The random walk construction of uniform spanning trees and uniform labelled trees
SIAM Journal on Discrete Mathematics
Token management schemes and random walks yield self-stabilizing mutual exclusion
PODC '90 Proceedings of the ninth annual ACM symposium on Principles of distributed computing
Random Walks on Regular and Irregular Graphs
SIAM Journal on Discrete Mathematics
Search and replication in unstructured peer-to-peer networks
ICS '02 Proceedings of the 16th international conference on Supercomputing
The cover time, the blanket time, and the Matthews bound
FOCS '00 Proceedings of the 41st Annual Symposium on Foundations of Computer Science
Deterministic approximation of the cover time
Random Structures & Algorithms
A new method to automatically compute processing times for random walks based distributed algorithms
ISPDC'03 Proceedings of the Second international conference on Parallel and distributed computing
Maximum hitting time for random walks on graphs
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
Topological adaptability for the distributed token circulation paradigm in faulty environment
ISPA'04 Proceedings of the Second international conference on Parallel and Distributed Processing and Applications
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Random walk based distributed algorithms make use of a token that circulates in the system according to a random walk scheme to achieve their goal. To study their efficiency and compare it to one of the deterministic solutions, one is led to compute certain quantities, namely the hitting times and the cover time. Until now, only bounds on these quantities were known. First, this paper presents two generalizations of the notions of hitting and cover times to weighted graphs. Indeed, the properties of random walks on symmetrically weighted graphs provide interesting results on random walk based distributed algorithms, such as local load balancing. Both of these generalizations are proposed to precisely represent the behaviour of these algorithms, and to take into account what the weights represent. Then, we propose an algorithm to compute the $n^2$ hitting times on a weighted graph of n vertices, which we improve to obtain a O($n^3$) complexity. This complexity is the lowest up to now. This algorithm computes both of the generalizations that we propose for the hitting times on a weighted graph. Finally, we provide the first algorithm to compute the cover time (in both senses) of a graph. We improve it to achieve a complexity of O($n^32^n$). The algorithms that we present are all robust to a topological change in a limited number of edges. This property allows us to use them on dynamic graphs.