab79e21014efe04b957,

title = "Many random walks are faster than one",

abstract = "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 jdelds 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 fit-connectivity and our results yield, in certain cases, an improvement upon some of the earlier bounds.",

keywords = "Cover time, Distributed algorithms, Graph search, Random walks, Speed-up",

author = "Noga Alon and Gady Kozma and Chen Avin and Zvi Lotker and Michal Koucky and Tuttle, {Mark R.}",

year = "2008",

month = jan,

day = "1",

doi = "10.1145/1378533.1378557",

language = "English",

isbn = "9781595939739",

series = "Annual ACM Symposium on Parallelism in Algorithms and Architectures",

publisher = "Association for Computing Machinery",

pages = "119--128",

booktitle = "SPAA'08 - Proceedings of the 20th Annual Symposium on Parallelism in Algorithms and Architectures",

note = "20th ACM Symposium on Parallelism in Algorithms and Architectures, SPAA'08 ; Conference date: 14-06-2008 Through 16-06-2008",

}