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Efficient compilation of high-level data parallel algorithms 94

Efficient compilation of high-level data parallel algorithms

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proceedings of the 6th annual acm symposium on parallel algorithms and architectures

作者： Suciu, Dan Tannen, Val Univ. of Pennsylvania Philadelpia

ISBN: (纸本)9780897916714

We present a high-level parallel calculus for nested sequences, NSC, offered as a possible theoretical “core” of an entire class of collection-oriented parallel languages. NSC is based on while-loops as opposed to general recursion. A formal, machine independent definition of the parallel time complexity and the work complexity of programs in NSC is given. Our main results are: (1) We give a translation method for a particular form of recursion, called map-recursion, into NSC, that preserves the time complexity and adds an arbitrarily small overhead to the work complexity, and (2) We give a compilation method for NSC into a very simple vector parallel machine, which preserves the time complexity and again adds an arbitrarily small overhead to the work complexity.

关键词： Calculations

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Modeling communication in parallel algorithms. A fruitful interaction between theory and systems? 94

Modeling communication in parallel algorithms. A fruitful in...

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proceedings of the 6th annual acm symposium on parallel algorithms and architectures

作者： Pal, Singh, Jaswinder Rothberg, Edward Gupta, Anoop Computer Systems Laboratory Stanford University Stanford CA Intel Supercomputer Systems 14924 NW Greenbrier Pkwy C06-09 Beaverton OR

ISBN: (纸本)9780897916714

Recently, several theoretical models of parallel architectures have been proposed to replace the PRAM as the model that is presented to an algorithm designer. A primary focus of the new models is to include the cost of interprocessor communication, which is increasingly important in modern parallel architectures. We argue that modeling the communication costs in the architecture or system is only one part of the problem. The other, and usually much more difficult, part is modeling the communication properties of the algorithm itself, which provides necessary inputs into the architectural model to determine overall complexity. In this context, we make three main points in this paper: (i) It is incomplete to describe communication without regard to its relationship with replication. We propose a description of the communication-replication relationship in terms of the working set hierarchy of an algorithm. (ii) Both inherent communication and the communication-replication relationship can be very difficult to model in irregular, dynamic computations that are crucial in many real-world applications. We present some examples that demonstrate this difficulty. (iii) We believe that substantial leverage can be obtained in this effort from the computer systems community, which can provide a hierarchy of simulation and profiling tools—from abstract to detailed—tailored to the needs of the algorithm designers. We propose an initial set of simulation tools, and we discuss possible future refinements to this set.

关键词： parallel architectures

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SCHEDULING MALLEABLE AND NONMALLEABLE parallel TASKS

SCHEDULING MALLEABLE AND NONMALLEABLE PARALLEL TASKS

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5th annual acm-SIAM symposium on Discrete algorithms

作者： LUDWIG, W TIWARI, P UNIV WISCONSIN DEPT COMP SCIMADISONWI 53706

ISBN: (纸本)0898713293

A malleable parallel task is one that can be executed on any number of processors, with its execution time being a function of the number of processors allotted to it. A nonmalleable parallel task is one that requires a specific number of processors. Given n independent parallel tasks and m identical processors, we consider the problem of scheduling these tasks to minimize makespan. We show that any algorithm for scheduling nonmalleable tasks can be extended to an algorithm for scheduling malleable tasks. The approximation factor of the new algorithm is identical to that of the original algorithm. Meanwhile, only an O(mn) term is added to the running time. Thus we get the best known approximation factor of a polynomial-time algorithm for scheduling malleable parallel tasks, and the fastest running time in which that factor can be achieved. These results can be extended to specific parallel architectures, where not only the number of processors allotted to a task, but also their configuration is a factor. Furthermore, we provide an algorithm for scheduling malleable tasks on a linear array of processors. In this case the addresses of the processors assigned to each task must be contiguous. Our algorithm has an approximation factor of 2, under a natural assumption on the task execution times. In contrast, the best known approximation factor for nonmalleable tasks in this case is 2.5. To the best of our knowledge, this is the only case where the best known approximation factor for malleable tasks is strictly less than that for nonmalleable tasks.

