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Optimal weighted loop fusion for parallel programs 97

Optimal weighted loop fusion for parallel programs

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proceedings of the 1997 9th annual acm symposium on parallel algorithms and architectures, SPAA

作者： Megiddo, Nimrod Sarkar, Vivek IBM Almaden Research Cent CA San Jose United States

ISBN: (纸本)9780897918909

Much of the computation involved in parallel programs occurs within loops, either nested loops as in parallel scientific applications or collections of loops as in stream-based applications. Loop fusion is a well-known program transformation that has shown to be effective in improving data locality in parallel programs by reducing inter-processor communication and improving register and cache locality. Weighted loop fusion is the problem of finding a legal partition of loop nests into fusible clusters so as to minimize the total inter-cluster weights. The loop nests may contain parallel or sequential loops;care is taken to ensure that a parallel loop does not get serialized after fusion. It has been shown in past work that the weighted loop fusion problem is NP-hard. Despite the NP-hardness property, we show how optimal solutions can be found efficiently (i.e., within the compile-time constraints of a product-quality optimizing compiler) for weighted loop fusion problem sizes that occur in practice. In this paper, we present an integer programming formulation for weighted loop fusion with size (number of variables and constraints) that is linearly proportional to the size of the input weighted loop fusion problem. The linear-sized formulation is key to making the execution time small enough for use in a product-quality optimizing compiler, since the natural integer programming formulation for this problem has cubic size for which the execution time would be too large to be practical. The linear-sized integer programming formulation can be solved efficiently using any standard optimization package but we also present a custom branch-and-bound algorithm that can be used if greater efficiency is desired. A prototype implementation of this approach has been completed, and preliminary compile-time measurements are included in the paper as validation of the practicality of this approach.

关键词： parallel processing systems

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Interprocessor communication speed and performance in distributed-memory parallel processors. 89

Interprocessor communication speed and performance in distri...

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16th annual International symposium on Computer Architecture

作者： Annaratone, Marco Pommerell, Claude Ruhl, Roland Swiss Fed Inst of Technology Zurich Switz

ISBN: (纸本)9780897913195

The authors have simulated several numerical and nonnumerical algorithms on five distributed-memory parallel processors (DMPPs). All five DMPPs have the same topology (a torus) and the same number of nodes. The architectures differ only in the speed of communication between neighboring nodes, with the computation unit unchanged. The authors quantify the effect that interprocessor communication speed and synchronization overhead have on the performance of the DMPPs. After introducing their rationale and reviewing related work, the authors present and discuss the results of the simulations.

关键词： Computer systems, Digital

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architectures and algorithms for millisecond-scale molecular dynamics simulations of proteins 41

Architectures and algorithms for millisecond-scale molecular...

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2008 - 41st annual IEEE/acm International symposium on Microarchitecture, MICRO-41

作者： Shaw, David E. Columbia's Medical School United States

ISBN: (纸本)9781424428366

The ability to perform long, accurate molecular dynamics (MD) simulations involving proteins and other biological macromolecules could in principle lead to important scientific advances and provide a powerful new tool for drug discovery. A wide range of biologically interesting phenomena, however, occur over time scales on the order of a millisecond - several orders of magnitude beyond the duration of the longest current MD simulations. Our research group is currently building a specialized, massively parallel machine, called Anton, which should soon be capable of executing millisecond-scale MD simulations of proteins at an atomic level of detail. Anton's highly accelerated execution of such simulations is attributable in large part to specialized logic for the high-speed calculation of pairwise interactions between particles and/or gridpoints separated by no more than some specified cutoff radius. In particular, each of Anton's 512 ASICs, which are implemented using 90-nm technology, includes a "high-throughput interaction subsystem" incorporating 32 highly specialized pipelines running at 800 MHz. During every cycle, each of these pipelines produces a pairwise-interaction result that would require approximately 50 arithmetic operations to calculate on a general-purpose processor. Novel algorithms and architectural features are used to greatly reduce the requirements for inter- and intra-chip communication, allowing Anton to feed these pipelines and collect their results at a speed sufficient to take advantage of the machine's computational power. The ASIC also includes a "flexible subsystem" based on eight programmable "geometry cores," each containing eight arithmetic pipelines. This talk will provide an overview of our work on parallel algorithms and machine architectures for high-speed MD simulation, with special attention to the respective roles of specialized vs. general-purpose hardware, and to the techniques used to minimize communication at various levels

关键词： Molecular dynamics

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parallel and output sensitive algorithms for combinatorial and linear algebra problems 93

Parallel and output sensitive algorithms for combinatorial a...

