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- W2076256087 abstract "A general technique for proving lower bounds on expected covering times of random walks on graphs in terms of expected hitting times between vertices is given. This technique is used to prove (i) A tight bound of $Omega ( | V |log^2 | V | )$ for the two-dimensional torus; (ii) A tight bound of $Omega ( | V |log ^2 | V |/ log d_{max } )$ for trees with maximum degree $d_{max } $; (iii) Tight bounds of $Omega ( mu ^ + log ^2 | V | )$ for rapidly mixing walks on vertex transitive graphs, where $mu^+$ denotes the maximum expected hitting time between vertices.In addition to these new results, the technique allows several known lower bounds on cover times to be systematically proved, often in a much simpler way.Finally, a different technique is used to prove an $Omega ( 1 / ( 1 - lambda _2 ) )$ lower bound on the cover time, where $lambda_2 $ is the second largest eigenvalue of the transition matrix. This was previously known only in the case where the walk starts in the stationary distribution [..." @default.
- W2076256087 created "2016-06-24" @default.
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- W2076256087 date "1990-01-01" @default.
- W2076256087 modified "2023-09-26" @default.
- W2076256087 title "A technique for lower bounding the cover time" @default.
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- W2076256087 doi "https://doi.org/10.1145/100216.100249" @default.
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