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      Hierarchical QR factorization algorithms for multi-core cluster systems

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          Abstract

          This paper describes a new QR factorization algorithm which is especially designed for massively parallel platforms combining parallel distributed multi-core nodes. These platforms make the present and the foreseeable future of high-performance computing. Our new QR factorization algorithm falls in the category of the tile algorithms which naturally enables good data locality for the sequential kernels executed by the cores (high sequential performance), low number of messages in a parallel distributed setting (small latency term), and fine granularity (high parallelism).

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          Flexible Development of Dense Linear Algebra Algorithms on Massively Parallel Architectures with DPLASMA

          George Bosilca, Aurelien Bouteiller, Anthony Danalis … (2011)
          Article 0 comments Cited 6 times – based on 0 reviews
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            Tile QR factorization with parallel panel processing for multicore architectures

            Bilel Hadri, Hatem Ltaief, Emmanuel Agullo … (2010)
            Article 0 comments Cited 4 times – based on 0 reviews     Review now
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              QR Factorization of Tall and Skinny Matrices in a Grid Computing Environment

              Emmanuel Agullo, Camille Coti, Jack Dongarra … (2009)
              Previous studies have reported that common dense linear algebra operations do not achieve speed up by using multiple geographical sites of a computational grid. Because such operations are the building blocks of most scientific applications, conventional supercomputers are still strongly predominant in high-performance computing and the use of grids for speeding up large-scale scientific problems is limited to applications exhibiting parallelism at a higher level. We have identified two performance bottlenecks in the distributed memory algorithms implemented in ScaLAPACK, a state-of-the-art dense linear algebra library. First, because ScaLAPACK assumes a homogeneous communication network, the implementations of ScaLAPACK algorithms lack locality in their communication pattern. Second, the number of messages sent in the ScaLAPACK algorithms is significantly greater than other algorithms that trade flops for communication. In this paper, we present a new approach for computing a QR factorization -- one of the main dense linear algebra kernels -- of tall and skinny matrices in a grid computing environment that overcomes these two bottlenecks. Our contribution is to articulate a recently proposed algorithm (Communication Avoiding QR) with a topology-aware middleware (QCG-OMPI) in order to confine intensive communications (ScaLAPACK calls) within the different geographical sites. An experimental study conducted on the Grid'5000 platform shows that the resulting performance increases linearly with the number of geographical sites on large-scale problems (and is in particular consistently higher than ScaLAPACK's).
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                Author and article information

                Journal
                Publication date Created: 07 October 2011
                Article
                ArXiV ID: 1110.1553
                SO-VID: 8a11332a-b043-426b-ad18-e9845c711da2
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                http://arxiv.org/licenses/nonexclusive-distrib/1.0/

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