Matrix multiplication via arithmetic progressions
Journal of Symbolic Computation - Special issue on computational algebraic complexity
A technique for lower bounding the cover time
SIAM Journal on Discrete Mathematics
Random Structures & Algorithms
The cover time, the blanket time, and the Matthews bound
FOCS '00 Proceedings of the 41st Annual Symposium on Foundations of Computer Science
Random walks, universal traversal sequences, and the complexity of maze problems
SFCS '79 Proceedings of the 20th Annual Symposium on Foundations of Computer Science
The cover time of the giant component of a random graph
Random Structures & Algorithms
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
The evolution of the cover time
Combinatorics, Probability and Computing
Random walks, interacting particles, dynamic networks: randomness can be helpful
SIROCCO'11 Proceedings of the 18th international conference on Structural information and communication complexity
Spectral sparsification of graphs: theory and algorithms
Communications of the ACM
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We exhibit a strong connection between cover times of graphs, Gaussian processes, and Talagrand's theory of majorizing measures. In particular, we show that the cover time of any graph G is equivalent, up to universal constants, to the square of the expected maximum of the Gaussian free field on G, scaled by the number of edges in G. This allows us to resolve a number of open questions. We give a deterministic polynomial-time algorithm that computes the cover time to within an O(1) factor for any graph, answering a question of Aldous and Fill (1994). We also positively resolve the blanket time conjectures of Winkler and Zuckerman (1996), showing that for any graph, the blanket and cover times are within an O(1) factor. The best previous approximation factor for both these problems was O((log log n)2) for n-vertex graphs, due to Kahn, Kim, Lovasz, and Vu (2000).