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parallelism versus memory allocation in pipelined router forwarding engines 04

Parallelism versus memory allocation in pipelined router for...

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SPAA 2004 - Sixteenth annual acm symposium on parallelism in algorithms and architectures

作者： Chung, Fan Graham, Ronald Varghese, George University of California San Diego United States

ISBN: (纸本)9781581138405

A crucial problem that needs to be solved is the allocation of memory to processors in a pipeline. Ideally, the processor memories should be totally separate (i.e., one port memories) in order to minimize contention;however, this minimizes memory sharing. Idealized sharing occurs by using a single shared memory for all processors but this maximizes contention. Instead, in this paper we show that perfect memory sharing of shared memory can be achieved with a collection of *two*-port memories, as long as the number of processors is less than the number of memories. We show that the problem of allocation is NP-complete in general, but has a fast approximation algorithm that comes within a factor of 3/2. The proof utilizes a new bin packing model, which is interesting in its own right. Further, for important special cases that arise in practice the approximation algorithm is indeed optimal. We also describe an incremental memory allocation algorithm that provides good memory utilization while allowing fast updates.

关键词： parallel processing systems

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Communication-optimal parallel algorithm for strassen's matrix multiplication 12

Communication-optimal parallel algorithm for strassen's matr...

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24th acm symposium on parallelism in algorithms and architectures, SPAA'12

作者： Ballard, Grey Demmel, James Holtz, Olga Lipshitz, Benjamin Schwartz, Oded EECS Department UC Berkeley Berkeley CA 94720 United States Mathematics Department CS Division UC Berkeley Berkeley CA 94720 United States Mathematics Department UC Berkeley TU Berlin Berkeley CA 94720 United States

ISBN: (纸本)9781450312134

parallel matrix multiplication is one of the most studied fundamental problems in distributed and high performance computing. We obtain a new parallel algorithm that is based on Strassen's fast matrix multiplication and minimizes communication. The algorithm outperforms all known parallel matrix multiplication algorithms, classical and Strassen-based, both asymptotically and in practice. A critical bottleneck in parallelizing Strassen's algorithm is the communication between the processors. Ballard, Demmel, Holtz, and Schwartz (SPAA '11) prove lower bounds on these communication costs, using expansion properties of the underlying computation graph. Our algorithm matches these lower bounds, and so is communication-optimal. It exhibits perfect strong scaling within the maximum possible range. Benchmarking our implementation on a Cray XT4, we obtain speedups over classical and Strassen-based algorithms ranging from 24% to 184% for a fixed matrix dimension n = 94080, where the number of processors ranges from 49 to 7203. Our parallelization approach generalizes to other fast matrix multiplication algorithms. Copyright 2012 acm.

关键词： parallel algorithms

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Work-Efficient Batch-Incremental Minimum Spanning Trees with Applications to the Sliding-Window Model 20

Work-Efficient Batch-Incremental Minimum Spanning Trees with...

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32nd acm symposium on parallelism in algorithms and architectures (SPAA)

作者： Anderson, Daniel Blelloch, Guy E. Tangwongsan, Kanat Carnegie Mellon Univ Pittsburgh PA 15213 USA Mahidol Univ Int Coll Bangkok Thailand

ISBN: (纸本)9781450369350

algorithms for dynamically maintaining minimum spanning trees (MSTs) have received much attention in both the parallel and sequential settings. While previous work has given optimal algorithms for dense graphs, all existing parallel batch-dynamic algorithms perform polynomial work per update in the worst case for sparse graphs. In this paper, we present the first work-efficient parallel batch-dynamic algorithm for incremental MST, which can insert l edges in O(l lg(1 + n/l)) work in expectation and O(polylog(n)) span w.h.p. The key ingredient of our algorithm is an algorithm for constructing a compressed path tree of an edge-weighted tree, which is a smaller tree that contains all pairwise heaviest edges between a given set of marked vertices. Using our batch-incremental MST algorithm, we demonstrate a range of applications that become efficiently solvable in parallel in the sliding-window model, such as graph connectivity, approximate MSTs, testing bipartiteness, k-certificates, cycle-freeness, and maintaining sparsifiers.

关键词： dynamic algorithms minimum spanning trees dynamic graphs parallel algorithms incremental algorithms

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Efficient execution of nondeterministic parallel programs on asynchronous systems 96

Efficient execution of nondeterministic parallel programs on...

