Random sampling with a reservoir
ACM Transactions on Mathematical Software (TOMS)
SIAM Journal on Computing
The random walk construction of uniform spanning trees and uniform labelled trees
SIAM Journal on Discrete Mathematics
A SubLinear Time Distributed Algorithm for Minimum-Weight Spanning Trees
SIAM Journal on Computing
Fast distributed construction of small k-dominating sets and applications
Journal of Algorithms
Distributed computing: a locality-sensitive approach
Distributed computing: a locality-sensitive approach
Distributed Algorithms
SIAM Journal on Computing
Random Leaders and Random Spanning Trees
Proceedings of the 3rd International Workshop on Distributed Algorithms
A self-stabilizing distributed algorithm for spanning tree construction in wireless ad hoc networks
Journal of Parallel and Distributed Computing - Special issue on wireless and mobile ad hoc networking and computing
Testing Random Variables for Independence and Identity
FOCS '01 Proceedings of the 42nd IEEE symposium on Foundations of Computer Science
Distributed approximation: a survey
ACM SIGACT News
The bin-covering technique for thresholding random geometric graph properties
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Random walk based node sampling in self-organizing networks
ACM SIGOPS Operating Systems Review
A decentralized algorithm for spectral analysis
Journal of Computer and System Sciences
Estimating PageRank on graph streams
Proceedings of the twenty-seventh ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
Many random walks are faster than one
Proceedings of the twentieth annual symposium on Parallelism in algorithms and architectures
Random walks, universal traversal sequences, and the complexity of maze problems
SFCS '79 Proceedings of the 20th Annual Symposium on Foundations of Computer Science
Generating random spanning trees
SFCS '89 Proceedings of the 30th Annual Symposium on Foundations of Computer Science
Efficient distributed approximation algorithms via probabilistic tree embeddings
Proceedings of the twenty-seventh ACM symposium on Principles of distributed computing
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
Faster Generation of Random Spanning Trees
FOCS '09 Proceedings of the 2009 50th Annual IEEE Symposium on Foundations of Computer Science
Random walks in distributed computing: a survey
IICS'04 Proceedings of the 4th international conference on Innovative Internet Community Systems
Expansion and the cover time of parallel random walks
Proceedings of the 29th ACM SIGACT-SIGOPS symposium on Principles of distributed computing
A tight unconditional lower bound on distributed randomwalk computation
Proceedings of the 30th annual ACM SIGACT-SIGOPS symposium on Principles of distributed computing
Resource location based on partial random walks in networks with resource dynamics
Proceedings of the 4th International Workshop on Theoretical Aspects of Dynamic Distributed Systems
Fast distributed computation in dynamic networks via random walks
DISC'12 Proceedings of the 26th international conference on Distributed Computing
Journal of the ACM (JACM)
Coalescing-branching random walks on graphs
Proceedings of the twenty-fifth annual ACM symposium on Parallelism in algorithms and architectures
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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. We first present a fast sublinear time distributed algorithm for performing random walks whose time complexity is sublinear in the length of the walk. Our algorithm performs a random walk of length l in Õ(√l D) rounds (with high probability) on an undirected network, where D is the diameter of the network. This improves over the previous best algorithm that ran in Õ(l2/3D1/3) rounds (Das Sarma et al., PODC 2009). We further extend our algorithms to efficiently perform k independent random walks in Õ(√kl D + k) rounds. We then show that there is a fundamental difficulty in improving the dependence on l any further by proving a lower bound of Ω(√l/log l + D) under a general model of distributed random walk algorithms. Our random walk algorithms are useful in speeding up distributed algorithms for a variety of applications that use random walks as a subroutine. We present two main applications. First, we give a fast distributed algorithm for computing a random spanning tree (RST) in an arbitrary (undirected) network which runs in Õ(√mD) rounds (with high probability; here m is the number of edges). Our second application is a fast decentralized algorithm for estimating mixing time and related parameters of the underlying network. Our algorithm is fully decentralized and can serve as a building block in the design of topologically-aware networks.