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Many random walks are faster than one
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SYSNO ASEP 0369986 Druh ASEP J - Článek v odborném periodiku Zařazení RIV J - Článek v odborném periodiku Poddruh J Článek ve WOS Název Many random walks are faster than one Tvůrce(i) Alon, N. (IL)
Avin, Ch. (IL)
Koucký, Michal (MU-W) RID, SAI, ORCID
Kozma, G. (IL)
Lotker, Z. (IL)
Tuttle, M.R. (US)Zdroj.dok. Combinatorics Probability & Computing. - : Cambridge University Press - ISSN 0963-5483
Roč. 20, č. 4 (2011), s. 481-502Poč.str. 22 s. Jazyk dok. eng - angličtina Země vyd. GB - Velká Británie Klíč. slova multiple random walks ; parallel random walks Vědní obor RIV BA - Obecná matematika CEP GP201/07/P276 GA ČR - Grantová agentura ČR GA201/05/0124 GA ČR - Grantová agentura ČR CEZ AV0Z10190503 - MU-W (2005-2011) UT WOS 000291604300001 EID SCOPUS 79958834552 DOI 10.1017/S0963548311000125 Anotace 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 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. Pracoviště Matematický ústav Kontakt Jarmila Štruncová, struncova@math.cas.cz, library@math.cas.cz, Tel.: 222 090 757 Rok sběru 2012
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