How to generate cryptographically strong sequences of pseudo-random bits
SIAM Journal on Computing
Pseudorandom generators for space-bounded computations
STOC '90 Proceedings of the twenty-second annual ACM symposium on Theory of computing
A technique for lower bounding the cover time
SIAM Journal on Discrete Mathematics
Birthday paradox, coupon collectors, caching algorithms and self-organizing search
Discrete Applied Mathematics
Collisions among random walks on a graph
SIAM Journal on Discrete Mathematics
Random Walks on Regular and Irregular Graphs
SIAM Journal on Discrete Mathematics
A tight upper bound on the cover time for random walks on graphs
Random Structures & Algorithms
A tight lower bound on the cover time for random walks on graphs
Random Structures & Algorithms
Design of On-Line Algorithms Using Hitting Times
SIAM Journal on Computing
A Pseudorandom Generator from any One-way Function
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
Improved approximation of the minimum cover time
Theoretical Computer Science
Efficiency of random walks for search in different network structures
Proceedings of the 2nd international conference on Performance evaluation methodologies and tools
How to Compute Times of Random Walks Based Distributed Algorithms
Fundamenta Informaticae
How to Compute Times of Random Walks Based Distributed Algorithms
Fundamenta Informaticae
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The cover time is the expected time it takes a random walk to cover all vertices of a graph. Despite the fact that it can be approximated with arbitrary precision by a simple polynomial time Monte-Carlo algorithm which simulates the random walk, it is not known whether the cover time of a graph can be computed in deterministic polynomial time. In the present paper we establish a deterministic polynomial time algorithm that, for any graph and any starting vertex, approximates the cover time within polylogarithmic factors. More generally, our algorithm approximates the cover time for arbitrary reversible Markov chains. The new aspect of our algorithm is that the starting vertex of the random walk may be arbitrary and is given as part of the input, whereas previous deterministic approximation algorithms for the cover time assume that the walk starts at the worst possible vertex. In passing, we show that the starting vertex can make a difference of up to a multiplicative factor of Θ(n3/2/√log n) in the cover time of an n-vertex graph.