TY - GEN

T1 - Many random walks are faster than one

AU - Alon, Noga

AU - Kozma, Gady

AU - Avin, Chen

AU - Lotker, Zvi

AU - Koucky, Michal

AU - Tuttle, Mark R.

N1 - Copyright:
Copyright 2014 Elsevier B.V., All rights reserved.

PY - 2008

Y1 - 2008

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 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.

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 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.

KW - Cover time

KW - Distributed algorithms

KW - Graph search

KW - Random walks

KW - Speed-up

UR - http://www.scopus.com/inward/record.url?scp=57349120535&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=57349120535&partnerID=8YFLogxK

U2 - 10.1145/1378533.1378557

DO - 10.1145/1378533.1378557

M3 - Conference contribution

AN - SCOPUS:57349120535

SN - 9781595939739

T3 - Annual ACM Symposium on Parallelism in Algorithms and Architectures

SP - 119

EP - 128

BT - SPAA'08 - Proceedings of the 20th Annual Symposium on Parallelism in Algorithms and Architectures

PB - Association for Computing Machinery

T2 - 20th ACM Symposium on Parallelism in Algorithms and Architectures, SPAA'08

Y2 - 14 June 2008 through 16 June 2008

ER -