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Analyzing reference patterns in automatic data distribution tools

INTERNATIONAL JOURNAL OF PARALLEL PROGRAMMING 1995年第6期23卷 515-535页

作者： Ayguade, E Labarta, J Garcia, J Girones, M Valero, M Computer Architecture Department Polytechnic University of Catalunya Barcelona Spain

Most of the approaches for automatic data distribution are based on the analysis of array reference patterns within loop nests. From this analysis, a graph recording preferences and conflicts in alignment is built. This graph is partitioned deciding the reference patterns that lead to local memory accesses and the ones that require access to remote data. The estimation of this data movement cost is usually performed by matching these nonaligned reference patterns with a collection of data movement primitives. In this paper, we show the main results of a set of experiments performed to analyze the complexity of the graph used to solve alignment and the chances for finding regular data distributions among processors. Three optimizations have been performed to increase the amount of reference patterns analyzed and the information that can be obtained from their analysis: expression substitution, subscript substitution, and induction variable detection. We also evaluate the effectiveness of these transformations.

关键词： parallelizing compilers automatic data distribution distributed-memory multiprocessors array accesses communication

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A PARALLEL ALGORITHM FOR THE REDUCTION OF A NONSYMMETRIC MATRIX TO BLOCK UPPER-HESSENBERG FORM

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PARALLEL COMPUTING 1995年第8期21卷 1189-1211页

作者： BERRY, MW DONGARRA, JJ KIM, YB UNIV TENNESSEE DEPT COMP SCI KNOXVILLE TN 37996 USA OAK RIDGE NATL LAB MATH SCI SECT OAK RIDGE TN 37831 USA

In this paper, we present an algorithm for the reduction to block upper-Hessenberg form which can be used to solve the nonsymmetric eigenvalue problem on message-passing multicomputers. On such multicomputers, a nonsymmetric matrix can be distributed across processing nodes logically configured into a two-dimensional mesh using the block-cyclic data distribution. Based on the matrix partitioning and mapping, the algorithm employs both Householder reflectors and Givens rotations within each reduction step. We analyze the arithmetic and communication complexities and describe the implementation details of the algorithm on message-passing multicomputers. We discuss two different implementations - synchronous and asynchronous - and present performance results on the Intel iPSC/860 and DELTA. We conclude with an evaluation of the algorithm's communication cost, and suggest areas for further improvement.

关键词： LINEAR ALGEBRA NONSYMMETRIC EIGENVALUE PROBLEM HESSENBERG FORM distributed-memory multiprocessors

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On parallel solvers for sparse triangular systems

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JOURNAL OF SYSTEMS ARCHITECTURE 2000年第8期46卷 675-685页

作者： González, P Cabaleiro, JC Pena, TF Univ Santiago Compostela Dept Elect & Comp Sci E-15706 Santiago Spain

In this paper we describe and compare two different methods for solving general sparse triangular systems in distributed memory multiprocessor architectures. The two methods involve some preprocessing overheads so they are primarily of interest in solving many systems with the same coefficient matrix. Both algorithms start off from the idea of the classical substitution method. The first algorithm we present introduces a concept of data driven flow and makes use of non-blocking communications in order to dynamically extract the inherent parallelism of sparse systems. The second algorithm uses a reordering technique for the unknowns, so the final system can be grouped in variable blocksizes where the rows are independent and can be solved in parallel. This latter technique is called level scheduling because of the way it is represented in the adjacency graph. These methods have been tested in the Fujitsu AP1000 and the Gray T3D and T3E multicomputers. The performance has been analysed using matrices from the Harwell-Boeing collection. (C) 2000 Elsevier Science B.V. All rights reserved.

