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• W2950870032 abstract "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 sampling random walks efficiently in a distributed network and its applications. Given bandwidth constraints, the goal is to minimize the number of rounds required to obtain random walk samples. All previous algorithms that compute a random walk sample of length $ell$ as a subroutine always do so naively, i.e., in $O(ell)$ rounds. The main contribution of this paper is a fast distributed algorithm for performing random walks. We present a 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 $ell$ in $tilde{O}(sqrt{ell D})$ rounds ($tilde{O}$ hides $polylog{n}$ factors where $n$ is the number of nodes in the network) with high probability on an undirected network, where $D$ is the diameter of the network. For small diameter graphs, this is a significant improvement over the naive $O(ell)$ bound. Furthermore, our algorithm is optimal within a poly-logarithmic factor as there exists a matching lower bound [Nanongkai et al. PODC 2011]. We further extend our algorithms to efficiently perform $k$ independent random walks in $tilde{O}(sqrt{kell D} + k)$ rounds. We also show that our algorithm can be applied to speedup the more general Metropolis-Hastings sampling. Our random walk algorithms can be used to speed up distributed algorithms in applications that use random walks as a subroutine, such as computing a random spanning tree and estimating mixing time and related parameters. Our algorithm is fully decentralized and can serve as a building block in the design of topologically-aware networks." @default.
• W2950870032 created "2019-06-27" @default.
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• W2950870032 date "2013-02-19" @default.
• W2950870032 modified "2023-10-07" @default.
• W2950870032 title "Distributed Random Walks" @default.
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• W2950870032 hasPublicationYear "2013" @default.
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