We prove upper and lower bounds and give an approximation algorithm for the cover time of the random walk on a graph. We introduce a parameter M motivated by the well-known Matthews bounds on the cover time, C, and prove that M/2≤C = O(M(ln ln n)2). We give a deterministic polynomial time algorithm to approximate M within a factor of 2; this then approximates C within a factor of O((ln ln n)2), improving the previous bound O(ln n) due to Matthews. The blanket time B was introduced by Winkler and Zuckerman: it is the expectation of the first time when all vertices are visited within a constant factor of the number of times suggested by the stationary distribution. Obviously C≤B. Winkler and Zuckerman conjectured B = O(C) and proved B = O(C ln n). Our bounds above are also valid for the blanket time, and so it follows that B = O(C(ln ln n)2).
|Number of pages||9|
|Journal||Annual Symposium on Foundations of Computer Science - Proceedings|
|Publication status||Published - Dec 1 2000|
|Event||41st Annual Symposium on Foundations of Computer Science (FOCS 2000) - Redondo Beach, CA, USA|
Duration: Nov 12 2000 → Nov 14 2000
ASJC Scopus subject areas
- Hardware and Architecture