Collisions among random walks on a graph
SIAM Journal on Discrete Mathematics
Design of On-Line Algorithms Using Hitting Times
SIAM Journal on Computing
The cover time, the blanket time, and the Matthews bound
FOCS '00 Proceedings of the 41st Annual Symposium on Foundations of Computer Science
Deterministic approximation of the cover time
Random Structures & Algorithms
| Hi-index | 5.23 |
Feige and Rabinovich, in [Feige and Rabinovich, Rand. Struct. Algorithms 23(1) (2003) 1-22], gave a deterministic O(log4n) approximation for the time it takes a random walk to cover a given graph starting at a given vertex. This approximation algorithm was shown to work for arbitrary reversible Markov chains. We build on the results of [Feige and Rabinovich, Rand. Struct. Algorithms 23(1) (2003) 1-22], and show that the original algorithm gives a O(log2n) approximation as it is, and that it can be modified to give a O(log n(log log n)2) approximation. Moreover, we show that given any c(n)-approximation algorithm for the maximum cover time (maximized over all initial vertices) of a reversible Markov chain, we can give a corresponding algorithm for the general cover time (of a random walk or reversible Markov chain) with approximation ratio O(c(n) log n).