On a random walk problem arising in self-stabilizing token management
PODC '91 Proceedings of the tenth annual ACM symposium on Principles of distributed computing
A technique for lower bounding the cover time
SIAM Journal on Discrete Mathematics
Trading Space for Time in Undirected $s-t$ Connectivity
SIAM Journal on Computing
Randomized algorithms
A tight upper bound on the cover time for random walks on graphs
Random Structures & Algorithms
A spectrum of time-space trade-offs for undirected s-tconnectivity
Journal of Computer and System Sciences - Special issue: papers from the 32nd and 34th annual symposia on foundations of computer science, Oct. 2–4, 1991 and Nov. 3–5, 1993
A tight lower bound on the cover time for random walks on graphs
Random Structures & Algorithms
A Chernoff Bound for Random Walks on Expander Graphs
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
The Effect of Faults on Network Expansion
Theory of Computing Systems
Testing Expansion in Bounded-Degree Graphs
FOCS '07 Proceedings of the 48th Annual IEEE Symposium on Foundations of Computer Science
Many random walks are faster than one
Proceedings of the twentieth annual symposium on Parallelism in algorithms and architectures
Expanders via random spanning trees
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Proceedings of the 28th ACM symposium on Principles of distributed computing
Efficient distributed random walks with applications
Proceedings of the 29th ACM SIGACT-SIGOPS symposium on Principles of distributed computing
The multi-agent rotor-router on the ring: a deterministic alternative to parallel random walks
Proceedings of the 2013 ACM symposium on Principles of distributed computing
| Hi-index | 0.00 |
We study the cover time of parallel random walks which was recently introduced by Alon et al. [2]. We consider k parallel (independent) random walks starting from arbitrary vertices. The expected number of steps until these k walks have visited all n vertices is called cover time of G. In this paper we present a lower bound on the cover time of Ω( √n/k • √(1/Φ(G))}, where Φ(G) is the geometric expansion (a.k.a. as edge expansion or conductance). This bound is matched for any 1 ≤ k ≤ n by binary trees up to logarithmic factors. Our lower bound combined with previous results also implies a new characterization of expanders. Roughly speaking, the edge expansion Φ(G) satisfies 1/Φ(G) = O(polylog(n)) if and only if G has a cover time of O(n/k • polylog (n)) for all 1 ≤ k ≤ n. We also present new upper bounds on the cover time with sublinear dependence on the (algebraic) expansion.