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Brief Announcement: On the I/O Complexity of Sequential and parallel Hybrid Integer Multiplication algorithms 22

Brief Announcement: On the I/O Complexity of Sequential and ...

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34th acm symposium on parallelism in algorithms and architectures (SPAA)

作者： De Stefani, Lorenzo Brown Univ Providence RI 02912 USA

ISBN: (纸本)9781450391467

Almost asymptotically tight lower bounds are derived for the Input/Output (I/O) complexity IOA(n, M) of a general class of hybrid algorithms computing the product of two integers, each represented with n digits in a given base s, in a two-level storage hierarchy with M words of fast memory, with different digits stored in different memory words. The considered hybrid algorithms combine the Toom-Cook-k (or Toom-k) fast integer multiplication approach with computational complexity Theta(c(k)n(logk) ((2k-1))), and "standard" integer multiplication algorithms which compute Omega(n(2)) digit multiplications. We present an Omega((n/max{M, n(0)})(logk (2k-1)) (max{1, n(0)/M})(2) M) lower bound for the I/O complexity of a class of "uniform, non-stationary" hybrid algorithms, where n(0) denotes the threshold size of sub-problems which are computed using standard algorithms with algebraic complexity Omega(n(2)). As a special case, our result yields an asymptotically tight Omega(n(2)/M) lower bound for the I/O complexity of any standard integer multiplication algorithm. As some sequential hybrid algorithms from this class exhibit I/O cost within a O(k(2)) multiplicative term of the corresponding lower bounds, the proposed lower bounds are almost asymptotically tight and indeed tight for constant values of k. By extending these results to a distributed memory model with P processors, we obtain both memory-dependent and memory-independent I/O lower bounds for parallel versions of hybrid integer multiplication algorithms. All the lower bounds are derived for the more general class of "non-uniform, non-stationary" hybrid algorithms that allow recursive calls to have a different structure, even when computing sub-problems with the same input size, and to use different versions of Toom-k.

关键词： Integer Multiplication I/O complexity Hybrid algorithms Lower Bounds parallel Model Distributed Memory

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parallel Cover Trees and their Applications 22

Parallel Cover Trees and their Applications

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34th acm symposium on parallelism in algorithms and architectures (SPAA)

作者： Gu, Yan Napier, Zachary Sun, Yihan Wang, Letong UC Riverside Riverside CA 92521 USA

ISBN: (纸本)9781450391467

The cover tree is the canonical data structure that efficiently maintains a dynamic set of points on a metric space and supports nearest and k-nearest neighbor searches. For most real-world datasets with reasonable distributions (constant expansion rate and bounded aspect ratio mathematically), single-point insertion, single-point deletion, and nearest neighbor search (NNS) only cost logarithmically to the size of the point set. Unfortunately, due to the complication and the use of depth-first traversal order in the cover tree algorithms, we were unaware of any parallel approaches for these cover tree algorithms. This paper shows highly parallel and work-efficient cover tree algorithms that can handle batch insertions (and thus construction) and batch deletions. Assuming constant expansion rate and bounded aspect ratio, inserting or deleting m points into a cover tree with n points takes O(m log n) expected work and polylogarithmic span with high probability. Our algorithms rely on some novel algorithmic insights. We model the insertion and deletion process as a graph and use a maximal independent set (MIS) to generate tree nodes without conflicts. We use three key ideas to guarantee work-efficiency: the prefix-doubling scheme, a careful design to limit the graph size on which we apply MIS, and a strategy to propagate information among different levels in the cover tree. We also use path-copying to make our parallel cover tree a persistent data structure, which is useful in several applications. Using our parallel cover trees, we show work-efficient (or near-work-efficient) and highly parallel solutions for a list of problems in computational geometry and machine learning, including Euclidean minimum spanning tree (EMST), single-linkage clustering, bichromatic closest pair (BCP), density-based clustering and its hierarchical version, and others. To the best of our knowledge, many of them are the first solutions to achieve work-efficiency and polylogarithmic span ass

关键词： cover tree parallel algorithms parallel data structures nearest neighbor search euclidean minimum spanning tree single-linkage clustering

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parallel Batch-Dynamic algorithms for k-Core Decomposition and Related Graph Problems 22

Parallel Batch-Dynamic Algorithms for k-Core Decomposition a...

