Algorithms for Optimal Replica Placement Under Correlated Failure in Hierarchical Failure Domains

In data centers, data replication is the primary method used to ensure avail-ability of customer data. To avoid correlated failure, cloud storage infras-tructure providers model hierarchical failure domains using a tree, and avoidplacing a large number of data replicas within the same failure domain (i.e.on the same branch of the tree). Typical best practices ensure that replicasare distributed across failure domains, but relatively little is known concern-ing optimization algorithms for distributing data replicas. Using a hierar-chical model, we answer how to distribute replicas across failure domainsoptimally. We formulate a novel optimization problem for replica placementin data centers. As part of our problem we formalize and explain a newcriterion for optimizing a replica placement. Our overall goal is to chooseplacements in which correlated failures disable as few replicas as possible.We provide two optimization algorithms for dependency models representedby trees. We first present an O(n+ρ log ρ) time dynamic programming algo-rithm for placing ρ replicas of a single file on the leaves (representing servers)of a tree with n vertices. We next consider the problem of placing replicasof m blocks of data, where each block may have different replication factors.For this problem, we give an exact algorithm which runs in polynomial timewhen the skew, the difference in the number of replicas between the largestand smallest blocks of data, is constant. A preliminary version of this work appeared in the Proceedings of the 9th Annual Inter-national Conference on Combinatorial Optimization and Applications (COCOA), 2015 [1].Email addresses: [email protected] (K. Alex Mills),[email protected] (R. Chandrasekaran), [email protected] (Neeraj Mittal)This work was supported, in part, by the National Science Foundation (NSF) undergrants numbered CNS-1115733 and CNS-1619197. Preprint submitted to Theoretical Computer ScienceJanuary 9, 2017arXiv:1701.01539v1[cs.DS]6Jan2017