Tight Bounds for the Cover Time of Multiple Random Walks
ICALP '09 Proceedings of the 36th International Colloquium on Automata, Languages and Programming: Part I
The Weighted Coupon Collector's Problem and Applications
COCOON '09 Proceedings of the 15th Annual International Conference on Computing and Combinatorics
How Well Do Random Walks Parallelize?
APPROX '09 / RANDOM '09 Proceedings of the 12th International Workshop and 13th International Workshop on Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques
Impact of local topological information on random walks on finite graphs
ICALP'03 Proceedings of the 30th international conference on Automata, languages and programming
Voronoi-like nondeterministic partition of a lattice by collectives of finite automata
Mathematical and Computer Modelling: An International Journal
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A particle that moves on a connected unidirected graph G with n vertices is considered. At each step the particle goes from the current vertex to one of its neighbors, chosen uniformly at random. The cover time is the first time when the particle has visited all the vertices in the graph, starting from a given vertex. Upper and lower bounds are presented that relate the expected cover time for a graph to the eigenvalues of the Markov chain that describes the above random walk. An interesting consequence is that regular expander graphs have expected cover time theta (n log n).