%0 Journal Article
%J Parallel Computing
%D 2013
%T Hierarchical QR Factorization Algorithms for Multi-core Cluster Systems
%A Jack Dongarra
%A Mathieu Faverge
%A Thomas Herault
%A Mathias Jacquelin
%A Julien Langou
%A Yves Robert
%K Cluster
%K Distributed memory
%K Hierarchical architecture
%K multi-core
%K numerical linear algebra
%K QR factorization
%X This paper describes a new QR factorization algorithm which is especially designed for massively parallel platforms combining parallel distributed nodes, where a node is a multi-core processor. These platforms represent 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). Each tile algorithm is uniquely characterized by its sequence of reduction trees. In the context of a cluster of nodes, in order to minimize the number of inter-processor communications (aka, ‘‘communication-avoiding’’), it is natural to consider hierarchical trees composed of an ‘‘inter-node’’ tree which acts on top of ‘‘intra-node’’ trees. At the intra-node level, we propose a hierarchical tree made of three levels: (0) ‘‘TS level’’ for cache-friendliness, (1) ‘‘low-level’’ for decoupled highly parallel inter-node reductions, (2) ‘‘domino level’’ to efficiently resolve interactions between local reductions and global reductions. Our hierarchical algorithm and its implementation are flexible and modular, and can accommodate several kernel types, different distribution layouts, and a variety of reduction trees at all levels, both inter-node and intra-node. Numerical experiments on a cluster of multi-core nodes (i) confirm that each of the four levels of our hierarchical tree contributes to build up performance and (ii) build insights on how these levels influence performance and interact within each other. Our implementation of the new algorithm with the DAGUE scheduling tool significantly outperforms currently available QR factorization software for all matrix shapes, thereby bringing a new advance in numerical linear algebra for petascale and exascale platforms.
%B Parallel Computing
%V 39
%P 212-232
%8 2013-05
%G eng
%N 4-5
%0 Journal Article
%J Journal of Parallel and Distributed Computing
%D 2013
%T Kernel-assisted and topology-aware MPI collective communications on multi-core/many-core platforms
%A Teng Ma
%A George Bosilca
%A Aurelien Bouteiller
%A Jack Dongarra
%K Cluster
%K Collective communication
%K Hierarchical
%K HPC
%K MPI
%K Multicore
%X Multicore Clusters, which have become the most prominent form of High Performance Computing (HPC) systems, challenge the performance of MPI applications with non-uniform memory accesses and shared cache hierarchies. Recent advances in MPI collective communications have alleviated the performance issue exposed by deep memory hierarchies by carefully considering the mapping between the collective topology and the hardware topologies, as well as the use of single-copy kernel assisted mechanisms. However, on distributed environments, a single level approach cannot encompass the extreme variations not only in bandwidth and latency capabilities, but also in the capability to support duplex communications or operate multiple concurrent copies. This calls for a collaborative approach between multiple layers of collective algorithms, dedicated to extracting the maximum degree of parallelism from the collective algorithm by consolidating the intra- and inter-node communications. In this work, we present HierKNEM, a kernel-assisted topology-aware collective framework, and the mechanisms deployed by this framework to orchestrate the collaboration between multiple layers of collective algorithms. The resulting scheme maximizes the overlap of intra- and inter-node communications. We demonstrate experimentally, by considering three of the most used collective operations (Broadcast, Allgather and Reduction), that (1) this approach is immune to modifications of the underlying process-core binding; (2) it outperforms state-of-art MPI libraries (Open MPI, MPICH2 and MVAPICH2) demonstrating up to a 30x speedup for synthetic benchmarks, and up to a 3x acceleration for a parallel graph application (ASP); (3) it furthermore demonstrates a linear speedup with the increase of the number of cores per compute node, a paramount requirement for scalability on future many-core hardware.
%B Journal of Parallel and Distributed Computing
%V 73
%P 1000-1010
%8 2013-07
%G eng
%U http://www.sciencedirect.com/science/article/pii/S0743731513000166
%N 7
%R 10.1016/j.jpdc.2013.01.015