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Brief Announcement: Hypergraph Partitioning for parallel Sparse Matrix-Matrix Multiplication 27

Brief Announcement: Hypergraph Partitioning for Parallel Spa...

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27th acm symposium on parallelism in algorithms and architectures (SPAA)

作者： Ballard, Grey Druinsky, Alex Knight, Nicholas Schwartz, Oded Sandia Natl Labs Livermore CA 94550 USA Lawrence Berkeley Natl Lab Berkeley CA USA Univ Calif Berkeley Berkeley CA 94720 USA Hebrew Univ Jerusalem Jerusalem Israel

ISBN: (纸本)9781450335881

The performance of parallel algorithms for sparse matrixmatrix multiplication is typically determined by the amount of interprocessor communication performed, which in turn depends on the nonzero structure of the input matrices. In this paper, we characterize the communication cost of a sparse matrix-matrix multiplication algorithm in terms of the size of a cut of an associated hypergraph that encodes the computation for a given input nonzero structure. Obtaining an optimal algorithm corresponds to solving a hypergraph partitioning problem. Our hypergraph model generalizes several existing models for sparse matrix-vector multiplication, and we can leverage hypergraph partitioners developed for that computation to improve application-specific algorithms for multiplying sparse matrices.

关键词： Matrix algebra

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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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Randomized Incremental Convex Hull is Highly parallel 20

Randomized Incremental Convex Hull is Highly Parallel

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

作者： Blelloch, Guy E. Gu, Yan Shun, Julian Sun, Yihan Carnegie Mellon Univ Pittsburgh PA 15213 USA UC Riverside Riverside CA USA MIT CSAIL 77 Massachusetts Ave Cambridge MA 02139 USA

ISBN: (纸本)9781450369350

The randomized incremental convex hull algorithm is one of the most practical and important geometric algorithms in the literature. Due to its simplicity, and the fact that many points or facets can be added independently, it is also widely used in parallel convex hull implementations. However, to date there have been no non-trivial theoretical bounds on the parallelism available in these implementations. In this paper, we provide a strong theoretical analysis showing that the standard incremental algorithm is inherently parallel. In particular, we show that for n points in any constant dimension, the algorithm has O(logn) dependence depth with high probability. This leads to a simple work-optimal parallel algorithm with polylogarithmic span with high probability. Our key technical contribution is a new definition and analysis of the configuration dependence graph extending the traditional configuration space, which allows for asynchrony in adding configurations. To capture the "true" dependence between configurations, we define the support set of configuration c to be the set of already added configurations that it depends on. We show that for problems where the size of the support set can be bounded by a constant, the depth of the configuration dependence graph is shallow ( O(logn) with high probability for input size n). In addition to convex hull, our approach also extends to several related problems, including half-space intersection and finding the intersection of a set of unit circles. We believe that the configuration dependence graph and its analysis is a general idea that could potentially be applied to more problems.

关键词： convex hull configuration space parallelism randomized incremental algorithms

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A constant-time optimal parallel string-matching algorithm 92

A constant-time optimal parallel string-matching algorithm

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24th annual acm symposium on Theory of Computing, STOC 1992

作者： Galil, Zvi Columbia University United States Tel-Aviv University Israel

Given a pattern string, we describe a way to preprocess it. We design a constant-time optimal parallel algorithm for finding all occurrences of the (prepro-cessed) pattern in any given text.

ISBN: (纸本)0897915119

Given a pattern string, we describe a way to preprocess it. We design a constant-time optimal parallel algorithm for finding all occurrences of the (prepro-cessed) pattern in any given text.

关键词： String searching algorithms

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Minimizing randomness in minimum spanning tree, parallel connectivity, and set maxima algorithms 13

Minimizing randomness in minimum spanning tree, parallel con...

