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93
Highly scalable parallel algorithms for sparse matrix factorization
 IEEE Transactions on Parallel and Distributed Systems
, 1994
"... In this paper, we describe a scalable parallel algorithm for sparse matrix factorization, analyze their performance and scalability, and present experimental results for up to 1024 processors on a Cray T3D parallel computer. Through our analysis and experimental results, we demonstrate that our algo ..."
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Cited by 120 (30 self)
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In this paper, we describe a scalable parallel algorithm for sparse matrix factorization, analyze their performance and scalability, and present experimental results for up to 1024 processors on a Cray T3D parallel computer. Through our analysis and experimental results, we demonstrate that our algorithm substantially improves the state of the art in parallel direct solution of sparse linear systems—both in terms of scalability and overall performance. It is a well known fact that dense matrix factorization scales well and can be implemented efficiently on parallel computers. In this paper, we present the first algorithm to factor a wide class of sparse matrices (including those arising from two and threedimensional finite element problems) that is asymptotically as scalable as dense matrix factorization algorithms on a variety of parallel architectures. Our algorithm incurs less communication overhead and is more scalable than any previously known parallel formulation of sparse matrix factorization. Although, in this paper, we discuss Cholesky factorization of symmetric positive definite matrices, the algorithms can be adapted for solving sparse linear least squares problems and for Gaussian elimination of diagonally dominant matrices that are almost symmetric in structure. An implementation of our sparse Cholesky factorization algorithm delivers up to 20 GFlops on a Cray T3D for mediumsize structural engineering and linear programming problems. To the best of our knowledge,
Scalable Load Balancing Techniques for Parallel Computers
, 1994
"... In this paper we analyze the scalability of a number of load balancing algorithms which can be applied to problems that have the following characteristics : the work done by a processor can be partitioned into independent work pieces; the work pieces are of highly variable sizes; and it is not po ..."
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Cited by 106 (16 self)
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In this paper we analyze the scalability of a number of load balancing algorithms which can be applied to problems that have the following characteristics : the work done by a processor can be partitioned into independent work pieces; the work pieces are of highly variable sizes; and it is not possible (or very difficult) to estimate the size of total work at a given processor. Such problems require a load balancing scheme that distributes the work dynamically among different processors. Our goal here is to determine the most scalable load balancing schemes for different architectures such as hypercube, mesh and network of workstations. For each of these architectures, we establish lower bounds on the scalability of any possible load balancing scheme. We present the scalability analysis of a number of load balancing schemes that have not been analyzed before. This gives us valuable insights into their relative performance for different problem and architectural characteristi...
Parallel Performance Prediction using Lost Cycles Analysis
 IN PROCEEDINGS OF SUPERCOMPUTING '94
, 1994
"... Most performance debugging and tuning of parallel programs is based on the "measuremodify" approach, which is heavily dependent on detailed measurements of programs during execution. This approach is extremely timeconsuming and does not lend itself to predicting performance under varying ..."
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Cited by 70 (1 self)
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Most performance debugging and tuning of parallel programs is based on the "measuremodify" approach, which is heavily dependent on detailed measurements of programs during execution. This approach is extremely timeconsuming and does not lend itself to predicting performance under varying conditions. Analytic modeling and scalability analysis provide predictive power, but are not widely used inpractice, due primarily to their emphasis on asymptotic behavior and the difficulty of developing accurate models that work for realworld programs. In this paper we describe a set of tools for performance tuning of parallel programs that bridges this gap between measurement and modeling. Our approach is based on lost cycles analysis, which involves measurement and modeling of all sources of overhead in a parallel program. We first describe a tool for measuring overheads in parallel programs that we have incorporated into the runtime environment for Fortran programs on the Kendall Square KSR1. We then describe a tool that ts these overhead measurements to analytic forms. We illustrate the use of these tools by analyzing the performance tradeoffs among parallel implementations of 2D FFT. These examples show how our tools enable programmers to develop accurate performance models of parallel applications without requiring extensive performance modeling expertise.
Statistical Scalability Analysis of Communication Operations in Distributed Applications
"... Current trends in high performance computing suggest that users will soon have widespread access to clusters of multiprocessors with hundreds, if not thousands, of processors. This unprecedented degree of parallelism will undoubtedly expose scalability limitations in existing applications, where sca ..."