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34th acm symposium on parallelism in algorithms and architectures (SPAA)

作者： Liu, Quanquan C. Shi, Jessica Yu, Shangdi Dhulipala, Laxman Shun, Julian Northeastern Univ Boston MA 02115 USA MIT CSAIL Cambridge MA USA Univ Maryland College Pk MD USA

ISBN: (纸本)9781450391467

Maintaining a k-core decomposition quickly in a dynamic graph has important applications in network analysis. The main challenge for designing efficient exact algorithms is that a single update to the graph can cause significant global changes. Our paper focuses on approximation algorithms with small approximation factors that are much more efficient than what exact algorithms can obtain. We present the first parallel, batch-dynamic algorithm for approximate k-core decomposition that is efficient in both theory and practice. Our algorithm is based on our novel parallel level data structure, inspired by the sequential level data structures of Bhattacharya et al. [STOC '15] and Henzinger et al. [2020]. Given a graph with n vertices and a batch of updates B, our algorithm provably maintains a (2 + epsilon)-approximation of the coreness values of all vertices (for any constant epsilon > 0) in O(|B| log(2) n) amortized work and /o(log(2) n log log n) depth (parallel time) with high probability. As a by-product, our k-core decomposition algorithm also gives a batch-dynamic algorithm for maintaining an O(alpha) out-degree orientation, where alpha is the current arboricity of the graph. We demonstrate the usefulness of our low out-degree orientation algorithm by presenting a new framework to formally study batch-dynamic algorithms in bounded-arboricity graphs. Our framework obtains new provably-efficient parallel batch-dynamic algorithms for maximal matching, clique counting, and vertex coloring. We implemented and experimentally evaluated our k-core decomposition algorithm on a 30-core machine with two-way hyperthreading on 11 graphs of varying densities and sizes. Compared to the state-of-the-art algorithms, our algorithm achieves up to a 114.52x speedup against the best parallel implementation, up to a 544.22x speedup against the best approximate sequential algorithm, and up to a 723.72x speedup against the best exact sequential algorithm. We also obtain results for our

关键词： parallel batch-dynamic algorithms k-core decomposition low out-degree orientation maximal matching k-clique counting vertex coloring

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Adaptive Massively parallel algorithms for Cut Problems 22

Adaptive Massively Parallel Algorithms for Cut Problems

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34th acm symposium on parallelism in algorithms and architectures (SPAA)

作者： Hajiaghayi, MohammadTaghi Knittel, Marina Olkowski, Jan Saleh, Hamed Univ Maryland College Pk MD 20742 USA

ISBN: (纸本)9781450391467

We study the Weighted Min Cut problem in the Adaptive Massively parallel Computation (AMPC) model. In 2019, Behnezhad et al. [3] introduced the AMPC model as an extension of the Massively parallel Computation (MPC) model. In the past decade, research on highly scalable algorithms has had significant impact on many massive systems. The MPC model, introduced in 2010 by Karloff et al. [16], which is an abstraction of famous practical frameworks such as MapReduce, Hadoop, Flume, and Spark, has been at the forefront of this research. While great strides have been taken to create highly efficient MPC algorithms for a range of problems, recent progress has been limited by the 1-vs-2 Cycle Conjecture [20], which postulates that the simple problem of distinguishing between one and two cycles requires Omega( log n) MPC rounds. In the AMPC model, each machine has adaptive read access to a distributed hash table even when communication is restricted (i.e., in the middle of a round). While remaining practical [4], this gives algorithms the power to bypass limitations like the 1-vs-2 Cycle Conjecture. We give the first sublogarithmic AMPC algorithm, requiring O(log logn) rounds, for (2 + epsilon)-approximate weighted Min Cut. Our algorithm is inspired by the divide and conquer approach of Ghaffari and Nowicki [11], which solves the ( 2 +epsilon)-approximate weighted Min Cut problem in O ( log n log log n) rounds of MPC using the classic result of Karger and Stein [15]. Our work is fullyscalable in the sense that the local memory of each machine is O(n(epsilon)) for any constant 0 < epsilon < 1. There are no o(logn)-round MPC algorithms for Min Cut in this memory regime assuming the 1-vs-2 Cycle Conjecture holds. The exponential speedup in the AMPC runtime is the result of decoupling the different layers of the divide and conquer algorithm and solving all layers in O (1) rounds in parallel. Finally, we extend our approach: we present an O (kappa log log n)-round AMPC algorithms fo

关键词： Massively parallel Computation minimum cut adaptivity

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Brief Announcement: A parallel (Δ, Γ)-Stepping Algorithm for the Constrained Shortest Path Problem 22

Brief Announcement: A Parallel (Δ, Γ)-Stepping Algorithm f...

