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Automatic Complexity Analysis of Explicitly parallel Programs 14

Automatic Complexity Analysis of Explicitly Parallel Program...

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26th acm symposium on parallelism in algorithms and architectures (SPAA)

作者： Hoefler, Torsten Kwasniewski, Grzegorz Swiss Fed Inst Technol Zurich Switzerland

ISBN: (纸本)9781450328210

The doubling of cores every two years requires programmers to expose maximum parallelism. Applications that are developed on today's machines will often be required to run on many more cores. Thus, it is necessary to understand how much parallelism codes can expose. The work and depth model provides a convenient mental framework to assess the required work and the maximum parallelism of algorithms and their parallel efficiency. We propose an automatic analysis to extract work and depth from a source-code. We do this by statically counting the number of loop iterations depending on the set of input parameters. The resulting expression can be used to assess work and depth with regards to the program inputs. Our method supports the large class of practically relevant loops with affine update functions and generates additional parameters for other expressions. We demonstrate how this method can be used to determine work and depth of several real-world applications. Our technique enables us to prove if the theoretically maximum parallelism is exposed in a practical implementation of a problem. This will be most important for future-proof software development.

关键词： Loop iterations Polyhedral model Work and depth analysis

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Improved sorting algorithms for parallel computers 87

Improved sorting algorithms for parallel computers

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15th annual Conference on Computer Science, CSC 1987

作者： Park, Arvin Balasubramanian, K. Department Computer Science Princeton University PrincetonNJ08544 United States

ISBN: (纸本)0897912187

We make observations that improve processor utilization and decrease communication overhead for several parallel sorting algorithms. These lead to constant factor improvements on the best previous parallel sorting bounds for both mesh-connected and linearly connected parallel architectures [2, 12] (Previous bounds were within a constant factor of optimal.). These improved bounds are achieved using fewer processors with greater processor utilization. © 1987 acm.

关键词： parallel architectures

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Asymptotically tight bounds for performing BMMC permutations on parallel disk systems 93

Asymptotically tight bounds for performing BMMC permutations...

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

作者： Cormen, Thomas H. Wisniewski, Leonard F. Department of Mathematics and Computer Science Dartmouth College United States

ISBN: (纸本)0897915992

We give asymptotically equal lower and upper bounds for the number of parallel I/O operations required to perform BMMC permutations (defined by a characteristic matrix that is nonsingular over GF{2)) on parallel disk systems. Under the Vitter-Shriver parallel-disk model with N records, D disks, block size B, and M records of RAM, we show a universal lower bound of Q (l + j)) parallel I/Os for performing a BMMC permutation, where 7 is the lower left lg(N/B) xlgB submatrix of the characteristic matrix. We adapt this lower bound to show that the algorithm for BPC permutations in [Cor93] is asymptotically optimal. We also present an algorithm that uses at most h (6 [is(m/b)1 + 5) parallel I/Os, which asymptotically matches the lower bound and improves upon the BMMC algorithm in [Cor93]. When rank(7) is low, this method is an improvement over the general-permutation bound of Although many BMMC permutations of practical interest fall into subclasses that might be explicitly invoked within the source code, we show how to detect in at most N/BD+ ['SW/H1] parallel I/Os whether a given vector of target addresses specifies a BMMC permutation. Thus, one can determine efficiently at run time whether a permutation to be performed is BMMC and then avoid the general-permutation algorithm and save parallel I/Os by using our algorithm. © 1993 acm.

关键词： Matrix algebra

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Analysis of multithreaded architectures for parallel computing 90

Analysis of multithreaded architectures for parallel computi...

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

作者： Saavedra-Barrera, Rafel H. Culler, David E. von Eicken, Thorsten Univ of California Berkeley CA United States

ISBN: (纸本)0897913701

Multithreading has been proposed as an architectural strategy for tolerating latency in multiprocessors and, through limited empirical studies, shown to offer promise. This paper develops an analytical model of multithreaded processor behavior based on a small set of architectural and program parameters. The model gives rise to a large Markov chain, which is solved to obtain a formula for processor efficiency in terms of the number of threads per processor, the remote reference rate, the latency, and the cost of switching between threads. It is shown that a multithreaded processor exhibits three operating regimes: linear (efficiency is proportional to the number of threads), transition, and saturation (efficiency depends only on the remote reference rate and switch cost). Formulae for regime boundaries are derived. The model is embellished to reflect cache degradation due to multithreading, using an analytical model of cache behavior, demonstrating that returns diminish as the number threads becomes large. Predictions from the embellished model correlate well with published empirical measurements. Prescriptive use of the model under various scenarios indicates that multithreading is effective, but the number of useful threads per processor is fairly small.

