Sevilla, Andrés and Mozo, Alberto and Lorenzo, M. Araceli and LopézPresa, José Luis and Manzano, Pilar and Fernández Anta, Antonio (2010) Biased Selection for Building SmallWorld Networks. In: The 14th International Conference on Principles of Distributed Systems (OPODIS 2010), 1417 December 2010, Tozeur, Tunisia.

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Abstract
Smallworld networks are currently present in many distributed applications and can be built augmenting a base network with longrange links using a probability distribution. Currently available distributed algorithms to select these longrange 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 gossipbased protocol), allows to select longrange 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 longrange neighbors in complete and incomplete tori, in order to build Kleinberg’s smallworld 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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