关键词： Storage allocation (computer)

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List ranking and list scan on the Cray C-90 94

List ranking and list scan on the Cray C-90

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6th annual acm symposium on parallel algorithms and architectures, SPAA 1994

作者： Reid-Miller, Margaret School of Computer Science Carnegie Mellon University PittsburghPA15213-3891 United States

ISBN: (纸本)0897916719

List ranking and list scan are two primitive operations used in many parallel algorithms that use list, trees, and graph data structures. But vectorizing and parallelizing list ranking is a challenge because it is highly communication intensive and dynamic. In addition, the serial algorithm is very simple and has very small constants. In order to compete, a parallel algorithm must also be simple and have small constants. A parallel algorithm due to Wyllie is such an algorithm, but it is not work efficient-its performance degrades for longer and longer linked lists. In contrast, work efficient PRAM algorithms developed to date have very large constants. We introduce a new fully vectorized and parallelized algorithm that both is work efficient and has small constants. It does not achieve O(log n) running time, but we contend that work efficiency and small constants is more important, given that vector and multiprocessor machines are used for problems that are much larger than the number of processors and, therefore, the O(log n) time is never achieved in practice. In particular, to the best of our knowledge, our implementation of list ranking and list scan on the Cray C-90 is the fastest implementation to date. In addition, it is the first implementation of which we are aware that outperforms fast workstations. The success of our algorithm is due to its relatively large grain size and simplicity of the inner loops, and the success of the implementation is due to pipelining reads and writes through vectorization to hide latency, minimizing load balancing by deriving equations for predicting and optimizing performance, and avoiding conditional tests except when load balancing. © 1994 acm.

关键词： parallel algorithms

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Studying overheads in massively parallel Min/Max-tree evaluation (extended abstract) 94

Studying overheads in massively parallel Min/Max-tree evalua...

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6th annual acm symposium on parallel algorithms and architectures, SPAA 1994

作者： Feldmann, Rainer Mysliwietz, Peter Monien, Burkhard Department of Mathematics and Computer Science University of Paderborn Germany

ISBN: (纸本)0897916719

In this paper we study the overheads arising in our algorithm for distributed evaluation of Min/Max trees. The overheads are classified into search overhead, performance loss, and decrease of work load. Several mechanisms are investigated to cope with these overheads in order to achieve a high performance. We study a combination of local, medium range, and global load distribution strategies that does not only show a good behavior in terms of work load, but also has a positive influence on the search overhead. The efficient use of a virtual shared memory, that is distributed among the processors, shows also a big contribution to the overall performance of the system. A carefully restricted application of parallelism using an improved version of the Young Brothers Wait Concept (YBWC) leads to a perfect behavior for minimal Min/Max trees and to a quite low search overhead, if well ordered trees are searched. Well ordered trees constitute the most important case in practice, since a couple of move ordering mechanisms are known that achieve a nearly optimal move ordering in many applications. The resulting combination of the methods shows an efficiency better than any previous approach. Experiments carried out using 256 DeBruijn-connected Transputers result in a speedup of 142 even applying restricted timing constraints. With a system consisting of 1024 grid connected Transputers we obtain a speedup of 344. Moreover the algorithm shows a very good scalability, especially using interconnection networks with logarithmic diameter. The experiments have been carried out using a Min/Max search program that incorporates all important state-of-the- art search techniques (Zugzwang, current vice world champion in computer chess) and therefore makes sure, that no artificial or simplifying assumptions on the structure of the problem are made. © 1994 acm.

关键词： Transputers

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Dynamic load balancing in parallel and distributed networks by random matchings (extended abstract) 94

Dynamic load balancing in parallel and distributed networks ...

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6th annual acm symposium on parallel algorithms and architectures, SPAA 1994

作者： Ghosh, Bhaskar Muthukrishnan, S. Department of Computer Science Yale University P.O. Box 208285 New HavenCT06520 United States Courant Institute of Mathematical Sciences New York University 251 Mercer Street New YorkNY10012-1185 United States