关键词： triangular systems level scheduling data driven distributed-memory multiprocessors message-passing interface (MPI)

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A VIEW OF THE LIMITATIONS, OPPORTUNITIES, AND CHALLENGES IN PARALLEL NONLINEAR OPTIMIZATION

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PARALLEL COMPUTING 1995年第6期21卷 875-905页

作者： SCHNABEL, RB Dept. of Computer Science Campus Box 430 University of Colorado Boulder CO 80309 USA

The availability and power of parallel and distributed computers is having a significant impact on how expensive problems are solved in all areas of numerical computation, and is likely to have an even larger impact in the future. This paper presents a view of how the consideration of parallelism is affecting, and is likely to affect, one important field within numerical computation, the field of nonlinear optimization. It does not attempt to survey the research that has been done in parallel nonlinear optimization. Rather it presents a set of examples, drawn mainly from our own research, that illustrate many of the limitations, opportunities, and challenges inherent in incorporating parallelism into the field of nonlinear optimization. These examples include parallel methods for unconstrained optimization problems with a small to moderate number of variables, parallel methods for large block bordered systems of nonlinear equations, and parallel methods for small-scale and large-scale global optimization problems. Our overall conclusions are mixed. For most generic optimization problems with a small to moderate number of variables, the consideration of parallelism does not appear to be leading to major algorithmic innovations. For many classes of large-scale problems, however, the consideration of parallelism appears to be creating opportunities for the development of interesting new methods that may be advantageous on parallel and sometimes even on sequential computers. In addition, a number of large-scale parallel optimization algorithms exhibit irregular, coarse-grain structure, which leads to interesting computer science challenges in areas such as dynamic scheduling and load-balancing.

关键词： NONLINEAR OPTIMIZATION UNCONSTRAINED OPTIMIZATION GENERIC OPTIMIZATION PARALLEL COMPUTERS distributed-memory multiprocessors

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HIERARCHICAL COMPILATION OF MACRO DATA-FLOW GRAPHS FOR multiprocessors WITH LOCAL memory

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IEEE TRANSACTIONS ON PARALLEL AND distributed SYSTEMS 1994年第7期5卷 720-736页

作者： PRASANNA, GNS AGARWAL, A MUSICUS, BR MIT COMP SCI LABCAMBRIDGEMA 02139 MIT ELECTR RES LABCAMBRIDGEMA 02139

This paper presents a hierarchical approach for compiling macro dataflow graphs for multiprocessors with local memory. Macro dataflow graphs comprise several nodes (or macro operations) that must be executed subject to prespecified precedence constraints. Programs consisting of multiple nested loops, where the precedence constraints between the loops are known, can be viewed as macro dataflow graphs. The hierarchical compilation approach comprises a processor allocation phase followed by a partitioning phase. In the processor allocation phase, using estimated speedup functions for the macro nodes, computationally efficient techniques establish the sequencing and parallelism of macro operations for close-to-optimal run-times. The second phase partitions the computations in each macro node to maximize communication locality for the level of parallelism determined by the processor allocation phase. The same approach can also be used for programs consisting of multiple-loop nests, when each of the nested loops can be characterized by a speedup function. These ideas have been implemented in a prototype structure-driven compiler, SDC, for expressions of matrix operations. The paper presents the performance of the compiler for several matrix expressions on a simulator of the Alewife multiprocessor.

关键词： PARALLEL PROCESSING PARALLEL COMPILATION PARALLELIZING COMPILERS COMMUNICATION LOCALITY TASK SCHEDULING distributed-memory multiprocessors CACHE-COHERENT multiprocessors

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THE FAST NUMERICAL-SOLUTION OF MILDLY NONLINEAR ELLIPTIC BOUNDARY-VALUE-PROBLEMS ON multiprocessors

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PARALLEL COMPUTING 1993年第10期19卷 1117-1128页

作者： PIROZZI, MA Naval University Institute Via A. De Gasperi 5 80138-Naples Italy

For the numerical solution of mildly nonlinear elliptic boundary value problems in a rectangle, the author already proposed in [14,15] a technique (PDFS) based on a fast method applied to the linear systems induced by a modified Picard iteration. This paper describes the implementation of the PDFS algorithm on a M X N grid using any distributed-memory multiprocessor in which a ring of p < min (M, N) processors can be embedded. The parallel PDFS features an adjustable parameter that controls the granularity of the algorithm and can be tuned to a specific architecture. A theoretical analysis shows that PDFS achieves a speedup of p in the limit of large problems sizes. Experimental timings of an implementation on a ring of transputers confirm the theoretical time model.

