The Cover Time of Cartesian Product Graphs
Let P = G□H be the cartesian product of graphs G,H. We relate the cover time COV[P] of P to the cover times of its factors. When one of the factors is in some sense larger than the other, its cover time dominates, and can become of the same order as the cover time of the product as a whole. Our main theorem effectively gives conditions for when this holds. The probabilistic technique which we introduce, based on the blanket time, is more general and may be of independent interest, as might some of our lemmas.
KeywordsRandom walks cover time blanket time effective resistance cartesian product graphs
Unable to display preview. Download preview PDF.
- 1.Aleliunas, R., Karp, R.M., Lipton, R.J., Lovász, L., Rackoff, C.: Random Walks, Universal Traversal Sequences, and the Complexity of Maze Problems. In: Proceedings of the 20th Annual IEEE Symposium on Foundations of Computer Science, pp. 218–223 (1979)Google Scholar
- 5.Ding, J., Lee, J.R., Peres, Y.: Cover times, blanket times and majorizing measures (2010) (manuscript)Google Scholar
- 6.Doyle, P.G., Laurie Snell, J.: Random walks and electrical networks (2006)Google Scholar
- 10.Levin, D.A., Peres, Y., Wilmer, E.L.: Markov Chains and Mixing Times (2009)Google Scholar