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ICALP
2009
Springer

Tight Bounds for the Cover Time of Multiple Random Walks

14 years 11 months ago
Tight Bounds for the Cover Time of Multiple Random Walks
We study the cover time of multiple random walks. Given a graph G of n vertices, assume that k independent random walks start from the same vertex. The parameter of interest is the speed-up defined as the ratio between the cover time of one and the cover time of k random walks. Recently Alon et al. developed several bounds that are based on the quotient between the cover time and maximum hitting times. Their technique gives a speed-up of (k) on many graphs, however, for many graph classes, k has to be bounded by O(log n). They also conjectured that, for any 1 k n, the speed-up is at most O(k) on any graph. As our main results, we prove the following: ? We present a new lower bound on the speed-up that depends on the mixing-time. It gives a speed-up of (k) on many graphs, even if k is as large as n. ? We prove that the speed-up is O(k log n) on any graph. Under rather mild conditions, we can also improve this bound to O(k), matching exactly the conjecture of Alon et al. ? We find the co...
Robert Elsässer, Thomas Sauerwald
Added 03 Dec 2009
Updated 03 Dec 2009
Type Conference
Year 2009
Where ICALP
Authors Robert Elsässer, Thomas Sauerwald
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