ISBN: (纸本)0897916719

The fundamental problems in dynamic load balancing and job scheduling in parallel and distributed computers involve moving load between processors. In this paper, we consider a new model for load movement in synchronous parallel and distributed machines. In each step of our model, each processor can transfer load to at most one neighbor;also, any amount of load can be moved along a communication link between two processors in one step. This is a reasonable model for load movement in significant classes of dynamic load balancing problems. We derive efficient algorithms for a number of task reallocation problems under our model of load movement. These include dynamic load balancing on processor networks, adaptive mesh re-partitioning such as those in finite element methods, and progressive job migration under dynamic generation and consumption of load. To obtain the above-mentioned results, we introduce and solve the abstract problem of Incremental Weight Migration (IWM) on arbitrary graphs. Our main result is a simple, randomized, algorithm for this problem which provably results in asymptotically optimal convergence towards the state where weights on the nodes of the graph are all equal. This algorithm utilizes an appropriate random set of edges forming a matching. Our algorithm for the IWM problem is used in deriving efficient algorithms for all the problems mentioned above. Our results are very general. The algorithms we derive are local, and hence, scalable. They work for arbitrary load distributions and for networks of arbitrary topology which can possibly undergo link failures. Of independent interest is our proof technique which we use to lower bound the convergence of our algorithms in terms of the eigenstructure of the underlying graph. Finally, we present preliminary experimental results analyzing issues in load balancing related to our algorithms. © 1994 acm.

关键词： parallel processing systems

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Efficient low-contention parallel algorithms 94

Efficient low-contention parallel algorithms

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proceedings of the 6th annual acm symposium on parallel algorithms and architectures

作者： Gibbons, Philip B. Matias, Yossi Ramachandran, Vijaya AT&T Bell Laboratories 600 Mountain Ave. Murray Hill NJ Dept. of Computer Sciences University of Texas Austin TX

ISBN: (纸本)9780897916714

The queue-read, queue-write (QRQW) PRAM model [GMR94] permits concurrent reading and writing, but at a cost proportional to the number of readers/writers to a memory location in a given step. The QRQW model reflects the contention properties of most parallel machines more accurately than either the well-studied CRCW or EREW models: the CRCW model does not adequately penalize algorithms with high contention to shared memory locations, while the EREW model is too strict in its insistence on zero contention at each step. Of primary practical and theoretical interest, then, is the design of fast and efficient QRQW algorithms for problems for which all previous algorithms either suffer from high contention, fail to be fast, or fail to be *** paper describes low-contention, fast, work-optimal QRQW PRAM algorithms for the fundamental problems of finding a random permutation, parallel hashing, load balancing, and sorting. There is no known fast, work-optimal EREW algorithm known for finding a random permutation or for parallel hashing. For load balancing, we improve upon the EREW result whenever the ratio of the maximum to the average load is not too large. We show that the logarithmic dependence of the QRQW running time on this ratio is inherent by providing a matching lower *** demonstrate the performance advantage of a QRQW random permutation algorithm, compared with the popular EREW algorithm, by implementing and running both algorithms on the MasPar ***, we extend the work-time framework for the design of parallel algorithms to account for contention, and relate it to the QRQW PRAM model. We use our QRQW load balancing algorithm, as well as the QRQW linear compaction algorithm in [GMR94], to provide automatic tools for processor allocation—an issue that needs to be handled when translating an algorithm from its work-time presentation into the explicit PRAM description.

关键词： parallel algorithms

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Experiences with parallel N-body simulation 94

Experiences with parallel N-body simulation

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proceedings of the 6th annual acm symposium on parallel algorithms and architectures

作者： Liu, Pangfeng Bhatt, Sandeep N. DIMACS Rutgers University Piscataway NJ Bell Communications Research Morristown NJ

ISBN: (纸本)9780897916714

This paper describes our experiences developing high-performance code for astrophysical N-body simulations. Recent N-body methods are based on an adaptive tree structure. The tree must be built and maintained across physically distributed memory; moreover, the communication requirements are irregular and adaptive. Together with the need to balance the computational work-load among processors, these issues pose interesting challenges and tradeoffs for high-performance *** implementation was guided by the need to keep solutions simple and general. We use a technique for implicitly representing a dynamic global tree across multiple processors which substantially reduces the programming complexity as well as the performance overheads of distributed memory architectures. The contributions include methods to vectorize the computation and minimize communication time which are theoretically and experimentally *** code has been tested by varying the number and distribution of bodies on different configurations of the Connection Machine CM-5. The overall performance on instances with 10 million bodies is typically over 30% of the peak machine rate. Preliminary timings compare favorably with other approaches.

