CORE: Augmenting Regenerating-Coding-Based Recovery for Single and Concurrent Failures in Distributed Storage Systems

Data availability is critical in distributed storage systems, especially when node failures are prevalent in real life. A key requirement is to minimize the amount of data transferred among nodes when recovering the lost or unavailable data of failed nodes. This paper explores recovery solutions based on regenerating codes, which are shown to provide fault-tolerant storage and minimum recovery bandwidth. Existing optimal regenerating codes are designed for single node failures. We build a system called CORE, which augments existing optimal regenerating codes to support a general number of failures including single and concurrent failures. We theoretically show that CORE achieves the minimum possible recovery bandwidth for most cases. We implement CORE and evaluate our prototype atop a Hadoop HDFS cluster testbed with up to 20 storage nodes. We demonstrate that our CORE prototype conforms to our theoretical findings and achieves recovery bandwidth saving when compared to the conventional recovery approach based on erasure codes.Comment: 25 page

What broke where for distributed and parallel applications — a whodunit story

Detection, diagnosis and mitigation of performance problems in today\u27s large-scale distributed and parallel systems is a difficult task. These large distributed and parallel systems are composed of various complex software and hardware components. When the system experiences some performance or correctness problem, developers struggle to understand the root cause of the problem and fix in a timely manner. In my thesis, I address these three components of the performance problems in computer systems. First, we focus on diagnosing performance problems in large-scale parallel applications running on supercomputers. We developed techniques to localize the performance problem for root-cause analysis. Parallel applications, most of which are complex scientific simulations running in supercomputers, can create up to millions of parallel tasks that run on different machines and communicate using the message passing paradigm. We developed a highly scalable and accurate automated debugging tool called PRODOMETER, which uses sophisticated algorithms to first, create a logical progress dependency graph of the tasks to highlight how the problem spread through the system manifesting as a system-wide performance issue. Second, uses this logical progress dependence graph to identify the task where the problem originated. Finally, PRODOMETER pinpoints the code region corresponding to the origin of the bug. Second, we developed a tool-chain that can detect performance anomaly using machine-learning techniques and can achieve very low false positive rate. Our input-aware performance anomaly detection system consists of a scalable data collection framework to collect performance related metrics from different granularity of code regions, an offline model creation and prediction-error characterization technique, and a threshold based anomaly-detection-engine for production runs. Our system requires few training runs and can handle unknown inputs and parameter combinations by dynamically calibrating the anomaly detection threshold according to the characteristics of the input data and the characteristics of the prediction-error of the models. Third, we developed performance problem mitigation scheme for erasure-coded distributed storage systems. Repair operations of the failed blocks in erasure-coded distributed storage system take really long time in networked constrained data-centers. The reason being, during the repair operation for erasure-coded distributed storage, a lot of data from multiple nodes are gathered into a single node and then a mathematical operation is performed to reconstruct the missing part. This process severely congests the links toward the destination where newly recreated data is to be hosted. We proposed a novel distributed repair technique, called Partial-Parallel-Repair (PPR) that performs this reconstruction in parallel on multiple nodes and eliminates network bottlenecks, and as a result, greatly speeds up the repair process. Fourth, we study how for a class of applications, performance can be improved (or performance problems can be mitigated) by selectively approximating some of the computations. For many applications, the main computation happens inside a loop that can be logically divided into a few temporal segments, we call phases. We found that while approximating the initial phases might severely degrade the quality of the results, approximating the computation for the later phases have very small impact on the final quality of the result. Based on this observation, we developed an optimization framework that for a given budget of quality-loss, would find the best approximation settings for each phase in the execution

Lagrange Coded Computing: Optimal Design for Resiliency, Security and Privacy

We consider a scenario involving computations over a massive dataset stored distributedly across multiple workers, which is at the core of distributed learning algorithms. We propose Lagrange Coded Computing (LCC), a new framework to simultaneously provide (1) resiliency against stragglers that may prolong computations; (2) security against Byzantine (or malicious) workers that deliberately modify the computation for their benefit; and (3) (information-theoretic) privacy of the dataset amidst possible collusion of workers. LCC, which leverages the well-known Lagrange polynomial to create computation redundancy in a novel coded form across workers, can be applied to any computation scenario in which the function of interest is an arbitrary multivariate polynomial of the input dataset, hence covering many computations of interest in machine learning. LCC significantly generalizes prior works to go beyond linear computations. It also enables secure and private computing in distributed settings, improving the computation and communication efficiency of the state-of-the-art. Furthermore, we prove the optimality of LCC by showing that it achieves the optimal tradeoff between resiliency, security, and privacy, i.e., in terms of tolerating the maximum number of stragglers and adversaries, and providing data privacy against the maximum number of colluding workers. Finally, we show via experiments on Amazon EC2 that LCC speeds up the conventional uncoded implementation of distributed least-squares linear regression by up to $13.43\times$, and also achieves a $2.36\times$-$12.65\times$ speedup over the state-of-the-art straggler mitigation strategies

Lagrange Coded Computing: Optimal Design for Resiliency, Security, and Privacy

We consider a scenario involving computations over a massive dataset stored distributedly across multiple workers, which is at the core of distributed learning algorithms. We propose Lagrange Coded Computing (LCC), a new framework to simultaneously provide (1) resiliency against stragglers that may prolong computations; (2) security against Byzantine (or malicious) workers that deliberately modify the computation for their benefit; and (3) (information-theoretic) privacy of the dataset amidst possible collusion of workers. LCC, which leverages the well-known Lagrange polynomial to create computation redundancy in a novel coded form across workers, can be applied to any computation scenario in which the function of interest is an arbitrary multivariate polynomial of the input dataset, hence covering many computations of interest in machine learning. LCC significantly generalizes prior works to go beyond linear computations. It also enables secure and private computing in distributed settings, improving the computation and communication efficiency of the state-of-the-art. Furthermore, we prove the optimality of LCC by showing that it achieves the optimal tradeoff between resiliency, security, and privacy, i.e., in terms of tolerating the maximum number of stragglers and adversaries, and providing data privacy against the maximum number of colluding workers. Finally, we show via experiments on Amazon EC2 that LCC speeds up the conventional uncoded implementation of distributed least-squares linear regression by up to 13.43×, and also achieves a 2.36×-12.65× speedup over the state-of-the-art straggler mitigation strategies

Quantum Computing: Pro and Con

I assess the potential of quantum computation. Broad and important applications must be found to justify construction of a quantum computer; I review some of the known quantum algorithms and consider the prospects for finding new ones. Quantum computers are notoriously susceptible to making errors; I discuss recently developed fault-tolerant procedures that enable a quantum computer with noisy gates to perform reliably. Quantum computing hardware is still in its infancy; I comment on the specifications that should be met by future hardware. Over the past few years, work on quantum computation has erected a new classification of computational complexity, has generated profound insights into the nature of decoherence, and has stimulated the formulation of new techniques in high-precision experimental physics. A broad interdisciplinary effort will be needed if quantum computers are to fulfill their destiny as the world's fastest computing devices. (This paper is an expanded version of remarks that were prepared for a panel discussion at the ITP Conference on Quantum Coherence and Decoherence, 17 December 1996.)Comment: 17 pages, LaTeX, submitted to Proc. Roy. Soc. Lond. A, minor correction