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Optimal Deterministic Massively parallel Connectivity on Forests 34

Optimal Deterministic Massively Parallel Connectivity on For...

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34th acm-SIAM annual symposium on Discrete algorithms (SODA)

作者： Balliu, Alkida Latypov, Rustam Maus, Yannic Olivetti, Dennis Uitto, Jara Gran Sasso Sci Inst Laquila Italy Aalto Univ Espoo Finland Graz Univ Technol Graz Austria

ISBN: (纸本)9781611977554

We show fast deterministic algorithms for fundamental problems on forests in the challenging low-space regime of the well-known Massive parallel Computation (MPC) model. A recent breakthrough result by Coy and Czumaj [STOC'22] shows that, in this setting, it is possible to deterministically identify connected components on graphs in O (log D + log log n) rounds, where D is the diameter of the graph and n the number of nodes. The authors left open a major question: is it possible to get rid of the additive log log n factor and deterministically identify connected components in a runtime that is completely independent of n? We answer the above question in the affirmative in the case of forests. We give an algorithm that identifies connected components in O (log D) deterministic rounds. The total memory required is O(n + m) words, where m is the number of edges in the input graph, which is optimal as it is only enough to store the input graph. We complement our upper bound results by showing that Omega(log D) time is necessary even for component-unstable algorithms, conditioned on the widely believed 1 vs. 2 cycles conjecture. Our techniques also yield a deterministic forest-rooting algorithm with the same runtime and memory bounds. Furthermore, we consider Locally Checkable Labeling problems (LCLs), whose solution can be verified by checking the O(1)-radius neighborhood of each node. We show that any LCL problem on forests can be solved in O(log D) rounds with a canonical deterministic algorithm, improving over the O(log n) runtime of Brandt, Latypov and Uitto [DISC'21]. We also show that there is no algorithm that solves all LCL problems on trees asymptotically faster.

关键词： Graph algorithms

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Many Sequential Iterative algorithms Can Be parallel and (Nearly) Work-efficient 22

Many Sequential Iterative Algorithms Can Be Parallel and (Ne...

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

作者： Shen, Zheqi Wan, Zijin Gu, Yan Sun, Yihan UC Riverside Riverside CA 92521 USA

ISBN: (纸本)9781450391467

Some recent papers showed that many sequential iterative algorithms can be directly parallelized, by identifying the dependences between the input objects. This approach yields many simple and practical parallel algorithms, but there are still challenges to achieve work-efficiency and high-parallelism. Work-efficiency means that the number of operations is asymptotically the same as the best sequential solution. This can be hard for certain problems where the number of dependences between objects is asymptotically more than optimal sequential work, and we cannot even afford the cost to generate them. To achieve high-parallelism, we always want it to process as many objects as possible in parallel. The goal is to achieve (O) over tilde (D) span for a problem with the deepest dependence length D. We refer to this property as round-efficiency. This paper presents work-efficient and round-efficient algorithms for a variety of classic problems and propose general approaches to do so. To efficiently parallelize many sequential iterative algorithms, we propose the phase-parallel framework. The framework assigns a rank to each object and processes the objects based on the order of their ranks. All objects with the same rank can be processed in parallel. To enable work-efficiency and high parallelism, we use two types of general techniques. Type 1 algorithms aim to use range queries to extract all objects with the same rank to avoid evaluating all the dependences. We discuss activity selection, and Dijkstra's algorithm using Type 1 framework. Type 2 algorithms aim to wake up an object when the last object it depends on is finished. We discuss activity selection, longest increasing subsequence (LIS), greedy maximal independent set (MIS), and many other algorithms using Type 2 framework. All of our algorithms are (nearly) work-efficient and round-efficient, and some of them (e.g., LIS) are the first to achieve the both. Many of them improve the previous best bounds. Moreover,

关键词： parallel algorithms phase-parallel framework parallel programming sequential iterative algorithms activity selection longest increasing subsequence maximal independent set independence system

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POSTER: parallel algorithms for Masked Sparse Matrix-Matrix Products 27

POSTER: Parallel Algorithms for Masked Sparse Matrix-Matrix ...

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27th acm SIGPLAN symposium on Principles and Practice of parallel Programming (PPoPP)

作者： Milakovic, Srdan Selvitopi, Oguz Nisa, Israt Budimlic, Zoran Buluc, Aydin Rice Univ Houston Houston TX USA Lawrence Berkeley Nat Lab Berkeley Berkeley CA USA AWS Palo Alto Palo Alto CA USA

ISBN: (纸本)9781450392044

Computing the product of two sparse matrices (SpGEMM) is a fundamental operation in various combinatorial and graph algorithms as well as various bioinformatics and data analytics applications for computing inner-product similarities. For an important class of algorithms, only a subset of the output entries are needed, and the resulting operation is known as Masked SpGEMM since a subset of the output entries is considered to be "masked out". In this work, we investigate various novel algorithms and data structures for this rather challenging and important computation, and provide guidelines on how to design a fast Masked-SpGEMM for shared-memory architectures.

