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
Cost-sensitive analysis of communication protocols
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Collisions among random walks on a graph
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Generating random spanning trees more quickly than the cover time
STOC '96 Proceedings of the twenty-eighth annual ACM symposium on Theory of computing
The small-world phenomenon: an algorithmic perspective
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
Distributed computing: a locality-sensitive approach
Distributed computing: a locality-sensitive approach
Spatial gossip and resource location protocols
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Search and replication in unstructured peer-to-peer networks
ICS '02 Proceedings of the 16th international conference on Supercomputing
Peer-to-Peer Membership Management for Gossip-Based Protocols
IEEE Transactions on Computers
Random Leaders and Random Spanning Trees
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A self-stabilizing distributed algorithm for spanning tree construction in wireless ad hoc networks
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Probability and Computing: Randomized Algorithms and Probabilistic Analysis
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Random Walk for Self-Stabilizing Group Communication in Ad Hoc Networks
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Random walk based node sampling in self-organizing networks
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ICDCS '07 Proceedings of the 27th International Conference on Distributed Computing Systems
Estimating PageRank on graph streams
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Many random walks are faster than one
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Generating random spanning trees
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Expanders via random spanning trees
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Quickly routing searches without having to move content
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Random walks in distributed computing: a survey
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Random walk with jumps in large-scale random geometric graphs
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Expansion and the cover time of parallel random walks
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A tight unconditional lower bound on distributed randomwalk computation
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SIROCCO'12 Proceedings of the 19th international conference on Structural Information and Communication Complexity
Fast distributed computation in dynamic networks via random walks
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Performing random walks in networks is a fundamental primitive that has found applications in many areas of computer science, including distributed computing. In this paper, we focus on the problem of performing random walks efficiently in a distributed network. Given bandwidth constraints, the goal is to minimize the number of rounds required to obtain a random walk sample. All previous algorithms that compute a random walk sample of length ℓ as a subroutine always do so naively, i.e., in O(ℓ) rounds. The main contribution of this paper is a fast distributed algorithm for performing random walks. We show that a random walk sample of length ℓ can be computed in Õ(ℓ2/3 D1/3) rounds on an undirected unweighted network, where D is the diameter of the network.1 When ℓ = Ω(D log n), this is an improvement over the naive O(ℓ) bound. (We show that Ω(min{D, ℓ}) is a lower bound and hence in general we cannot have a running time faster than the diameter of the graph.) We also show that our algorithm can be applied to speedup the more general Metropolis-Hastings sampling. We extend our algorithms to perform a large number, k, of random walks efficiently. We show how k destinations can be sampled in Õ((kℓ)2/3 D1/3) rounds if k ≤ ℓ2 and Õ((kℓ)1/2) rounds otherwise. We also present faster algorithms for performing random walks of length larger than (or equal to) the mixing time of the underlying graph. Our techniques can be useful in speeding up distributed algorithms for a variety of applications that use random walks as a subroutine.