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Communication-optimal parallel minimum spanning tree algorithms extended abstract

Communication-optimal parallel minimum spanning tree algorit...

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proceedings of the 1998 10th annual acm symposium on parallel algorithms and architectures, SPAA

作者： Adler, M. Dittrich, W. Juurlink, B. Kutylowski, M. Rieping, I. Univ of Toronto Toronto Ont Canada

Lower and upper bounds for finding a minimum spanning tree (MST) in a weighted undirected graph on the BSP model are presented. We provide the first non-trivial lower bounds on the communication volume required to solve the MST problem. Let p denote the number of processors, n the number of nodes of the input graph, and m the number of edges of the input graph. We show that in the worst case a total of Ω(k·min(m, pn)) bits need to be transmitted in order to solve the MST problem, where k is the number of bits required to represent a single edge weight. This implies that if each message contains k bits, any BSP algorithm for finding an MST requires communication time Ω(g · min(m/p, n)), where g is the gap parameter of the BSP model. In addition, we present two algorithms whose running times match the lower bounds in different situations. Both algorithms perform linear work and use a number of super-steps independent of the input size. The first algorithm is simple but can employ at most m/n processors efficiently. Hence, it should be applied in situations where the input graph is relatively dense. The second algorithm is a randomized algorithm that performs linear work with high probability, provided that m ≥ n · log p. This is the first linear work BSP algorithm for finding an MST in sparse graphs.

关键词： parallel algorithms

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Fast fault-tolerant parallel communication and on-line maintenance using information dispersal 90

Fast fault-tolerant parallel communication and on-line maint...

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SPAA '90 - proceedings of the 2nd annual acm symposium on parallel algorithms and architectures

作者： Lyuu, Yuh-Dauh Harvard Univ Cambridge MA United States

ISBN: (纸本)0897913701

Space-efficient Information Dispersal Algorithm (IDA) [11] is applied to parallel communication in the hypercube. Let N denote the size of the network. Our communication scheme runs in 2·log N + 1 time using constant size buffers. Its probability of successful routing is at least 1 - N-2.419·log N+1.5, proving Rabin's conjecture. The same scheme also tolerates O(N) random link failures with high probability. The scheme runs within the said time bound without long delay. On-line and efficient wire testing and replacement on the hypercube can be realized if our fault-tolerant routing scheme is used. Let α denote the total number of links in the hypercube. It is shown that ≈ α/352 wires can be disabled simultaneously without disrupting the ongoing computation or degrading the routing performance much.

关键词： Computer systems, Digital

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Beyond Nested parallelism: Tight Bounds on Work-Stealing Overheads for parallel Futures 09

Beyond Nested Parallelism: Tight Bounds on Work-Stealing Ove...

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21st acm symposium on parallelism in algorithms and architectures

作者： Spoonhower, Daniel Blelloch, Guy E. Gibbons, Phillip B. Harper, Robert Carnegie Mellon Univ Pittsburgh PA 15213 USA

ISBN: (纸本)9781605586069

Work stealing is a popular method of scheduling fine-grained parallel tasks. The performance of work stealing has been extensively studied, both theoretically and empirically, but primarily for the restricted class of nested-parallel (or fully strict) computations. we extend this prior work by considering a broader class of programs that also supports pipelined parallelism through the use of parallel futures. Though the overhead of work-stealing schedulers is often quantified in terms of the number of steals, we show that a broader metric, the number of deviations, is a better way to quantify work-stealing overhead for less restrictive forms of parallelism, including parallel futures. For such parallelism, we prove bounds on work-stealing overheads-scheduler time and cache misses-as a function of the number of deviations Deviations can occur, for example, when work is stolen or when a future is touched. We also show instances where deviations can occur independently of steals and touches. Next, we prove that, under work stealing, the expected number of deviations is O(Pd+td) in a P-processor execution of a computation with span d and t touches of futures. Moreover, this bound is existentially tight for any work-stealing scheduler that is parsimonious (those where processors steal only when their queues are empty);this class includes all prior work-stealing schedulers. We also present empirical measurements of the number of deviations incurred by a classic application of futures, Halstead's quicksort, using our parallel implementation of ML. Finally, we identify a family of applications that use futures and, in contrast to quicksort, incur significantly smaller overheads.