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34th acm symposium on parallelism in algorithms and architectures (SPAA)

作者： Bahreini, Tayebeh Fisher, Nathan Grosu, Daniel Wayne State Univ Detroit MI USA

ISBN: (纸本)9781450391467

We design a parallel algorithm for the Constrained Shortest Path (CSP) problem. The CSP problem is known to be NP-hard and there exists a pseudo-polynomial time sequential algorithm that solves it. To design the parallel algorithm, we extend the techniques used in the design of the Delta-stepping algorithm for the single-source shortest paths problem.

关键词： constrained shortest path delta-stepping parallel algorithm

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A Deterministic parallel Reduction from Weighted Matroid Intersection Search to Decision 33

A Deterministic Parallel Reduction from Weighted Matroid Int...

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annual acm-SIAM symposium on Discrete algorithms (SODA)

作者： Ghosh, Sumanta Gurjar, Rohit Raj, Roshan Indian Inst Technol Dept Comp Sci Mumbai Maharashtra India

ISBN: (纸本)9781611977073

Given two matroids on the same ground set, the matroid intersection problem asks for a common base, i.e., a subset of the ground set that is a base in both the matroids. The weighted version of the problem asks for a common base with maximum weight. In the general case, when the two matroids are given via rank oracles, the question of its parallel complexity is completely open. In the case of linearly representable matroids, the problem is known to have randomized parallel (RNC) algorithms, when the given weights are polynomially bounded. Finding a deterministic parallel (NC) algorithm in this case, even for the decision question, has been a long standing open question. We make some progress towards understanding the parallel complexity of matroid intersection by showing that the weighted matroid intersection (WMI) search problem is equivalent to its decision version, in a parallel model of computation. More precisely, we give an NC algorithm for WMI-search using an oracle access to WMI-decision. This resolves an open question posed by Anari and Vazirani (ITCS 2020).

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iQAN: Fast and Accurate Vector Search with Efficient Intra-Query parallelism on Multi-Core architectures 23

iQAN: Fast and Accurate Vector Search with Efficient Intra-Q...

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28th acm SIGPLAN annual symposium on Principles and Practice of parallel Programming, PPoPP 2023

作者： Peng, Zhen Zhang, Minjia Li, Kai Jin, Ruoming Ren, Bin College of William & Mary WilliamsburgVA United States Microsoft AI and Research BellevueWA United States Kent State University KentOH United States

ISBN: (纸本)9798400700156

Vector search has drawn a rapid increase of interest in the research community due to its application in novel AI applications. Maximizing its performance is essential for many tasks but remains preliminary understood. In this work, we investigate the root causes of the scalability bottleneck of using intra-query parallelism to speedup the state-of-the-art graph-based vector search systems on multi-core architectures. Our in-depth analysis reveals several scalability challenges from both system and algorithm perspectives. Based on the insights, we propose iQAN, a parallel search algorithm with a set of optimizations that boost convergence, avoid redundant computations, and mitigate synchronization overhead. Our evaluation results on a wide range of real-world datasets show that iQAN achieves up to 37.7× and 76.6× lower latency than state-of-the-art sequential baselines on datasets ranging from a million to a hundred million datasets. We also show that iQAN achieves outstanding scalability as the graph size or the accuracy target increases, allowing it to outperform the state-of-the-art baseline on two billion-scale datasets by up to 16.0× with up to 64 cores. © 2023 Owner/Author.

关键词： Scalability

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Exploring the Use of WebAssembly in HPC 23

Exploring the Use of WebAssembly in HPC

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28th acm SIGPLAN annual symposium on Principles and Practice of parallel Programming, PPoPP 2023

作者： Chadha, Mohak Krueger, Nils John, Jophin Jindal, Anshul Gerndt, Michael Benedict, Shajulin Computer Architecture and Parallel Systems Technische Universität München Germany Department of Computer Science and Engg. Indian and Institute of Information Technology Kottayam Kerala India

