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
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
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
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
A Least-Resistance Path in Reasoning about Unstructured Overlay Networks
Euro-Par '09 Proceedings of the 15th International Euro-Par Conference on Parallel Processing
Universal adaptive self-stabilizing traversal scheme: Random walk and reloading wave
Journal of Parallel and Distributed Computing
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Random walk based distributed algorithms make use of a tokenthat circulates in the system according to a random walk scheme toachieve their goal. To study their efficiency and compare it to oneof the deterministic solutions, one is led to compute certainquantities, 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 ofhitting and cover times to weighted graphs. Indeed, the propertiesof random walks on symmetrically weighted graphs provideinteresting results on random walk based distributed algorithms,such as local load balancing. Both of these generalizations areproposed 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 timeson a weighted graph of n vertices, which we improve to obtain aO(n^3) complexity. This complexity is the lowest up to now. Thisalgorithm computes both of the generalizations that we propose forthe hitting times on a weighted graph.Finally, we provide the first algorithm to compute the covertime (in both senses) of a graph. We improve it to achieve acomplexity of O(n^32^n). The algorithms that we present are allrobust to a topological change in a limited number of edges. Thisproperty allows us to use them on dynamic graphs.