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5th annual acm symposium on parallel algorithms and architectures, SPAA 1993

作者： Cheriyan, Joseph Reif, John H. Department of Combinatorics and Optimization University of Waterloo ONN2L 3G1 Canada Department of Computer Science Duke University DurhamNC27706 United States

ISBN: (纸本)0897915992

The notion of output sensitive parallel algorithms for linear algebra problems is formalized in this paper, and such algorithms are presented for finding the rank of an n x n matrix in randomized parallel time 0(log n + logR) using 0(n2 + M(R)) processors, and for finding a maximum linearly independent subset of an n-set of n-dimensional vectors in randomized parallel time 0((log n) log3 R) using (n2 + RM(R)) processors (R is the size of the subset). Also, output sensitive TLSfC algorithms for some combinatorial problems are developed. The best TLSfC algorithm known for finding a maximum linearly independent subset of an n-set of n-dimensional vectors is given;the randomized parallel time is 0(logn) using 0(M(n)) processors. Note that this problem is likely harder than the problem of rinding a basis for the space spanned by the input vectors. An output sensitive TUfC algorithm for computing greatest common divisors of polynomials is developed. This result is due to the second author. A minimum vertex cover in a bipartite graph and a minimum X-Y vertex separator in a digraph can be found in randomized parallel time 0(log3 n) using 0(M(n)) processors (n is the number of vertices). This result is due to the first author. Note that this is the best complexity bound known for TLhfC algorithms, and matches the best TLSfC complexity bounds for the associated decision problems. © 1993 acm.

关键词： Graph theory

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Portable parallel programs using architecture-aware libraries 12

Portable parallel programs using architecture-aware librarie...

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27th annual acm symposium on Applied Computing, SAC 2012

作者： Zaraket, Fadi Noureddine, Mohamad Sabra, Mohamed Jaber, Ameen American University of Beirut Lebanon

ISBN: (纸本)9781450308571

Programs written for an architecture with n processors require a re-write when migrated to an m processor architecture {(m > n)} to benefit from additional resources. Compiler based solutions do not match manual optimizations. Annotation based and api-based solutions such as the OpenMP and the Intel Array Building Blocks work well with data parallel programs and do not scale well with branching programs. We present Portable parallel Programming (TripleP), a parallel programming methodology that is composed of a declarative programming language, a set of libraries of data structures and algorithms optimized per architecture, and a synthesizer. We evaluated TripleP with the computation of array median, and breadth first traversal of a graph. Our results show that TripleP enables portable programs that benefit from additional resources across architectures with near optimal performance gains. © 2012 Authors.

关键词： parallel programming

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parallel construction and query of suffix trees for two-dimensional matrices 93

Parallel construction and query of suffix trees for two-dime...

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5th annual acm symposium on parallel algorithms and architectures, SPAA 1993

作者： Giancarlo, Raffaele Grossi, Roberto AT and T Bell Laboratories Murray HillNJ07974 United States University of Palermo Italy Dipartimento di Informatica Università di Pisa Pisa56125 Italy Dipartimento di Sistemi e Informatica Università di Firenze Firenze50134 Italy

ISBN: (纸本)0897915992

We give efficient CRCW PRAM algorithms for the construction of two data structures, the Lsuffix Tree of a square matrix and the Nested Suffix Tree of a general matrix. The Lsuffix tree, introduced by Giancarlo [11], represents all square submatrices of a square matrix. The nested suffix tree, introduced here, represents all rectangular submatrices of a given general matrix. Both data structures can be seen as a generalization to matrices of the suffix tree of a string [18]. We remark that the problem of building a tree data structure representing all rectangular submatrices of a given matrix has been shown to be computationally harder than the problem of building a tree data structure representing only the square submatrices of a given matrix [10]. Thus, our attention for the important special case of square submatrices is justified. Once those two data structures are available, we can answer quickly and in parallel, a wide variety of queries that have many important applications in low-level image processing [20], visual databases [12] and two-dimensional data compression [16, 21, 22]. All matrices in this abstract have entries defined over an ordered alphabet E. © 1993 acm.

