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Many Random Walks Are Faster Than One
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@MISC{Alon_manyrandom,
author = {Noga Alon and Chen Avin and Gady Kozma and Zvi Lotker and Mark R. Tuttle},
title = {Many Random Walks Are Faster Than One},
year = {}
}
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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 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.
Keyphrases
many random walk faster cover time undirected s-t-connectivity parallel walk several independent random walk space efficient algorithm certain case parallel yield logarithmic speed-up natural graph intriguing question large collection result yield many random walk entire graph random walk exponential speed-up expected time probabilistic distribution
