This paper describes a number of optimizations that can be used to support the efficient execution of irregular problems on distributed memory parallel machines. These primitives (1) coordinate interprocessor data movement, (2) manage the storage of, and access to, copies of off-processor data, (3) minimize interprocessor communication requirements and (4) support a shared name space. We present a detailed performance and scalability analysis of the communication primitives. This performance and scalability analysis is carried out using a workload generator, kernels from real applications and a large unstructured adaptive application (the molecular dynamics code CHARMM). 1 Introduction Over the past few years we have developed a methodology to produce efficient distributed memory code for sparse and unstructured problems in which array accesses are made through a level of indirection. In such problems the dependency structure is determined by variable values known only at runtime. In...

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...

. Statistics of a parallel workload on a 128-node iPSC/860 located at NASA Ames are presented. It is shown that while the number of sequential jobs dominates the number of parallel jobs, most of the resources (measured in node-seconds) were consumed by parallel jobs. Moreover, most of the sequential jobs were for system administration. The average runtime of jobs grew with the number of nodes used, so the total resource requirements of large parallel jobs were larger by more than the number of nodes they used. The job submission rate during peak day activity was somewhat lower than one every two minutes, and the average job size was small. At night, submission rate was low but job sizes and system utilization were high, mainly due to NQS. Submission rate and utilization over the weekend were lower than on weekdays. The overall utilization was 50%, after accounting for downtime. About 2/3 of the applications were executed repeatedly, some for a significant number of times....

The scalability of a parallel algorithm on a parallel architecture is a measure of its capacity to effectively utilize an increasing number of processors. Scalability analysis may be used to select the best algorithm-architecture combination for a problem under different constraints on the growth of the problem size and the number of processors. It may be used to predict the performance of a parallel algorithm and a parallel architecture for a large number of processors from the known performance on fewer processors. For a fixed problem size, it may be used to determine the optimal number of processors to be used and the maximum possible speedup that can be obtained. The objective of this paper is to critically assess the state of the art in the theory of scalability analysis, and motivate further research on the development of new and more comprehensive analytical tools to study the scalability of parallel algorithms and architectures. We survey a number of techniques and formalisms t...

A vast amount of work has been done in recent years on the design, analysis, implementation and verification of special purpose parallel computing systems. This paper presents a survey of various aspects of this work. A long, but by no means complete, bibliography is given. 1. Introduction Turing [365] demonstrated that, in principle, a single general purpose sequential machine could be designed which would be capable of efficiently performing any computation which could be performed by a special purpose sequential machine. The importance of this universality result for subsequent practical developments in computing cannot be overstated. It showed that, for a given computational problem, the additional efficiency advantages which could be gained by designing a special purpose sequential machine for that problem would not be great. Around 1944, von Neumann produced a proposal [66, 389] for a general purpose storedprogram sequential computer which captured the fundamental principles of...

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The problem of computing good graph colorings arises in many diverse applications, such as in the estimation of sparse Jacobians and in the development of efficient, parallel iterative methods for solving sparse linear systems. In this paper we present an asynchronous graph coloring heuristic well suited to distributed memory parallel computers. We present experimental results obtained on an Intel iPSC/860 which demonstrate that, for graphs arising from finite element applications, the heuristic exhibits scalable performance and generates colorings usually within three or four colors of the best-known linear time sequential heuristics. For bounded degree graphs, we show that the expected running time of the heuristic under the P-RAM computation model is bounded by EO(log(n)= log log(n)). This bound is an improvement over the previously known best upper bound for the expected running time of a random heuristic for the graph coloring problem. Key words: distributed memory computers, grap...

We construct massively parallel adaptive finite element methods for the solution of hyperbolic conservation laws. Spatial discretization is performed by a discontinuous Galerkin finite element method using a basis of piecewise Legendre polynomials. Temporal discretization utilizes a Runge-Kutta method. Dissipative fluxes and projection limiting prevent oscillations near solution discontinuities. The resulting method is of high order and may be parallelized efficiently on MIMD computers. We demonstrate parallel efficiency through computations on a 1024-processor nCUBE/2 hypercube. We present results using adaptive-refinement to reduce the computational cost of the method, and tiling, a dynamic, element-based data migration system that maintains global load balance of the adaptive method by overlapping neighborhoods of processors that each perform local balancing. 1. Introduction We are studying massively parallel adaptive finite element methods for solving systems of-dimensional hyper...

Dense linear systems of equations are quite common in science and engineering, arising in boundary element methods, least squares problems and other settings. Massively parallel computers will be necessary to solve the large systems required by scientists and engineers, and scalable parallel algorithms for the linear algebra applications must be devised for these machines. A critical step in these algorithms is the mapping of matrix elements to processors. In this paper, we study the use of the torus--wrap mapping in general dense matrix algorithms, from both theoretical and practical viewpoints. We prove that, under reasonable assumptions, this assignment scheme leads to dense matrix algorithms that achieve (to within a constant factor) the lower bound on interprocessor communication. We also show that the torus--wrap mapping allows algorithms to exhibit less idle time, better load balancing and less memory overhead than the more common row and column mappings. Finally, we discuss ...

In this paper three models of parallel speedup are studied. They are fixed-size speedup, fixed-time speedup and memory-bounded speedup. The latter two consider the relationship between speedup and problem scalability. Two sets of speedup formulations are derived for these three models. One set considers uneven workload allocation and communication overhead and gives more accurate estimation. Another set considers a simplified case and provides a clear picture on the impact of the sequential portion of an application on the possible performance gain from parallel processing. The simplified fixed-size speedup is Amdahl's law. The simplified fixed-time speedup is Gustafson's scaled speedup. The simplified memory-bounded speedup contains both Amdahl's law and Gustafson's scaled speedup as special cases. This study leads to a better understanding of parallel processing.