关键词： Matrix algebra

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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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parallel graph contraction 89

Parallel graph contraction

引用

1st annual acm symposium on parallel algorithms and architectures, SPAA 1989

作者： Phillips, Cynthia A. Laboratory for Computer Science Massachusetts Institute of Technology CambridgeMA02139 United States

ISBN: (纸本)089791323X

This paper shows how n-node, e-edge graphs can be contracted in a manner similar to the parallel tree contraction algorithm due to Miller and Reif. We give an O((n + e)/lgn)-processor deterministic algorithm that contracts a graph in O(lg 2 n) time in the EREW PRAM model. We also give art O(n/lg n)-processor randomized algorithm that with high probability can contract a bounded-degree graph in O(lg n+lg 2 γ) time, where γ is the maximum genus of any connected component of the graph. (The algorithm can be made to run in deterministic O(lg n lg∗ n + lg 2 γ) time using known techniques.) This algorithm does not require a priori knowledge of the genus of the graph to be contracted. The contraction algorithm for boundeddegree graphs can be used directly to solve the problem of region labeling in vision systems, i.e., determining the connected components of bounded-degree planar graphs in O(lgn) time, thus improving the best previous bound of O(lg 2 n). © 1989 acm.

关键词： Trees (mathematics)

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Highly efficient dictionary matching in parallel 93

Highly efficient dictionary matching in parallel

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5th annual acm symposium on parallel algorithms and architectures, SPAA 1993

作者： Muthukrishnan, S. Palem, K. Courant Institute of Mathematical Sciences 251 Mercer Street New YorkNY10012-1185 United States IBM Research Division T. J. Watson Research Center P. O. Box 704 Yorktown HeightsNY10598 United States

ISBN: (纸本)0897915992

We present highly efficient parallel algorithms for several well-studied dictionary matching problems. Our algorithms are faster and more efficient in terms of their parallel work, compared to previously known results. For static dictionary matching, we present an algorithm that preprocesses the dictionary and matches the text in O(logm) parallel time and 0(M + n log m) work, given any dictionary of size M whose longest pattern is m characters long, and a text of size n. We have further improved this algorithm to solve static dictionary matching with only 0((M + n)vlog m) work, if the characters are drawn from an alphabet of constant size. A distinguishing feature of these algorithms and the one stated below for matching in higher dimensions, is that in contrast with previous work, the running times, and work overheads when applicable, are dependent only on the length of the longest pattern m. We present a parallel algorithm for d-dimensional dictionary matching that runs in O(logm) time and matches the text in 0(M + nlogm) work for any fixed d. We present a new and more efficient parallel algorithm for dynamic dictionary matching. Insertions into and deletions from the dictionary, as well as matching the text can be done with optimal speedup in 0(A log M) work and 0(log M) time. Here, A denotes the length of the string to be inserted, deleted or matched into a dictionary of size M. All of the above algorithms are designed by applying the shrink-and-spawn technique that we introduce in this paper. We also show that this technique leads to parallel algorithms that only do optimal (linear) work, for multi-dimensional pattern matching and related problems [KLP89,Rab93]. Our algorithms are deterministic, as those in [KLP89], but however, are much simpler and preserve the efficiency as well as the speed of those presented there. © 1993 acm.

关键词： parallel algorithms

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Optimal parallel suffix-prefix matching algorithm and applications 89

Optimal parallel suffix-prefix matching algorithm and applic...

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1st annual acm symposium on parallel algorithms and architectures, SPAA 1989

作者： Kedera, Zvi M. Landau, Gad M. Palem, Krishna V. Department of Computer Science Courant Institute of Mathematical Sciences New York University 251 Mercer St. New YorkNY United States Computer Science Division Polytechnic Univ. 333 Jay St. Brooklyn New YorkNY11201 United States IBM Research Division P. O. Box 704 Yorktown HeightsNY10598 United States

ISBN: (纸本)089791323X

Our main result in this paper is a parallel algorithm for suffiz-prefix matching that has optimal speedup on a CRCW PRAM. It runs in time O(logn) using n/log n processors. This algorithm is important because we utihze suffix-prefix matching as a fundamental building block to solve several pattern and string matching problems such as: 1. String Matching, 2. Multi-pattern string matching, 3. Multidimensional Pattern Matching, 4. Pattern Occurrence Detection, 5. Incremental String Matching. © 1989 acm.

关键词： Pattern matching

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