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Biased Selection for Building Small-World Networks

Sevilla, Andrés and Mozo, Alberto and Lorenzo, M. Araceli and Lopéz-Presa, José Luis and Manzano, Pilar and Fernández Anta, Antonio (2010) Biased Selection for Building Small-World Networks. In: The 14th International Conference on Principles of Distributed Systems (OPODIS 2010), 14-17 December 2010, Tozeur, Tunisia.

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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 x 1000 network).

Item Type: Conference or Workshop Papers (Paper)
Subjects: Q Science > Q Science (General)
Q Science > QA Mathematics > QA75 Electronic computers. Computer science
T Technology > T Technology (General)
T Technology > TK Electrical engineering. Electronics Nuclear engineering
Divisions: Faculty of Engineering, Science and Mathematics > School of Electronics and Computer Science
Depositing User: Acosta Angel
Date Deposited: 14 Feb 2012 13:17
Last Modified: 03 Dec 2014 12:20
URI: http://eprints.networks.imdea.org/id/eprint/46

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