关键词： scheduling work stealing futures performance bounds

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Lower bounds for randomized exclusive write PRAMs 95

Lower bounds for randomized exclusive write PRAMs

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proceedings of the 7th annual acm symposium on parallel algorithms and architectures, SPAA'95

作者： MacKenzie, Philip D. Sandia Natl Lab Albuquerque NM United States

ISBN: (纸本)9780897917179

In this paper we study the question: How useful is randomization in speeding up Exclusive Write PRAM computations? Our results give further evidence that randomization is of limited use in these types of computations. First we examine a compaction problem on both the CREW and EREW PRAM models, and we present randomized lower bounds which match the best deterministic lower bounds known. (For the CREW PRAM model, the lower bound is asymptotically optimal). These are the first non-trivial randomized lower bounds known for the compaction problem on these models. We show that our lower bounds also apply to the problem of approximate compaction. Next we examine the problem of computing boolean functions on the CREW PRAM model, and we present a randomized lower bound which improves on the previous best randomized lower bound for many boolean functions, including the OR function. (The previous lower bounds for these functions were asymptotically optimal, but we improve the constant multiplicative factor). We also give an alternate proof for the randomized lower bound on PARITY, which was already optimal to within a constant additive factor. Lastly, we give a randomized lower bound for integer merging on an EREW PRAM which matches the best deterministic lower bound known. In all our proofs, we use the Random Adversary method, which has previously only been used for proving lower bounds on models with Concurrent Write capabilities. Thus this paper also serves to illustrate the power and generality of this method for proving parallel randomized lower bounds.

关键词： parallel processing systems

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HARP: A fast spectral partitioner

HARP: A fast spectral partitioner

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

作者： Simon, Horst D. Sohn, Andrew Biswas, Rupak Lawrence Berkeley Natl Lab Berkeley United States

Partitioning unstructured graphs is central to the parallel solution of computational science and engineering problems. Spectral partitioners, such recursive spectral bisection (RSB), have proven effective in generating high-quality partitions of realistically-sized meshes. The major problem which hindered their widespread use was their long execution times. This paper presents a new inertial spectral partitioner, called HARP. The main objective of the proposed approach is to quickly partition the meshes at runtime in a manner that works efficiently for real applications in the context of distributed-memory machines. The underlying principle of HARP is to find the eigenvectors of the unpartitioned vertices and then project them onto the eigenvectors of the original mesh. Results for various meshes ranging in size from 1000 to 100,000 vertices indicate that HARP can indeed partition meshes rapidly at runtime. Experimental results show that our largest mesh can be partitioned sequentially in only a few seconds on an SP2 which is several times faster than other spectral partitioners while maintaining the solution quality of the proven RSB method. A parallel MPI version of HARP has also been implemented on IBM SP2 and Cray T3E. parallel HARP, running on 64 processors SP2 and T3E, can partition a mesh containing more than 100,000 vertices into 64 subgrids in about half a second. These results indicate that graph partitioning can now be truly embedded in dynamically-changing real-world applications.

关键词： parallel processing systems

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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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Communication-Optimal parallel and Sequential Cholesky Decomposition 09

Communication-Optimal Parallel and Sequential Cholesky Decom...

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21st acm symposium on parallelism in algorithms and architectures

作者： Ballard, Grey Demmel, James Holtz, Olga Schwartz, Oded Univ Calif Berkeley Dept Comp Sci Berkeley CA 94720 USA