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13th annual acm/SIAM symposium on Discrete algorithms

作者： Pettie, S Ramachandran, V Univ Texas Dept Comp Sci Austin TX 78712 USA

ISBN: (纸本)089871513X

There are several fundamental problems for which there are optimal randomized algorithms, but whose deterministic complexity remains unresolved. Among such problems are the minimum spanning tree problem, the set maxima problem, the problem of computing connected components and (minimum) spanning trees in parallel and the problem of performing sensitivity analysis on shortest path trees and minimum spanning trees. For each of these problems there is an optimal randomized algorithm which uses a linear number of random bits. We propose new algorithms (or adapt old ones) for these problems which preserve optimality while saving an exponential number of random bits. In the case of computing minimum spanning trees and MST/SSSP sensitivity analysis, we reduce the dependence on randomness to log* n random bits. We also consider the problem of selection, for which we give two algorithms which make an expected 1.5n + o(n) comparisons;one uses 0 (log n) random bits and is uniform, the other uses 0 (log log n) random bits and is non-uniform.

关键词： Sensitivity analysis

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An Optimal Approximation for Submodular Maximization under a Matroid Constraint in the Adaptive Complexity Model 2019

An Optimal Approximation for Submodular Maximization under a...

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51st annual acm SIGACT symposium on Theory of Computing (STOC)

作者： Balkanski, Eric Rubinstein, Aviad Singer, Yaron Harvard Univ Sch Engn & Appl Sci Cambridge MA 02138 USA Stanford Univ Dept Comp Sci Stanford CA 94305 USA

ISBN: (纸本)9781450367059

In this paper we study submodular maximization under a matroid constraint in the adaptive complexity model. This model was recently introduced in the context of submodular optimization to quantify the information theoretic complexity of black-box optimization in a parallel computation model. Informally, the adaptivity of an algorithm is the number of sequential rounds it makes when each round can execute polynomially-many function evaluations in parallel. Since submodular optimization is regularly applied on large datasets we seek algorithms with low adaptivity to enable speedups via parallelization. Consequently, a recent line of work has been devoted to designing constant factor approximation algorithms for maximizing submodular functions under various constraints in the adaptive complexity model. Despite the burst in work on submodular maximization in the adaptive complexity model, the fundamental problem of maximizing a monotone submodular function under a matroid constraint has remained elusive. In particular, all known techniques fail for this problem and there are no known constant factor approximation algorithms whose adaptivity is sublinear in the rank of the matroid k or in the worst case sublinear in the size of the ground set n. In this paper we present an approximation algorithm for the problem of maximizing a monotone submodular function under a matroid constraint in the adaptive complexity model. The approximation guarantee of the algorithm is arbitrarily close to the optimal 1 - 1/e and it has near optimal adaptivity of O(log(n)log(k)). This result is obtained using a novel technique of adaptive sequencing which departs from previous techniques for submodular maximization in the adaptive complexity model. In addition to our main result we show how to use this technique to design other approximation algorithms with strong approximation guarantees and polylogarithmic adaptivity.

关键词： Adaptivity submodular optimization matroids parallel algorithms

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Control Flow Coalescing on a Hybrid Dataflow/von Neumann GPGPU 48

Control Flow Coalescing on a Hybrid Dataflow/von Neumann GPG...

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48th annual IEEE/acm International symposium on Microarchitecture (MICRO)

作者： Voitsechov, Dani Etsion, Yoav Technion Israel Inst Technol Elect Engn Haifa Israel Technion Israel Inst Technol Elect Engn IL-32000 Haifa Israel Technion Israel Inst Technol Elect Engn & Comp Sci IL-32000 Haifa Israel

ISBN: (纸本)9781450340342

We propose the hybrid dataflow/von Neumann vector graph instruction word (VGIW) architecture. This data-parallel architecture concurrently executes each basic block's dataflow graph (graph instruction word) for a vector of threads, and schedules the different basic blocks based on von Neumann control flow semantics. The VGIW processor dynamically coalesces all threads that need to execute a specific basic block into a thread vector and, when the block is scheduled, executes the entire thread vector concurrently. The proposed control flow coalescing model enables the VGIW architecture to overcome the control flow divergence problem, which greatly impedes the performance and power efficiency of data-parallel architectures. Furthermore, using von Neumann control flow semantics enables the VGIW architecture to overcome the limitations of the recently proposed single-graph multiple-flows (SGMF) dataflow GPGPU, which is greatly constrained in the size of the kernels it can execute. Our evaluation shows that VGIW can achieve an average speedup of 3x (up to 11x) over an NVIDIA GPGPU, while providing an average 1.75x better energy efficiency (up to 7x).

