Direct QR factorizations for tall-and-skinny matrices in MapReduce architectures

The QR factorization and the SVD are two fundamental matrix decompositions with applications throughout scientific computing and data analysis. For matrices with many more rows than columns, so-called "tall-and-skinny matrices," there is a numerically stable, efficient, communication-avoiding algorithm for computing the QR factorization. It has been used in traditional high performance computing and grid computing environments. For MapReduce environments, existing methods to compute the QR decomposition use a numerically unstable approach that relies on indirectly computing the Q factor. In the best case, these methods require only two passes over the data. In this paper, we describe how to compute a stable tall-and-skinny QR factorization on a MapReduce architecture in only slightly more than 2 passes over the data. We can compute the SVD with only a small change and no difference in performance. We present a performance comparison between our new direct TSQR method, a standard unstable implementation for MapReduce (Cholesky QR), and the classic stable algorithm implemented for MapReduce (Householder QR). We find that our new stable method has a large performance advantage over the Householder QR method. This holds both in a theoretical performance model as well as in an actual implementation

A Tale of Two Data-Intensive Paradigms: Applications, Abstractions, and Architectures

Scientific problems that depend on processing large amounts of data require overcoming challenges in multiple areas: managing large-scale data distribution, co-placement and scheduling of data with compute resources, and storing and transferring large volumes of data. We analyze the ecosystems of the two prominent paradigms for data-intensive applications, hereafter referred to as the high-performance computing and the Apache-Hadoop paradigm. We propose a basis, common terminology and functional factors upon which to analyze the two approaches of both paradigms. We discuss the concept of "Big Data Ogres" and their facets as means of understanding and characterizing the most common application workloads found across the two paradigms. We then discuss the salient features of the two paradigms, and compare and contrast the two approaches. Specifically, we examine common implementation/approaches of these paradigms, shed light upon the reasons for their current "architecture" and discuss some typical workloads that utilize them. In spite of the significant software distinctions, we believe there is architectural similarity. We discuss the potential integration of different implementations, across the different levels and components. Our comparison progresses from a fully qualitative examination of the two paradigms, to a semi-quantitative methodology. We use a simple and broadly used Ogre (K-means clustering), characterize its performance on a range of representative platforms, covering several implementations from both paradigms. Our experiments provide an insight into the relative strengths of the two paradigms. We propose that the set of Ogres will serve as a benchmark to evaluate the two paradigms along different dimensions.Comment: 8 pages, 2 figure

Desarrollo de algoritmos genéticos utilizando diferentes frameworks de MapReduce: MPI vs. Hadoop

MapReduce es un paradigma popular, que permite a los usuarios no especializados utilizar grandes plataformas computacionales paralelas de manera transparente. Hadoop es la implementación más utilizada de este paradigma y, de hecho, para una gran cantidad de usuarios, la palabra Hadoop y MapReduce son intercambiables. Pero, hay otros framewoks que implementan este paradigma de programación, como MapReduce-MPI. Dado que las técnicas de optimización pueden beneficiarse enormemente de este tipo de modelado informático de uso intensivo de datos, en esta línea de investigacón analizamos el efecto del rendimiento del desarrollo de algoritmos genéticos (GA) utilizando diferentes marcos de MapReduce (MRGA).Eje: Agentes y Sistemas Inteligentes.Red de Universidades con Carreras en Informátic

Desarrollo de algoritmos genéticos utilizando diferentes frameworks de MapReduce: MPI vs. Hadoop

MapReduce es un paradigma popular, que permite a los usuarios no especializados utilizar grandes plataformas computacionales paralelas de manera transparente. Hadoop es la implementación más utilizada de este paradigma y, de hecho, para una gran cantidad de usuarios, la palabra Hadoop y MapReduce son intercambiables. Pero, hay otros framewoks que implementan este paradigma de programación, como MapReduce-MPI. Dado que las técnicas de optimización pueden beneficiarse enormemente de este tipo de modelado informático de uso intensivo de datos, en esta línea de investigacón analizamos el efecto del rendimiento del desarrollo de algoritmos genéticos (GA) utilizando diferentes marcos de MapReduce (MRGA).Eje: Agentes y Sistemas Inteligentes.Red de Universidades con Carreras en Informátic