关键词： NONLINEAR ELLIPTIC PDE PARALLEL ALGORITHM distributed-memory multiprocessors

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A fast numerical method for mildly nonlinear parabolic initial boundary value problems .2. The parallel implementation on the intel touchstone delta system

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PARALLEL COMPUTING 1996年第9期22卷 1281-1285页

作者： Pirozzi, MA Naval University Institute Via A. De Gasperi 5 80138 Naples Italy

This paper describes the parallel implementation of a fast method for solving mildly nonlinear parabolic initial boundary value problems on the Intel Touchstone Delta system. A theoretical time complexity analysis shows that the solver achieves a perfect speedup in the limit of large problem sizes. Experimental times confirm the analytical performance model.

关键词： nonlinear parabolic PDE parallel algorithms distributed-memory multiprocessors

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Generalized multiprocessor scheduling and applications to matrix computations

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IEEE TRANSACTIONS ON PARALLEL AND distributed SYSTEMS 1996年第6期7卷 650-664页

作者： Prasanna, GNS Musicus, BR BBN LABS INC CAMBRIDGEMA 02138

This paper considerably extends the multiprocessor scheduling technique in [1], [2], and applies it to matrix arithmetic compilation. In [1], [2] we presented several new results in the theory of homogeneous multiprocessor scheduling. A directed acyclic graph (DAG) of tasks is to be scheduled. Tasks are assumed to be parallelizable-as more processors are applied to a task, the time taken to complete it decreases, yielding some speedup. Because of communication, synchronization, and task scheduling overhead, this speedup increases less than linearly with the number of processors applied. The optimal scheduling problems is to determine the number of processors assigned to each task, and task sequencing, to minimize the finishing time. Using optimal control in the special case where the speedup function of each task is p(alpha), where p is the amount of processing power applied to the task, a closed form solution for task graphs formed from parallel and series connections was derived [1], [2]. This paper extends three results for arbitrary DAGS. The optimality conditions impose nonlinear constraints on the flow of processing power from predecessors to successors, and on the finishing times of siblings. This paper presents a fast algorithm for determining and solving these nonlinear equations. The algorithm utilizes the structure of the finishing time equations to efficiently run a conjugate gradient minimization, leading to the optimal solution. The algorithm has been tested on a variety of DAGs commonly encountered in matrix arithmetic. The results show that if the p(alpha) speedup assumption holds the schedules produced are superior approaches. The algorithm has been applied to compiling matrix arithmetic [9], for the MT Alewife machine, a distributed-shared memory multiprocessor. While matrix arithmetic tasks do not exactly satisfy the p(alpha) speedup assumptions, the algorithm can be applied as a good heuristic. The results show that the schedules produced by our

关键词： DAG scheduling multiprocessor scheduling multiprocessor compilation parallel processing communication locality task scheduling distributed-memory multiprocessors

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Parallel iterative solvers involving fast wavelet transforms for the solution of BEM systems

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ADVANCES IN ENGINEERING SOFTWARE 2002年第7-10期33卷 417-426页

作者： González, P Cabaleiro, JC Pena, TF Univ A Coruna Dept Elect & Syst La Coruna 15071 Spain Univ Santiago de Compostela Dept Elect & Comp Sci Santiago De Compostela 15782 Spain

This paper describes the parallelization of a strategy to speed up the convergence of iterative methods applied to boundary element method (BEM) systems arising from problems with non-smooth boundaries and mixed boundary conditions. The aim of the work is the application of fast wavelet transforms as a black box transformation in existing boundary element codes. A new strategy was proposed, applying wavelet transforms on the interval, so it could be used in case of non-smooth coefficient matrices. Here, we describe the parallel iterative scheme and we present some of the results we have obtained. (C) 2002 Civil-Comp Ltd and Elsevier Science Ltd. All rights reserved.

关键词： dense and sparse linear systems boundary element method (BEM) wavelet transform lifting scheme iterative solvers distributed-memory multiprocessors

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Parallel iterative solvers involving fast wavelet transforms for the solution of BEM systems

Parallel iterative solvers involving fast wavelet transforms...

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2nd International Conference on Engineering Computational Technology/5th International Conference on Computational Structures Technology

作者： González, P Cabaleiro, JC Pena, TF Univ A Coruna Dept Elect & Syst La Coruna 15071 Spain Univ Santiago de Compostela Dept Elect & Comp Sci Santiago De Compostela 15782 Spain

关键词： dense and sparse linear systems boundary element method (BEM) wavelet transform lifting scheme iterative solvers distributed-memory multiprocessors

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