关键词： Computer architecture

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On parallel k-Center Clustering 23

On Parallel k-Center Clustering

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35th acm symposium on parallelism in algorithms and architectures (SPAA)

作者： Coy, Sam Czumaj, Artur Mishra, Gopinath Univ Warwick Coventry W Midlands England

ISBN: (纸本)9781450395458

We consider the classic k-center problem in a parallel setting, on the low-local-space Massively parallel Computation (MPC) model, with local space per machine of O(n(delta)), where delta is an element of(0, 1) is an arbitrary constant. As a central clustering problem, the k-center problem has been studied extensively. Still, until very recently, all parallel MPC algorithms have been requiring Omega(k) or even Omega(kn(delta)) local space per machine. While this setting covers the case of small values of k, for a large number of clusters these algorithms require large local memory, making them poorly scalable. The case of large k, k >= Omega(n(delta)), has been considered recently for the low-local-space MPC model by Bateni et al. (2021), who gave an O(log log n)-round MPC algorithm that produces k(1 + o(1)) centers whose cost has multiplicative approximation of O(log log log n). In this paper we extend the algorithm of Bateni et al. and design a low-local-space MPC algorithm that in O(log log..) rounds returns a clustering with k(1 + o(1)) clusters that is an O(log*n)-approximation for k-center.

关键词： MPC k-center clustering parallel computing MapReduce

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Provably good and practically efficient parallel race detection for fork-join programs 16

Provably good and practically efficient parallel race detect...

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28th acm symposium on parallelism in algorithms and architectures, SPAA 2016

作者： Utterback, Robert Agrawal, Kunal Fineman, Jeremy T. Lee, I-Ting Angelina Washington University St. Louis United States Georgetown University United States

ISBN: (纸本)9781450342100

If a parallel program has determinacy race(s), different schedules can result in memory accesses that observe different values - various race-detection tools have been designed to find such bugs. A key component of race detectors is an algorithm for series-parallel (SP) maintenance, which identifies whether two accesses are logically parallel. This paper describes an asymptotically optimal algorithm, called WSP-Order, for performing SP maintenance in programs with fork-join (or nested) parallelism. Given a fork-join program with T1 work and T∞ span, WSP-Order executes it while also maintaining SP relationships in O(T1/P + T∞) time on P processors, which is asymptotically optimal. At the heart of WSP-Order is a work-stealing scheduler designed specifically for SP maintenance. We also implemented C-RACER, a race-detector based on WSP-Order within the Cilk Plus runtime system, and evaluated its performance on five benchmarks. Empirical results demonstrate that when run sequentially, it performs almost as well as previous best sequential race detectors. More importantly, when run in parallel, it achieves almost as much speedup as the original program without race-detection. © 2016 acm.

关键词： Maintenance

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Evaluating Graph Coloring on GPUs 11

Evaluating Graph Coloring on GPUs

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16th acm symposium on Principles and Practice of parallel Programming

作者： Grosset, A. V. Pascal Zhu, Peihong Liu, Shusen Venkatasubramanian, Suresh Hall, Mary Univ Utah Sch Comp Salt Lake City UT 84112 USA

ISBN: (纸本)9781450301190

This paper evaluates features of graph coloring algorithms implemented on graphics processing units (GPUs), comparing coloring heuristics and thread decompositions. As compared to prior work on graph coloring for other parallel architectures, we find that the large number of cores and relatively high global memory bandwidth of a GPU lead to different strategies for the parallel implementation. Specifically, we find that a simple uniform block partitioning is very effective on GPUs and our parallel coloring heuristics lead to the same or fewer colors than prior approaches for distributed-memory cluster architecture. Our algorithm resolves many coloring conflicts across partitioned blocks on the GPU by iterating through the coloring process, before returning to the CPU to resolve remaining conflicts. With this approach we get as few color (if not fewer) than the best sequential graph coloring algorithm and performance is close to the fastest sequential graph coloring algorithms which have poor color quality.

