Abstract
Small-world networks are currently present in many distributed applications and can be built augmenting a base network with long-range links using a probability distribution. Currently available distributed algorithms to select these long-range neighbors are designed ad hoc for specific probability distributions. In this paper we propose a new algorithm called Biased Selection (BS) that, using a uniform sampling service (that could be implemented with, for instance, a gossip-based protocol), allows to select long-range neighbors with any arbitrary distribution in a distributed way. This algorithm is of iterative nature and has a parameter r that gives its number of iterations. We prove that the obtained sampling distribution converges to the desired distribution as r grows. Additionally, we obtain analytical bounds on the maximum relative error for a given value of this parameter r. Although the BS algorithm is proposed in this paper as a tool to sample nodes in a network, it can be used in any context in which sampling with an arbitrary distribution is required, and only uniform sampling is available.
The BS algorithm has been used to choose long-range neighbors in complete and incomplete tori, in order to build Kleinberg’s small-world networks. We observe that using a very small number of iterations (1) BS has similar error as a simulation of the Kleinberg’s harmonic distribution and (2) the average number of hops with greedy routing is no larger with BS than in a Kleinberg network. Furthermore, we have observed that before converging to the performance of a Kleinberg network, the average number of hops with BS is significantly smaller (up to 14 % smaller in a 1000 ×1000 network).
This research was supported in part by Comunidad de Madrid grant S2009TIC-1692 and Spanish MICINN grant TIN2008–06735-C02-01.
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Sevilla, A., Mozo, A., Lorenzo, M.A., López-Presa, J.L., Manzano, P., Fernández Anta, A. (2010). Biased Selection for Building Small-World Networks. In: Lu, C., Masuzawa, T., Mosbah, M. (eds) Principles of Distributed Systems. OPODIS 2010. Lecture Notes in Computer Science, vol 6490. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-17653-1_3
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