关键词： Memory architecture

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Dynamic parallel tree contraction 94

Dynamic parallel tree contraction

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proceedings of the 6th annual acm symposium on parallel algorithms and architectures

作者： Reif, John H. Tate, Stephen R. Carnegie Mellon Univ. Pittsburgh PA Univ. of North Texas Denton TX

ISBN: (纸本)9780897916714

parallel tree contraction has been found to be a useful and quite powerful tool for the design of a wide class of efficient graph algorithms. We propose a corresponding technique for the parallel solution of incremental problems. As our computational model, we assume a variant of the CRCW PRAM where we can dynamically activate processors by a forking *** consider a dynamic binary tree T of ≤ n nodes and unbounded depth. We describe a procedure, which we call the dynamic parallel tree contraction algorithm, which incrementally processes various parallel modification requests and queries:(1)parallel requests to add or delete leaves of T, or modify labels of internal nodes or leaves of T, and also(2) parallel tree contraction queries which require recomputingvalues at specified nodes. Each modification or query is with respect to a set of nodes U in *** dynamic parallel tree contraction algorithm is a randomized algorithm that takes O(log(|U|log n)) expected parallel time using O(|U|log n/log(|U|log n) processors. We give a large number of applications (with the same bounds), including:(a) maintaining the usual tree properties (such as number of ancestors, preorder, etc.),(b) Eulerian tour,(c) expression evaluation,(d) least common ancestor, and(e) canonical forms of ***, there where no known parallel algorithms for incrementally maintaining and solving such problems in parallel time less than Θ(log n).In deriving our incremental algorithms, we solve a key subproblem, namely a processor activation problem, within the same asymptotic bounds, which may be useful in the design of other parallel incremental algorithms. This algorithm uses an interesting persistent parallel data structures involving a non-trivial *** a subsequent paper, we apply our dynamic parallel tree contraction technique to various incremental graph problems: maintaining various properties, (such as coloring, minimum covering set, maximum matching, etc.). of parall

关键词： Trees (mathematics)

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O(log2 n) time efficient parallel factorization of dense, sparse separable and banded matrices 94

O(log2 n) time efficient parallel factorization of dense, sp...

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proceedings of the 6th annual acm symposium on parallel algorithms and architectures

作者： Reif, John H. Carnegie Mellon Univ. Pittsburgh PA

ISBN: (纸本)9780897916714

Known polylog parallel algorithms for the solution of linear systems and related problems require computation of the characteristic polynomial or related forms, which are known to be highly unstable in practice. However, matrix factorizations of various types, bypassing computation of the characteristic polynomial, are used extensively in sequential numerical computations and are essential in many *** paper gives new parallel methods for various exact factorizations of several classes of matrices. We assume the input matrices are n × n with either integer entries of size ≤ 2no(1). We make no other assumption on the input. We assume the arithmetic PRAM model of parallel computation. Our main result is a reduction of the known parallel time bounds for these factorizations from O(log3n) to O(log2n). Our results are work efficient; we match the best known work bounds of parallel algorithms with polylog time bounds, and are within a log n factor of the work bounds for the best known sequential algorithms for the same *** exact factorizations we compute for symmetric positive definite matrices include: 1. recursive factorization sequences and trees,2. LU factorizations,3. QR factorizations, and4. reduction to upper Hessenberg *** classes of matrices for which we can efficiently compute these factorizations include:1. dense matrices, in time O(log2n) with processor bound P(n) (the number of processors needed to multiply two n × n matrices in O(log n time),2. block diagonal matrices, in time O(log2b with P(b)n/b processors,3. sparse matrices which are s(n)-separable (recursive factorizations only), in time O(log2n) with P(s(n)) processors where s(n) is of the form n γ for 0 < γ < 1, and4. banded matrices, in parallel time O((logn) log b) with P(b)n/b *** factorizations also provide us similarly efficient algorithms for exact computation (given arbitrary rational matrices that need not be symmetric positive definite) of the following: 1

关键词： dense matrices Newton iteration sparse matrices LU factorization parallel algorithms banded matrices linear systems

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