关键词： Masked-SpGEMM Sparse Matrix GraphBLAS

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Deterministic algorithms for the Lov′asz Local Lemma: simpler, more general, and more parallel 33

Deterministic algorithms for the Lov′asz Local Lemma: simpl...

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annual acm-SIAM symposium on Discrete algorithms (SODA)

作者： Harris, David G. Univ Maryland Dept Comp Sci College Pk MD 20742 USA

ISBN: (纸本)9781611977073

The Lov ' asz Local Lemma (LLL) is a keystone principle in probability theory, guaranteeing the existence of configurations which avoid a collection B of "bad" events which are mostly independent and have low probability. In its simplest "symmetric" form, it asserts that whenever a bad-event has probability p and affects at most d bad-events, and epd < 1, then a configuration avoiding all B exists. A seminal algorithm of Moser & Tardos (2010) (which we call the MT algorithm) gives nearly-automatic randomized algorithms for most constructions based on the LLL. However, deterministic algorithms have lagged behind. We address three specific shortcomings of the prior deterministic algorithms. First, our algorithm applies to the LLL criterion of Shearer (1985);this is more powerful than alternate LLL criteria and also removes a number of nuisance parameters and leads to cleaner and more legible bounds. Second, we provide parallel algorithms with much greater flexibility in the functional form of the bad-events. Third, we provide a derandomized version of the MT-distribution, that is, the distribution of the variables at the termination of the MT algorithm. We show applications to non-repetitive vertex coloring, independent transversals, strong coloring, and other problems. These give deterministic algorithms which essentially match the best previous randomized sequential and parallel algorithms.

关键词： parallel algorithms

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***: On-Demand Data-parallel Acceleration for Mobile Systems on Chip 55

***: On-Demand Data-Parallel Acceleration for Mobile Systems...

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55th annual IEEE/acm International symposium on Microarchitecture (MICRO)

作者： Ta, Tuan Al-Hawaj, Khalid Cebry, Nick Ou, Yanghui Hall, Eric Golden, Courtney Batten, Christopher Cornell Univ Sch Elect & Comp Engn Ithaca NY 14853 USA

ISBN: (数字)9781665462723

ISBN: (纸本)9781665462723

Single-ISA heterogeneous multi-core architectures offer a compelling high-performance and high-efficiency solution to executing task-parallel workloads in mobile systems on chip (SoCs). In addition to task-parallel workloads, many data-parallel applications, such as machine learning, computer vision, and data analytics, increasingly run on mobile SoCs to provide real-time user interactions. Next-generation scalable vector architectures, such as the RISC-V Vector Extension and Arm SVE, have recently emerged as unified vector abstractions for both large- and small-scale systems. In this paper, we propose novel area-efficient high-performance architectures called *** that support next-generation vector architectures to efficiently accelerate data-parallel workloads in conventional *** systems. *** architectures reconfigure multiple little cores on demand to work as a decoupled vector engine when executing data-parallel workloads. Our results show that a *** system can achieve 1.6x performance speedup over an area-comparable *** system equipped with an integrated vector unit across multiple data-parallel applications and 1.7x speedup compared to an aggressive decoupled vector engine for task-parallel workloads.

关键词： Support vector machines Microarchitecture Scalability Computer architecture Silicon Real-time systems System-on-chip

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PPoPP 2023 - Proceedings of the 28th acm SIGPLAN annual symposium on Principles and Practice of parallel Programming

PPoPP 2023 - Proceedings of the 28th ACM SIGPLAN Annual Symp...

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

ISBN: (纸本)9798400700156

The proceedings contain 43 papers. The topics discussed include: provably good randomized strategies for data placement in distributed key-value stores;provably fast and space-efficient parallel biconnectivity;practically and theoretically efficient garbage collection for multiversioning;fast and scalable channels in Kotlin coroutines;high-performance GPU-to-CPU transpilation and optimization via high-level parallel constructs;lifetime-based optimization for simulating quantum circuits on a new Sunway supercomputer;merchandiser: data placement on heterogeneous memory for task-parallel HPC applications with load-balance awareness;visibility algorithms for dynamic dependence analysis and distributed coherence;Block-STM: scaling blockchain execution by turning ordering curse to a performance blessing;TDC: towards extremely efficient CNNs on GPUs via hardware-aware tucker decomposition;and improving energy saving of one-sided matrix decompositions on CPU-GPU heterogeneous systems.

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HAM-SpMSpV: an Optimized parallel Algorithm for Masked Sparse Matrix-Sparse Vector Multiplications on multi-core CPUs 24

HAM-SpMSpV: an Optimized Parallel Algorithm for Masked Spars...

