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Well Balanced Designs for Data Placement

Jean-Claude Bermond 1 Alain Jean-Marie 2, 3 Dorian Mazauric 1, 3 Joseph Yu 1 
1 MASCOTTE - Algorithms, simulation, combinatorics and optimization for telecommunications
CRISAM - Inria Sophia Antipolis - Méditerranée , Laboratoire I3S - COMRED - COMmunications, Réseaux, systèmes Embarqués et Distribués
2 MAORE - Methods, Algorithms for Operations REsearch
LIRMM - Laboratoire d'Informatique de Robotique et de Microélectronique de Montpellier
3 MAESTRO - Models for the performance analysis and the control of networks
CRISAM - Inria Sophia Antipolis - Méditerranée
Abstract : The problem we consider in this article is motivated by data placement, in particular data replication in distributed storage and retrieval systems. We are given a set V of v servers along with b files (data, documents). Each file is replicated on exactly k servers. A placement consists in finding a family of b subsets of V (representing the files) called blocks, each of size k. Each server has some probability to fail and we want to find a placement which minimizes the variance of the number of available files. It was conjectured that there always exists an optimal placement (with variance better than that of any other placement for any value of the probability of failure). We show that the conjecture is true, if there exists a well balanced design, that is a family of blocks, each of size k, such that each j-element subset of V , 1 ≤ j ≤ k, belongs to the same or almost the same number of blocks (difference at most one). The existence of well balanced designs is a difficult problem as it contains as a subproblem the existence of Steiner systems. We completely solve the case k = 2 and give bounds and constructions for k = 3 and some values of v and b.
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Submitted on : Friday, November 14, 2014 - 2:02:16 PM
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  • HAL Id : inria-00618656, version 3


Jean-Claude Bermond, Alain Jean-Marie, Dorian Mazauric, Joseph Yu. Well Balanced Designs for Data Placement. [Research Report] RR-7725, Inria. 2011. ⟨inria-00618656v3⟩



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