关键词： SIMD GPGPU dataflow reconfigurable architectures

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parallel algorithms and concentration bounds for the Lovasz Local Lemma via witness-DAGs 28

Parallel algorithms and concentration bounds for the Lovasz ...

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28th annual acm-SIAM symposium on Discrete algorithms (SODA)

作者： Haeupler, Bernhard Harris, David G. Carnegie Mellon Univ Sch Comp Sci Pittsburgh PA 15213 USA Univ Maryland Dept Comp Sci College Pk MD 20742 USA

ISBN: (纸本)9781611974782

The Lovasz Local Lemma (LLL) is a cornerstone principle in the probabilistic method of combinatorics, and a seminal algorithm of Moser & Tardos (2010) provides an efficient randomized algorithm to implement it. This algorithm can be parallelized to give an algorithm that uses polynomially many processors and runs in O(log(3) n) time, stemming from O(log n) adaptive computations of a maximal independent set (MIS). Chung et al. (2014) developed faster local and parallel algorithms, potentially running in time O(log(2) n), but these algorithms work under significantly more stringent conditions than the LLL. We give a new parallel algorithm that works under essentially the same conditions as the original algorithm of Moser & Tardos but uses only a single MIS computation, thus running in O(log(2) n) time. This conceptually new algorithm also gives a clean combinatorial description of a satisfying assignment which might be of independent interest. Our techniques extend to the deterministic LLL algorithm given by Chandrasekaran et al. (2013) leading to an NC-algorithm running in time O(log(2) n) as well. We also provide improved bounds on the runtimes of the sequential and parallel resampling-based algorithms originally developed by Moser & Tardos. Our bounds extend to any problem instance in which the tighter Shearer LLL criterion is satisfied. We also improve on the analysis of Kolipaka & Szegedy (2011) to give tighter concentration results.

关键词： parallel algorithms

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PROCEEDINGS OF THE NINETEENTH annual acm symposium ON THEORY OF COMPUTING.

PROCEEDINGS OF THE NINETEENTH ANNUAL ACM SYMPOSIUM ON THEORY...

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Proceedings of the Nineteenth annual acm symposium on Theory of Computing.

作者： Anon

This conference proceedings contains 50 papers. The topics covered include: algorithms;graph theory;parallel processing;automata;Boolean circuits;computational geometry;cryptography;complexity;distributed computing.

关键词： COMPUTER METATHEORY

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String matching with wildcards in the massively parallel computation model 21

String matching with wildcards in the massively parallel com...

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33rd acm symposium on parallelism in algorithms and architectures, SPAA 2021

作者： Hajiaghayi, Mohammadtaghi Saleh, Hamed Seddighin, Saeed Sun, Xiaorui University of Maryland College ParkMD United States Toyota Technological Institute ChicagoIL United States University of Illinois ChicagoIL United States

ISBN: (纸本)9781450380706

We study distributed algorithms for string matching problem in presence of wildcard characters. Given a string T (a text), we look for all occurrences of another string P (a pattern) as a substring of string T. Each wildcard character in the pattern matches a specific class of strings based on its type. String matching is one of the most fundamental problems in computer science, especially in the fields of bioinformatics and machine learning. Persistent effort has led to a variety of algorithms for the problem since 1960s. With rise of big data and the inevitable demand to solve problems on huge data sets, there have been many attempts to adapt classic algorithms into the MPC framework to obtain further efficiency. MPC is a recent framework for parallel computation of big data, which is designed to capture the MapReduce-like algorithms. In this paper, we study the string matching problem in the MPC model and consider three types of wildcards: '?' wildcard: In this setting, the pattern is allowed to contain special '?' characters or don't cares that match any character of the text. String matching with don't cares could be solved by fast convolutions, and we give a constant round MPC algorithm for which by showing FFT could be implemented in a constant number of MPC rounds. '+' wildcard: '+' wildcard is a special character that allows for arbitrary repetitions of a character. When the pattern contains '+' wildcard characters, our algorithm runs in a constant number of MPC rounds by a reduction from subset matching problem. '∗' wildcard: '∗' is a special character that matches with any substring of the text. When '∗' is allowed in the pattern, we solve two special cases of the problem in logarithmic rounds. © 2021 acm.

关键词： Pattern matching

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