A technique for lower bounding the cover time (1992) [20 citations — 2 self]
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@INPROCEEDINGS{Zuckerman92atechnique,author = {David Zuckerman},
title = {A technique for lower bounding the cover time},
booktitle = {SIAM J. Disc. Math},
year = {1992},
pages = {81--87},
publisher = {ACM Press}
}
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Abstract:
We give a general technique for proving lower bounds on expected covering times of random walks on graphs in terms of expected hitting times between vertices. We use this technique to prove: i) A tight bound of \Omega\Gamma jV j log 2 jV j) for the 2-dimensional torus. ii) A tight bound of \Omega\Gamma jV j log 2 jV j = log dmax) for trees with maximum degree dmax. iii) Tight bounds of \Omega\Gamma �� log jV j) for rapidly mixing walks on vertex transitive graphs, where �� denotes the maximum expected hitting time between vertices. In addition to these new results, our technique allows us to systematically prove several known lower bounds on cover times, often in a much simpler way. Finally, we use a different technique to prove an\Omega
