Algorithms for optimal replica placement under correlated failure in hierarchical failure domains Abstract   In data centers, data replication is the primary method used to ensure availability of customer data. To avoid correlated failure, cloud storage infrastructure providers model hierarchical failure domains using a tree, and avoid placing 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 replicas are distributed across failure domains, but relatively little is known concerning optimization algorithms for distributing data replicas. Using a hierarchical model, we answer how to distribute replicas across failure domains optimally. We formulate a novel optimization problem for replica placement in data centers. As part of our problem, we formalize and present a new criterion for optimizing a replica placement. Our overall goal is to choose placements in which correlated failures disable as few replicas as possible.  In this work, we provide two optimization algorithms for dependency models represented by trees. We first present an    O  (  n    xcfx81  log  xe2x81xa1  xcfx81  )    time dynamic programming algorithm for optimally placing xcfx81 replicas of a single block on the leaves (representing servers) of a tree with n vertices. We next consider the problem of optimally placing replicas of multiple blocks of data, where every block may have a different replication factor. For this problem, we give a dynamic programming algorithm that runs in    O  (  n      xcfx81    max      3      xcexb4    2      m    poly  (  xcexb4  )    )   , where m denotes the number of blocks,      xcfx81    max      denotes the maximum replication factor of a block, and xcexb4 denotes the maximum difference in the replication factors of any two blocks. The running time of the algorithm is polynomial when the xcexb4, which we refer to as the skew, is a constant.

StorageReliabilityRepair TradeOffs in Distributed Storage System For reliability purpose, data redundancy is anessential in distributed storage system. In the evolving of data redundancy schemes, storagereliabilityrepair tradeoffs always exist. From replication to erasure codes, higher reliability achieves with lower storage cost, but the higher repair penalty can not be ignored. Optimized data redundancy schemes like regenerating codes or basic pyramid codes are proposed to relieve the high repair penalty. In order to study the storagereliabilityrepair tradeoffs, we propose a new model based on the standard Markov Chain, it takes the irregular fault tolerance, latent sector error and correlated failures into account, and measures the storage and repair cost from system perspective. Through interscheme and intrascheme discussions, we find some principles about choosing data redundancy schemes and corresponding parameters to achieve better storagereliabilityrepair tradeoffs. Our goal is to provide system designers and administrators with concrete information to help them achieve proper storagereliabilityrepair tradeoffs.