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Proceedings of the 1996 8th annual acm symposium on parallel algorithms and architectures

作者： Aumann, Yonatan Bender, Michael A. Zhang, Lisa Bar-Ilan Univ Ramat-Gan Israel

ISBN: (纸本)9780897918091

We consider the problem of asynchronous execution of parallel programs. The original program is assumed to be designed for a synchronous system, while the actual system may be asynchronous. We seek an automatic execution scheme, which allows the asynchronous system to execute the synchronous program. Previous solutions to this problem provide a solution only for the case where the original program is deterministic. Here, we provide the first solution for the nondeterministic case (e.g. randomized programs). Our scheme is based on a novel agreement protocol for this setting. Our protocol allows n asynchronous processors to agree on n word-sized values in O(n log n log log n) total work. Total work is defined to be the summation of the number of steps performed by all processes (including busy waiting).

关键词： parallel processing systems

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Optimal VLSI architectures for multidimensional DFT 89

Optimal VLSI architectures for multidimensional DFT

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

作者： Bilardi, Gianfranco Hornick, Scot W. Sarrafzadeh, Majid Department of Computer Science Cornell University Upson Hall IthacaNY14853 United States Andersen Consulting Center for Strategic Tech. Res. 100 S. Wacker ChicagoIL60606 United States Dept. of Elec. Eng. and Comp. Sci. Technological Institute Northwestern University EvanstonIL60208 United States

ISBN: (纸本)089791323X

A family of VLSI architectures for computing an (n 1 × n 2 × • • " × nd)-point multidimensional D1VF (MDDFT) over Zm, the ring of integers modulo M, is presented. These architectures achieve VLSI area A = 0 ((NZlog2M)/T 2) for any comptitation time T ϵ [ω(logN),O (ωNlogM)], where N = I'Int and it is k=l assumed that logM = O(logN). A lower bound argument is developed to show that the proposed architectures are area-Time optimal. The appficability of these architectures to computation of the MDDFT over the complex field is also discussed. Using fixed-point arithmetic with b bits of precision, their area-Time performance is AT2= O(N2b 2) for any computation time T ϵ [ω(logN),O(√Nb)]. © 1989 acm.

关键词： Fixed point arithmetic

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Greedy sequential maximal independent set and matching are parallel on average 12

Greedy sequential maximal independent set and matching are p...

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24th acm symposium on parallelism in algorithms and architectures, SPAA'12

作者： Blelloch, Guy E. Fineman, Jeremy T. Shun, Julian Carnegie Mellon University United States Georgetown University United States

ISBN: (纸本)9781450312134

The greedy sequential algorithm for maximal independent set (MIS) loops over the vertices in an arbitrary order adding a vertex to the resulting set if and only if no previous neighboring vertex has been added. In this loop, as in many sequential loops, each iterate will only depend on a subset of the previous iterates (i.e. knowing that any one of a vertex's previous neighbors is in the MIS, or knowing that it has no previous neighbors, is sufficient to decide its fate one way or the other). This leads to a dependence structure among the iterates. If this structure is shallow then running the iterates in parallel while respecting the dependencies can lead to an efficient parallel implementation mimicking the sequential algorithm. In this paper, we show that for any graph, and for a random ordering of the vertices, the dependence length of the sequential greedy MIS algorithm is polylogarithmic (O(log2 n) with high probability). Our results extend previous results that show polylogarithmic bounds only for random graphs. We show similar results for greedy maximal matching (MM). For both problems we describe simple linear-work parallel algorithms based on the approach. The algorithms allow for a smooth tradeoff between more parallelism and reduced work, but always return the same result as the sequential greedy algorithms. We present experimental results that demonstrate efficiency and the tradeoff between work and parallelism. Copyright 2012 acm.

关键词： parallel algorithms

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New algorithms for Efficient parallel String Comparison 10

New Algorithms for Efficient Parallel String Comparison

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22nd acm symposium on parallelism in algorithms and architectures

作者： Krusche, Peter Tiskin, Alexander Univ Warwick Dept Comp Sci Coventry CV4 7AL W Midlands England

ISBN: (纸本)9781450300797

In this paper. we show new parallel algorithms for a set of classical string comparison problems. computation of string alignments. longest common subsequences (LCS) or edit distances, and longest increasing subsequence computation. These problems have a wide range of applications, in particular in computational biology and signal processing. We discuss the scalability of our new parallel algorithms in computation time, in memory, and in commumcation Our new algorithms are based on an efficient parallel method for (min, +)-multiplication of distance matrices The core result of this paper is a scalable parallel algorithm for multiplying Implicit simple unit-Monge matrices of size n x n on p processors using lime O(n log n/p), communication O(n log p/p) and O( log p) supersteps. This algorithm allows us to implement scalable LCS computation for two strings of length n using time O(n(2)/p) and communication O(n/root P) requiring local memory of size O(n/root P) on each processor Furthermore, our algorithm can be used to obtain the first generally work-scalable algorithm for computing the longest increasing subsequence (LIS) Our algorithm for LIS computation requires computation O(n log(2) n/p), communication O(n log(2) p/p), and O(log(2) p) supersteps for computing the LIS of a sequence of length n This is within a log n factor of work-optimality for the LIS problem. which can be solved sequentially in time O(n log n) in the comparison-based model. Our LIS algorithm is also within a log p-factor of achieving perfectly scalable communication and furthermore has perfectly scalable memory size requirements of O(n/p) per processor

