Efficient Block Cyclic Data Redistribution

Implementing linear algebra kernels on distributed memory parallel computers raises the problem of data distribution of matrices and vectors among the processors. Block-cyclic distribution seems to suit well for most algorithms. But one has to choose a good compromise for the size of the blocks (to achieve a good computation and communication efficiency and a good load balancing). This choice heavily depends on each operation, so it is essential to be able to go from one distribution to another very quickly. We present here the algorithms we implemented in the SCALAPACK library. A complexity study is made that proves the efficiency of our solution. Timing results on the Intel Paragon and the Cray T3D corroborates the results. We show the gain that can be obtained using the good data distribution with 3 numerical kernels and our redistribution routines

Vienna FORTRAN: A FORTRAN language extension for distributed memory multiprocessors

Exploiting the performance potential of distributed memory machines requires a careful distribution of data across the processors. Vienna FORTRAN is a language extension of FORTRAN which provides the user with a wide range of facilities for such mapping of data structures. However, programs in Vienna FORTRAN are written using global data references. Thus, the user has the advantage of a shared memory programming paradigm while explicitly controlling the placement of data. The basic features of Vienna FORTRAN are presented along with a set of examples illustrating the use of these features

ReSHAPE: A Framework for Dynamic Resizing and Scheduling of Homogeneous Applications in a Parallel Environment

Applications in science and engineering often require huge computational resources for solving problems within a reasonable time frame. Parallel supercomputers provide the computational infrastructure for solving such problems. A traditional application scheduler running on a parallel cluster only supports static scheduling where the number of processors allocated to an application remains fixed throughout the lifetime of execution of the job. Due to the unpredictability in job arrival times and varying resource requirements, static scheduling can result in idle system resources thereby decreasing the overall system throughput. In this paper we present a prototype framework called ReSHAPE, which supports dynamic resizing of parallel MPI applications executed on distributed memory platforms. The framework includes a scheduler that supports resizing of applications, an API to enable applications to interact with the scheduler, and a library that makes resizing viable. Applications executed using the ReSHAPE scheduler framework can expand to take advantage of additional free processors or can shrink to accommodate a high priority application, without getting suspended. In our research, we have mainly focused on structured applications that have two-dimensional data arrays distributed across a two-dimensional processor grid. The resize library includes algorithms for processor selection and processor mapping. Experimental results show that the ReSHAPE framework can improve individual job turn-around time and overall system throughput.Comment: 15 pages, 10 figures, 5 tables Submitted to International Conference on Parallel Processing (ICPP'07

ELSI: A Unified Software Interface for Kohn-Sham Electronic Structure Solvers

Solving the electronic structure from a generalized or standard eigenproblem is often the bottleneck in large scale calculations based on Kohn-Sham density-functional theory. This problem must be addressed by essentially all current electronic structure codes, based on similar matrix expressions, and by high-performance computation. We here present a unified software interface, ELSI, to access different strategies that address the Kohn-Sham eigenvalue problem. Currently supported algorithms include the dense generalized eigensolver library ELPA, the orbital minimization method implemented in libOMM, and the pole expansion and selected inversion (PEXSI) approach with lower computational complexity for semilocal density functionals. The ELSI interface aims to simplify the implementation and optimal use of the different strategies, by offering (a) a unified software framework designed for the electronic structure solvers in Kohn-Sham density-functional theory; (b) reasonable default parameters for a chosen solver; (c) automatic conversion between input and internal working matrix formats, and in the future (d) recommendation of the optimal solver depending on the specific problem. Comparative benchmarks are shown for system sizes up to 11,520 atoms (172,800 basis functions) on distributed memory supercomputing architectures.Comment: 55 pages, 14 figures, 2 table

A Lower Bound Technique for Communication in BSP

Communication is a major factor determining the performance of algorithms on current computing systems; it is therefore valuable to provide tight lower bounds on the communication complexity of computations. This paper presents a lower bound technique for the communication complexity in the bulk-synchronous parallel (BSP) model of a given class of DAG computations. The derived bound is expressed in terms of the switching potential of a DAG, that is, the number of permutations that the DAG can realize when viewed as a switching network. The proposed technique yields tight lower bounds for the fast Fourier transform (FFT), and for any sorting and permutation network. A stronger bound is also derived for the periodic balanced sorting network, by applying this technique to suitable subnetworks. Finally, we demonstrate that the switching potential captures communication requirements even in computational models different from BSP, such as the I/O model and the LPRAM