ISBN: (纸本)9798400700156

Containerization approaches based on namespaces offered by the Linux kernel have seen an increasing popularity in the HPC community both as a means to isolate applications and as a format to package and distribute them. However, their adoption and usage in HPC systems faces several challenges. These include difficulties in unprivileged running and building of scientific application container images directly on HPC resources, increasing heterogeneity of HPC architectures, and access to specialized networking libraries available only on HPC systems. These challenges of container-based HPC application development closely align with the several advantages that a new universal intermediate binary format called WebAssembly (Wasm) has to offer. These include a lightweight userspace isolation mechanism and portability across operating systems and processor architectures. In this paper, we explore the usage of Wasm as a distribution format for MPI-based HPC applications. To this end, we present MPIWasm, a novel Wasm embedder for MPI-based HPC applications that enables high-performance execution of Wasm code, has low-overhead for MPI calls, and supports high-performance networking interconnects present on HPC systems. We evaluate the performance and overhead of MPIWasm on a production HPC system and AWS Graviton2 nodes using standardized HPC benchmarks. Results from our experiments demonstrate that MPIWasm delivers competitive native application performance across all scenarios. Moreover, we observe that Wasm binaries are 139.5x smaller on average as compared to the statically-linked binaries for the different standardized benchmarks. © 2023 acm.

关键词： Containers

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Training one DeePMD Model in Minutes: a Step towards Online Learning 24

Training one DeePMD Model in Minutes: a Step towards Online ...

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29th acm SIGPLAN annual symposium on Principles and Practice of parallel Programming (PPoPP)

作者： Hu, Siyu Zhao, Tong Sha, Qiuchen Li, Enji Meng, Xiangyu Liu, Liping Wang, Lin-Wang Tan, Guangming Jia, Weile Chinese Acad Sci Inst Comp Technol State Key Lab Proc Beijing Peoples R China Univ Chinese Acad Sci Beijing Peoples R China China Univ Petr Qingdao Inst Software Coll Comp Sci & Technol Qingdao Peoples R China Chinese Acad Sci Inst Semicond Beijing Peoples R China

ISBN: (纸本)9798400704352

Neural Network Molecular Dynamics (NNMD) has become a major approach in material simulations, which can speedup the molecular dynamics (MD) simulation for thousands of times, while maintaining ab initio accuracy, thus has a potential to fundamentally change the paradigm of material simulations. However, there are two time-consuming bottlenecks of the NNMD developments. One is the data access of ab initio calculation results. The other, which is the focus of the current work, is reducing the training time of NNMD model. The training of NNMD model is different from most other neural network training because the atomic force (which is related to the gradient of the network) is an important physical property to be fit. Tests show the traditional stochastic gradient methods, like the Adam algorithms, cannot efficiently deploy the multisample minibatch algorithm. As a result, a typical training (taking the Deep Potential Molecular Dynamics (DeePMD) as an example) can take many hours. In this work, we designed a heuristic minibatch quasi-Newtonian optimizer based on Extended Kalman Filter method. An early reduction of gradient and error is adopted to reduce memory footprint and communication. The memory footprint, communication and settings of hyper-parameters of this new method are analyzed in detail. Computational innovations such as customized kernels of the symmetry-preserving descriptor are applied to exploit the computing power of the heterogeneous architecture. Experiments are performed on 8 different datasets representing different real case situations, and numerical results show that our new method has an average speedup of 32.2 compared to the Reorganized Layer-wised Extended Kalman Filter with 1 GPU, reducing the absolute training time of one DeePMD model from hours to several minutes, making it one step toward online training.

关键词： parallel training Molecular dynamics First principle ab initio GPU

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Proceedings of the 38th acm/SIGAPP symposium on Applied Computing, SAC 2023

Proceedings of the 38th ACM/SIGAPP Symposium on Applied Comp...

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38th annual acm symposium on Applied Computing, SAC 2023

ISBN: (纸本)9781450395175

The proceedings contain 259 papers. The topics discussed include: EdGCon: auto-assigner of iconicity ratings grounded by lexical properties to aid in generation of technical gestures;a semantic evidence-based approach to continuous cloud service certification;digital forgetting using key decay;on the measurement of performance metrics for virtualization-enhanced architectures;COSTA: a cost-driven solution for migrating applications in multi-cloud environments;towards a high-interaction physics-aware honeynet for industrial control systems;enhancing polar codes efficiency on 3D flash memory by exploiting multiple error variations;traffic intersections as agents: a model checking approach for analyzing communicating agents;an extensible framework for implementing byzantine fault-tolerant protocols;detection of adversarial attacks by observing deep features with structured data algorithms;and proof of swarm based ensemble learning for federated learning applications.

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