关键词： BSP algorithms longest common subsequences longest increasing subsequences

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SPAA 2022 - Proceedings of the 34th acm symposium on parallelism in algorithms and architectures

SPAA 2022 - Proceedings of the 34th ACM Symposium on Paralle...

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34th acm symposium on parallelism in algorithms and architectures, SPAA 2022

ISBN: (纸本)9781450391467

The proceedings contain 44 papers. The topics discussed include: deterministic distributed sparse and ultra-sparse spanners and connectivity certificates;fully polynomial-time distributed computation in low-treewidth graphs;adaptive massively parallel algorithms for cut problems;preparing for disaster: leveraging precomputation to efficiently repair graph structures upon failures;the energy complexity of Las Vegas leader election;a fully-distributed peer-to-peer protocol for byzantine-resilient distributed hash tables;brief announcement: the (limited) power of multiple identities: asynchronous byzantine reliable broadcast with improved resilience through collusion;brief announcement: composable dynamic secure emulation;and robust and optimal contention resolution without collision detection.

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parallel LEAST-SQUARES SOLUTION OF GENERAL AND TOEPLITZ-LIKE LINEAR-SYSTEMS

PARALLEL LEAST-SQUARES SOLUTION OF GENERAL AND TOEPLITZ-LIKE...

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2ND annual SYMP OF THE ASSOC FOR COMPUTING MACHINERY : parallel algorithms AND architectures ( SPAA 90 ) / AEGEAN WORKSHOP ON COMPUTING

作者： PAN, V Lehman Coll CUNY Bronx United States

We use O(log2 n) parallel arithmetic steps and n2 processors to compute the least-squares solution x = A+b to a linear system of equations, Ax = b, given a g × h matrix A and a vector b, both filled with integers... 详细信息

ISBN: (纸本)0897913701

We use O(log² n) parallel arithmetic steps and n² processors to compute the least-squares solution x = A⁺b to a linear system of equations, Ax = b, given a g × h matrix A and a vector b, both filled with integers or with rational numbers, provided that g + h ≤ 2n and that A is given with its displacement generator of length r = O(1) and thus has displacement rank O(1). For a vector b and for a general p × q matrix A (with p + q ≤ n), we compute A⁺ and A⁺b by using O(log² n) parallel arithmetic steps and n^2.851 processors, and we may also compute A⁺b by using O(n^2.376) arithmetic operations.

关键词： Computer Programming

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The Pochoir Stencil Compiler 11

The Pochoir Stencil Compiler

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23rd annual symposium on parallelism in algorithms and architectures

作者： Tang, Yuan Chowdhury, Rezaul Kuszmaul, Bradley C. Luk, Chi-Keung Leiserson, Charles E. MIT Comp Sci & Artificial Intelligence Lab Cambridge MA 02139 USA

ISBN: (纸本)9781450307437

A stencil computation repeatedly updates each point of a d-dimensional grid as a function of itself and its near neighbors. parallel cache-efficient stencil algorithms based on "trapezoidal decompositions" are known, but most programmers find them difficult to write. The Pochoir stencil compiler allows a programmer to write a simple specification of a stencil in a domain-specific stencil language embedded in C++ which the Pochoir compiler then translates into high-performing Cilk code that employs an efficient parallel cache-oblivious algorithm. Pochoir supports general d-dimensional stencils and handles both periodic and aperiodic boundary conditions in one unified algorithm. The Pochoir system provides a C++ template library that allows the user's stencil specification to be executed directly in C++ without the Pochoir compiler (albeit more slowly), which simplifies user debugging and greatly simplified the implementation of the Pochoir compiler itself. A host of stencil benchmarks run on a modern multicore machine demonstrates that Pochoir outperforms standard parallel-loop implementations, typically running 2-10 times faster. The algorithm behind Pochoir improves on prior cache-efficient algorithms on multidimensional grids by making "hyperspace" cuts, which yield asymptotically more parallelism for the same cache efficiency.

关键词： C plus cache-oblivious algorithm Cilk compiler embedded domain-specific language multicore parallel computation stencil trapezoidal decomposition

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