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Cited by 48 (2 self)
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Current trends in high performance computing suggest that users will soon have widespread access to clusters of multiprocessors with hundreds, if not thousands, of processors. This unprecedented degree of parallelism will undoubtedly expose scalability limitations in existing applications, where scalability is the ability of a parallel algorithm on a parallel architecture to effectively utilize an increasing number of processors. Users will need precise and automated techniques for detecting the cause of limited scalability. This paper addresses this dilemma. First, we argue that users face numerous challenges in understanding application scalability: managing substantial amounts of experiment data, extracting useful trends from this data, and reconciling performance information with their application's design. Second, we propose a solution to automate this data analysis problem by applying fundamental statistical techniques to scalability experiment data. Finally, we evaluate our operational prototype on several applications, and show that statistical techniques offer an effective strategy for assessing application scalability. In particular, we find that nonparametric correlation of the number of tasks to the ratio of the time for communication operations to overall communication time provides a reliable measure for identifying communication operations that scale poorly. 1
An Extensible MetaLearning Approach for Scalable and Accurate Inductive Learning
, 1996
"... Much of the research in inductive learning concentrates on problems with relatively small amounts of data. With the coming age of ubiquitous network computing, it is likely that orders of magnitude more data in databases will be available for various learning problems of real world importance. Som ..."
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Cited by 48 (8 self)
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Much of the research in inductive learning concentrates on problems with relatively small amounts of data. With the coming age of ubiquitous network computing, it is likely that orders of magnitude more data in databases will be available for various learning problems of real world importance. Some learning algorithms assume that the entire data set fits into main memory, which is not feasible for massive amounts of data, especially for applications in data mining. One approach to handling a large data set is to partition the data set into subsets, run the learning algorithm on each of the subsets, and combine the results. Moreover, data can be inherently distributed across multiple sites on the network and merging all the data in one location can be expensive or prohibitive. In this thesis we propose, investigate, and evaluate a metalearning approach to integrating the results of mul...
Unstructured Tree Search on SIMD Parallel Computers
 IEEE Transactions on Parallel and Distributed Systems
, 1994
"... In this paper, we present new methods for load balancing of unstructured tree computations on largescale SIMD machines, and analyze the scalability of these and other existing schemes. An efficient formulation of tree search on a SIMD machine comprises of two major components: (i) a triggering mech ..."
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Cited by 38 (15 self)
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In this paper, we present new methods for load balancing of unstructured tree computations on largescale SIMD machines, and analyze the scalability of these and other existing schemes. An efficient formulation of tree search on a SIMD machine comprises of two major components: (i) a triggering mechanism, which determines when the search space redistribution must occur to balance search space over processors; and (ii) a scheme to redistribute the search space. We have devised a new redistribution mechanism and a new triggering mechanism. Either of these can be used in conjunction with triggering and redistribution mechanisms developed by other researchers. We analyze the scalability of these mechanisms, and verify the results experimentally. The analysis and experiments show that our new load balancing methods are highly scalable on SIMD architectures. Their scalability is shown to be no worse than that of the best load balancing schemes on MIMD architectures. We verify our theoretical...
Scalability of parallel algorithms for the allpairs shortest path problem
 in the Proceedings of the International Conference on Parallel Processing
, 1991
"... Abstract This paper uses the isoefficiency metric to analyze the scalability of several parallel algorithms for finding shortest paths between all pairs of nodes in a densely connected graph. Parallel algorithms analyzed in this paper have either been previously presented elsewhere or are small vari ..."
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Cited by 36 (14 self)
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Abstract This paper uses the isoefficiency metric to analyze the scalability of several parallel algorithms for finding shortest paths between all pairs of nodes in a densely connected graph. Parallel algorithms analyzed in this paper have either been previously presented elsewhere or are small variations of them. Scalability is analyzed with respect to mesh, hypercube and sharedmemory architectures. We demonstrate that isoefficiency functions are a compact and useful predictor of performance. In fact, previous comparative predictions of some of the algorithms based on experimental results are shown to be incorrect whereas isoefficiency functions predict correctly. We find the classic tradeoffs of hardware cost vs. time and memory vs. time to be represented here as tradeoffs of hardware cost vs. scalability and memory vs. scalability.
Performance and scalability of preconditioned conjugate gradient methods on parallel computers
 Department of Computer Science, University of Minnesota
, 1995
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Ordinal Optimization of DEDS
, 1996
"... . In this paper we argue that ordinal rather than cardinal optimization, i.e., concentrating on finding good, better, or best designs rather than on estimating accurately the performance value of these designs, offers a new, efficient, and complementary approach to the performance optimization of sy ..."
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Cited by 28 (4 self)
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. In this paper we argue that ordinal rather than cardinal optimization, i.e., concentrating on finding good, better, or best designs rather than on estimating accurately the performance value of these designs, offers a new, efficient, and complementary approach to the performance optimization of systems. Some experimental and analytical evidence is offered to substantiate this claim. The main purpose of the paper is to call attention to a novel and promising approach to system optimization. Original: Aug. 20, 1991 First Revision: Nov. 22, 1991 Second Revision: Jan 29, 1992 Acknowledgement: This work is supported by NSF grants CDR8803012, DDM8914277, ONR contracts N0001490J1093, N0001489J1023, and Army contracts DAAL0383 K0171, DAAL91G0194. Ordinal Optimization of DEDS Version: 11/12/96 2 1. Introduction and Rationale The problem of stochastic optimization of a multivariable function J(q) º E[L(x(t; q,x)] (1) where q, is the design parameter, L, some performance fun...