ISBN: (纸本)9781605586069

Numerical algorithms have two kinds of costs: arithmetic and communication, by which we mean either moving data between levels of a memory hierarchy (in the sequential case) or over a network connecting processors (in the parallel case). Communication costs often dominate arithmetic costs, so it is of interest to design algorithms minimizing communication. In this paper we first extend known lower bounds on the communication cost (both for bandwidth and for latency) of conventional (O(n(3))) matrix multiplication to Cholesky factorization, which is used for solving dense symmetric positive definite linear systems. Second, we compare the cost of various Cholesky decomposition implementations to this lower bound, and draw the following conclusions: (1) "Naive" sequential algorithms for Cholesky attain neither the bandwidth nor latency lower bounds. (2) The sequential blocked algorithm in LAPACK (with the right block size), as well as various recursive algorithms [AP00, GJ01, ACW01, ST04] and one based on work of Toledo [Tol97], can attain the bandwidth lower bound. (3) The LAPACK algorithm can also attain the latency bound if used with blocked data structures rather than column-wise or row-wise matrix data structures, though the Toledo algorithm cannot. (4) The recursive sequential algorithm due to [AP00], attains the bandwidth and latency lower bounds at every level of a multi-level memory hierarchy, in a "cache-oblivious" way. (5) The parallel implementation of Cholesky in the ScaLA-PACK library (again with the right block-size) attains both the bandwidth and latency lower bounds to within a poly-logarithmic factor. Combined with prior results in [DGHL08a, DGHL08b, DGX08] this gives a complete set;of communication-optimal algorithms for O(n(3)) implementations of three basic factorizations of dense linear algebra: LU with pivoting, QR and Cholesky. But it goes beyond this prior work on sequential LU and QR by optimizing communication for any number of levels of memo

关键词： communication avoiding Cholesky decomposition lower bound bandwidth latency algorithm

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MediaBench: A tool for evaluating and synthesizing multimedia and communications systems

MediaBench: A tool for evaluating and synthesizing multimedi...

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30th annual IEEE/acm International symposium on Microarchitecture (MICRO-30)

作者： Lee, CH Potkonjak, M Mangione-Smith, WH Univ Calif Los Angeles Dept Comp Sci Los Angeles CA 90024 USA

ISBN: (纸本)0818679778

Over the last decade, significant advances have been made in compilation technology for capitalizing on instruction-level parallelism (ILP). The vast majority of ILP compilation research has been conducted in the context of general-purpose computing, and more specifically the SPEC benchmark suite. At the same time, number of microprocessor architectures have emerged which have VLIW and SIMD structures that are well matched to the needs of the ILP compilers. Most of these processors are targeted at embedded applications such as multimedia and communications, rather than general-purpose systems. Conventional wisdom, and a history of hand optimization of inner-loops, suggests that ILP compilation techniques are well suited to these applications. Unfortunately, there currently exists a gap between the compiler community and embedded applications developers. This paper presents MediaBench, a benchmark suite that has been designed to fill this gap. This suite has been constructed through a three-step process: intuition and market driven initial selection, experimental measurement to establish uniqueness, and integration with system synthesis algorithms to establish usefulness.

关键词： parallel processing systems

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Efficient computations on fault-prone BSP machines 97

Efficient computations on fault-prone BSP machines

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

作者： Kontogiannis, Spyros C. Pantzio, Grammati E. Spirakis, Paul G. Patras Univ Patras Greece

ISBN: (纸本)9780897918909

In this paper general simulations of algorithms designed for fully operational BSP machines on BSP machines with faulty or unavailable processors, are developed. The fail-stop model is considered for the fault occurrences, that is, if a processor fails or becomes unavailable, it remains so until the end of the computation. The faults are random, in the sense that a processor may fail independently with probability at most a, where a is a constant. Two possible settings for fault occurrences are considered: the static case where the faults are static (the faulty or unavailable processors are already known at the beginning of the computation), and the dynamic case where the processors may become faulty or unavailable during the computation. In the case of static faults, a simulation of an n-processor fault-free BSP machine on a faulty n-processor BSP machine is presented with constant slowdown per local computation step and O(log n·max{L, g}) slowdown per communication step, given that a preprocessing has been done that needs O(n/log n·max{L, g}) time (L and g are the parameters of the simulating BSP machine). In the case of dynamic faults, a simulation of an n-processor fault-free BSP machine on an cn·log n-processor faulty BSP machine is presented. No dynamic faults may occur during certain periods of the simulation. The simulations are randomized and Monte Carlo: they are guaranteed to be correct with high probability, and the time bounds always hold. To our knowledge, no previous work on the fault tolerance of the BSP model exists.

关键词： parallel processing systems

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