Many random walks are faster then one

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F11%3A00369986" target="_blank" >RIV/67985840:_____/11:00369986 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1017/S0963548311000125" target="_blank" >http://dx.doi.org/10.1017/S0963548311000125</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1017/S0963548311000125" target="_blank" >10.1017/S0963548311000125</a>

Result language
angličtina
Original language name
Many random walks are faster then one
Original language 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 - theexpected 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 probablistic 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.
Czech name
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Czech description
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Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
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Project
Result was created during the realization of more than one project. More information in the Projects tab.
Continuities
Z - Vyzkumny zamer (s odkazem do CEZ)

Publication year
2011
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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