关键词： algorithms Performance Graph coloring parallel algorithm GPU CUDA

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Faster parallel Algorithm for Approximate Shortest Path 2020

Faster Parallel Algorithm for Approximate Shortest Path

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52nd annual acm SIGACT symposium on Theory of Computing (STOC)

作者： Li, Jason Carnegie Mellon Univ Pittsburgh PA 15213 USA

ISBN: (纸本)9781450369794

We present the firstm polylog(n) work, polylog(n) time algorithm in the PRAM model that computes (1 + epsilon)-approximate single-source shortest paths on weighted, undirected graphs. This improves upon the breakthrough result of Cohen [Jacm'00] that achieves O(m(1+epsilon 0)) work and polylog(n) time. While most previous approaches, including Cohen's, leveraged the power of hopsets, our algorithm builds upon the recent developments in continuous optimization, studying the shortest path problem from the lens of the closely-related minimum transshipment problem. To obtain our algorithm, we demonstrate a series of near-linearwork, polylogarithmic-time reductions between the problems of approximate shortest path, approximate transshipment, and l(1)-embeddings, and establish a recursive algorithm that cycles through the three problems and reduces the graph size on each cycle. As a consequence, we also obtain faster parallel algorithms for approximate transshipment and l(1)-embeddings with polylogarithmic distortion. The minimum transshipment algorithm in particular improves upon the previous best m(1+o(1)) work sequential algorithm of Sherman [SODA'17]. To improve readability, the paper is almost entirely self-contained, save for several staple theorems in algorithms and combinatorics.

关键词： parallel algorithms Shortest Path Minimum Transshipment

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Deterministic Massively parallel Connectivity*† 2022

Deterministic Massively Parallel Connectivity*†

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54th annual acm SIGACT symposium on Theory of Computing (STOC)

作者： Coy, Sam Czumaj, Artur Univ Warwick Coventry W Midlands England

ISBN: (纸本)9781450392648

We consider the problem of designing fundamental graph algorithms on the model of Massive parallel Computation (MPC). The input to the problem is an undirected graph G with n vertices and m edges, and with D being the maximum diameter of any connected component in G. We consider the MPC with low local space, allowing each machine to store only Theta(n(delta)) words for an arbitrary constant delta > 0, and with linear global space (which is the number of machines times the local space available), that is, with optimal utilization. In a recent breakthrough, Andoni et al. (FOCS'18) and Behnezhad et al. (FOCS'19) designed parallel randomized algorithms that in O (logD + log log n) rounds on an MPC with low local space determine all connected components of a graph, improving on the classic bound of O ( log n) derived from earlier works on PRAM algorithms. In this paper, we show that asymptotically identical bounds can be also achieved for deterministic algorithms: we present a deterministic MPC low local space algorithm that in O (log D + log log n) rounds determines connected components of the input graph. Our result matches the complexity of state of the art randomized algorithms for this task. The techniques developed in our paper can be also applied to several related problems, giving new deterministic MPC algorithms for problems like finding a spanning forest, minimum spanning forest, etc. We complement our upper bounds by extending a recent lower bound for connectivity on an MPC conditioned on the 1-vs-2-cycles conjecture (which requires D >= log1+Omega(1) n), by showing a related conditional hardness of Omega( log D ) MPC rounds for the entire spectrum of D, covering a particularly interesting range when D <= O( log n).

关键词： derandomization connectivity MapReduce MPC massively parallel algorithms

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Dynamic Graph algorithms with Batch Updates in the Massively parallel Computation Model 32

Dynamic Graph Algorithms with Batch Updates in the Massively...

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32nd annual acm-SIAM symposium on Discrete algorithms (SODA)

作者： Nowicki, Krzysztof Onak, Krzysztof Univ Wroclaw Wroclaw Poland IBM Res Hawthorne NY USA

ISBN: (纸本)9781611976465

We study dynamic graph algorithms in the Massively parallel Computation model, which was inspired by practical data processing systems. Our goal is to provide algorithms that can efficiently handle large batches of edge insertions and deletions. We show algorithms that require fewer rounds to update a solution to problems such as Minimum Spanning Forest, 2-Edge Connected Components, and Maximal Matching than would be required by their static counterparts to compute it from scratch. They work in the most restrictive memory regime, in which local memory per machine is strongly sublinear in the number of graph vertices. Improving on the size of the batch they can handle efficiently would improve on the round complexity of known static algorithms on sparse graphs. Our algorithms can process batches of updates of size Theta(S), for Minimum Spanning Forest and 2-Edge Connected Components, and Theta(S1-epsilon), for Maximal Matching, in O(1) rounds, where S is the local memory of a single machine.

关键词： Scheduling algorithms

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