%0 Journal Article %1 sarma2015efficient %A Sarma, Atish Das %A Molla, Anisur Rahaman %A Pandurangan, Gopal %D 2015 %J Journal of Parallel and Distributed Computing %K computation distributed_computing methods parallel_computing random_walks %P 84 - 94 %R http://dx.doi.org/10.1016/j.jpdc.2015.01.002 %T Efficient random walk sampling in distributed networks %U http://www.sciencedirect.com/science/article/pii/S0743731515000039 %V 77 %X Abstract Performing random walks in networks is a fundamental primitive that has found numerous applications in communication networks such as token management, load balancing, network topology discovery and construction, search, and peer-to-peer membership management. While several such algorithms are ubiquitous, and use numerous random walk samples, the walks themselves have always been performed naively. In this paper, we focus on the problem of performing random walk sampling efficiently in a distributed network. Given bandwidth constraints, the goal is to minimize the number of rounds and messages required to obtain several random walk samples in a continuous online fashion. We present the first round and message optimal distributed algorithms that present a significant improvement on all previous approaches. The theoretical analysis and comprehensive simulations of our algorithms show that they perform very well in different types of networks of differing topologies. In particular, our results show how several random walks can be performed continuously (when source nodes are provided only at runtime, i.e., online), such that each walk of length ℓ can be performed exactly in just O ̃ ( ℓ D ) rounds11 Throughout this paper, O ̃ hides polylogarithmic factors in the number of nodes in the network. (where D is the diameter of the network), and O ( ℓ ) messages. This significantly improves upon both, the naive technique that requires O ( ℓ ) rounds and O ( ℓ ) messages, and the sophisticated algorithm of Das Sarma et al. (2013) that has the same round complexity as this paper but requires Ω ( m ℓ ) messages (where m is the number of edges in the network). Our theoretical results are corroborated through extensive simulations on various topological data sets. Our algorithms are fully decentralized, lightweight, and easily implementable, and can serve as building blocks in the design of topologically-aware networks.

@article{sarma2015efficient, abstract = {Abstract Performing random walks in networks is a fundamental primitive that has found numerous applications in communication networks such as token management, load balancing, network topology discovery and construction, search, and peer-to-peer membership management. While several such algorithms are ubiquitous, and use numerous random walk samples, the walks themselves have always been performed naively. In this paper, we focus on the problem of performing random walk sampling efficiently in a distributed network. Given bandwidth constraints, the goal is to minimize the number of rounds and messages required to obtain several random walk samples in a continuous online fashion. We present the first round and message optimal distributed algorithms that present a significant improvement on all previous approaches. The theoretical analysis and comprehensive simulations of our algorithms show that they perform very well in different types of networks of differing topologies. In particular, our results show how several random walks can be performed continuously (when source nodes are provided only at runtime, i.e., online), such that each walk of length ℓ can be performed exactly in just O ̃ ( ℓ D ) rounds11 Throughout this paper, O ̃ hides polylogarithmic factors in the number of nodes in the network. (where D is the diameter of the network), and O ( ℓ ) messages. This significantly improves upon both, the naive technique that requires O ( ℓ ) rounds and O ( ℓ ) messages, and the sophisticated algorithm of Das Sarma et al. (2013) that has the same round complexity as this paper but requires Ω ( m ℓ ) messages (where m is the number of edges in the network). Our theoretical results are corroborated through extensive simulations on various topological data sets. Our algorithms are fully decentralized, lightweight, and easily implementable, and can serve as building blocks in the design of topologically-aware networks. }, added-at = {2016-03-15T23:50:47.000+0100}, author = {Sarma, Atish Das and Molla, Anisur Rahaman and Pandurangan, Gopal}, biburl = {https://www.bibsonomy.org/bibtex/2f557cea9a9e3bad68b47f030c246cdef/peter.ralph}, doi = {http://dx.doi.org/10.1016/j.jpdc.2015.01.002}, interhash = {5459fa0cb511f3fa32f1066d61a54675}, intrahash = {f557cea9a9e3bad68b47f030c246cdef}, issn = {0743-7315}, journal = {Journal of Parallel and Distributed Computing }, keywords = {computation distributed_computing methods parallel_computing random_walks}, pages = {84 - 94}, timestamp = {2016-03-15T23:50:47.000+0100}, title = {Efficient random walk sampling in distributed networks }, url = {http://www.sciencedirect.com/science/article/pii/S0743731515000039}, volume = 77, year = 2015 }