TY - JOUR

T1 - Many random walks are faster than one

AU - Alon, Noga

AU - Avin, Chen

AU - Koucký, Michal

AU - Kozma, Gady

AU - Lotker, Zvi

AU - Tuttle, Mark R.

PY - 2011/7

Y1 - 2011/7

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=79958834552&partnerID=8YFLogxK

U2 - 10.1017/S0963548311000125

DO - 10.1017/S0963548311000125

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AN - SCOPUS:79958834552

SN - 0963-5483

VL - 20

SP - 481

EP - 502

JO - Combinatorics Probability and Computing

JF - Combinatorics Probability and Computing

IS - 4

ER -