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33rd International symposium on High-Performance parallel and Distributed Computing (HPDC)

作者： Xu, Lei Jia, Haipeng Zhang, Yunquan Wang, Luhan Jiang, Xianmeng Univ Chinese Acad Sci Chinese Acad Sci Inst Comp Technol Sch Comp Sci & Technol Beijing Peoples R China Chinese Acad Sci Inst Comp Technol Beijing Peoples R China

ISBN: (纸本)9798400704130

The efficiency of Sparse Matrix-Sparse Vector Multiplication (SpM-SpV) is critically important in fields such as machine learning and graph analytics. In certain algorithms, masked SpMSpV computes only a subset of the result entries. Despite its significance, this selective computation poses unique challenges, and existing algorithms often struggle to exploit the sparsity of the input and the mask vectors concurrently. To boost the efficiency of masked SpMSpV on shared memory architectures, we introduce a hybrid adaptive masked SpMSpV algorithm (HAM-SpMSpV) designed to select the efficient kernel automatically based on input features. This approach builds upon the foundation of a conventional algorithm, incorporating two novel masked SpMSpVs: the pre-bucketing masked SPA-based algorithm and the pre-masking bucketed hash-based algorithm. The newly proposed algorithms significantly expedite computation, especially in scenarios with high sparsity in input vectors and masks. Our evaluation involved extensive testing across a diverse range of real-world graphs, utilizing various sparsity of input vectors and masks. This rigorous testing confirmed that our approach notably outperforms existing solutions. Specifically, it achieves a speedup of up to 1.96 times compared to SuiteSparse:GraphBLAS and a remarkable 6.28 times relative to MKL Graph, demonstrating significant advancements in SpMSpV efficiency.

关键词： Sparse Matrix-Sparse Vector Multiplication (SpMSpV) Mask Shared Memory Adaptive Method

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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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Simple parallel algorithms for Single-Site Dynamics 2022

Simple Parallel Algorithms for Single-Site Dynamics

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

作者： Liu, Hongyang Yin, Yitong Nanjing Univ State Key Lab Novel Software Technol Nanjing Jiangsu Peoples R China

ISBN: (纸本)9781450392648

The single-site dynamics are a canonical class of Markov chains for sampling from high-dimensional probability distributions, e.g. the ones represented by graphical models. We give a simple and generic parallel algorithm that can faithfully simulate single-site dynamics. When the chain asymptotically satisfies the l(p) -Dobrushin's condition, specifically, when the Dobrushin's influence matrix has constantly bounded l(p)-induced operator norm for an arbitrary p epsilon [1, 8], the parallel simulation of.. steps of single-site updates succeeds within Omicron (Nu / n + log n) depth of parallel computing using (O) over tilde (m) processors, where n is the number of sites and.. is the size of graphical model. Since the Dobrushin's condition is almost always satisfied asymptotically by mixing chains, this parallel simulation algorithm essentially transforms single-site dynamics with optimal o (n log n) mixing time to RNC algorithms for sampling. In particular we obtain RNC samplers, for the Ising models on general graphs in the uniqueness regime, and for satisfying solutions of CNF formulas in a local lemma regime. With non-adaptive simulated annealing, these RNC samplers can be transformed routinely to RNC algorithms for approximate counting. A key step in our parallel simulation algorithm, is a so-called "universal coupling" procedure, which tries to simultaneously couple all distributions over the same sample space. We construct such a universal coupling, that for every pair of distributions the coupled probability is at least their Jaccard similarity. We also prove that this is optimal in the worst case. The universal coupling and its applications are of independent interests.

关键词： Single-site dynamics Markov chain Monte Carlo sampling

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parallel Batch-Dynamic Minimum Spanning Forest and the Efficiency of Dynamic Agglomerative Graph Clustering 22

Parallel Batch-Dynamic Minimum Spanning Forest and the Effic...

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

作者： Tseng, Tom Dhulipala, Laxman Shun, Julian MIT CSAIL Cambridge MA 02139 USA Univ Maryland College Pk MD USA

ISBN: (纸本)9781450391467

Hierarchical agglomerative clustering (HAC) is a popular algorithm for clustering data, but despite its importance, no dynamic algorithms for HAC with good theoretical guarantees exist. In this paper, we study dynamic HAC on edge-weighted graphs. As single-linkage HAC reduces to computing a minimum spanning forest (MSF), our first result is a parallel batch-dynamic algorithm for maintaining MSFs. On a batch of k edge insertions or deletions, our batch-dynamic MSF algorithm runs in O(k log(6) n) expected amortized work and O(log(4) n) span with high probability. It is the first fully dynamic MSF algorithm handling batches of edge updates with polylogarithmic work per update and polylogarithmic span. Using our MSF algorithm, we obtain a parallel batch-dynamic algorithm that can answer queries about single-linkage graph HAC clusters. Our second result is that dynamic graph HAC is significantly harder for other common linkage functions. For example, assuming the strong exponential time hypothesis, dynamic graph HAC requires Omega(n(1-o(1))) work per update or query on a graph with n vertices for complete linkage, weighted average linkage, and average linkage. For complete linkage and weighted average linkage, the bound still holds even for incremental or decremental algorithms and even if we allow poly(n)-approximation. For average linkage, the bound weakens to Omega(n(1/2-o(1))) for incremental and decremental algorithms, and the bounds still hold when allowing n(o(1))-approximation.

关键词： parallel algorithms Dynamic algorithms Graph Clustering

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