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Brief Announcement: Upper and Lower Bounds for Edit Distance in Space-Efficient MPC 24

Brief Announcement: Upper and Lower Bounds for Edit Distance...

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36th acm symposium on parallelism in algorithms and architectures (SPAA)

作者： Das, Debarati Gilbert, Jacob Hajiaghayi, MohammadTaghi Kociumaka, Tomasz Saha, Barna Penn State Univ State Coll PA 16802 USA Univ Maryland College Pk MD USA Max Planck Inst Informat Saarland Informat Campus Saarbrucken Germany Univ Calif San Diego San Diego CA USA

ISBN: (纸本)9798400704161

In the Massively parallel Computation (MPC) model, data is distributed across multiple processors, and we call an algorithm space-efficient if each machine has n(1-epsilon+o(1)) memory with a machine count of Omega(n(epsilon)). In this paper, we study the string edit distance problem in the MPC model, presenting both a new algorithm and lower-bound results. A space-efficient MPC algorithm computing the exact edit distance using O(n(epsilon)) communication rounds is known by updating the algorithm of Chowdhury and Ramachandran (SPAA 2008). A key contribution of our work is the introduction of the first space-efficient MPC algorithm, which uses subpolynomial number of rounds and provides an n(o(1))-approximation of edit distance, where.. denotes the length of the input strings. Further, we complement this algorithm with new lower-bound results. The Orthogonal Vector (O.V.) conjecture states that no truly subquadratic time algorithm exists for the Orthogonal Vector problem, and it follows directly from the Strong Exponential Time Hypothesis (SETH). Drawing inspiration from this, we propose the Strong O.V. Conjecture that posits that there is no space-efficient MPC algorithm capable of solving O.V. using n(epsilon-Omega(1)) communication rounds. The Strong O.V. conjecture has far-reaching consequences, yielding the first (or strengthened) lower bounds for a myriad of problems in the MPC model including graph diameter estimation, computing Frechet distance, longest common subsequence, and dynamic time warping. Via an MPC reduction from O.V. to edit distance, we give the first conditional lower bound for string edit distance in the MPC model showing that there does not exist any space-efficient, n(epsilon-Omega(1))-round MPC exact edit distance algorithm.

关键词： Massively parallel Computations Edit Distance Approximation Hardness

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Theoretically Efficient parallel Graph algorithms Can Be Fast and Scalable 18

Theoretically Efficient Parallel Graph Algorithms Can Be Fas...

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30th acm symposium on parallelism in algorithms and architectures (SPAA)

作者： Dhulipala, Laxman Blelloch, Guy E. Shun, Julian Carnegie Mellon Univ Pittsburgh PA 15213 USA MIT CSAIL Cambridge MA USA

ISBN: (纸本)9781450357999

There has been significant recent interest in parallel graph processing due to the need to quickly analyze the large graphs available today. Many graph codes have been designed for distributed memory or external memory. However, today even the largest publicly-available real-world graph (the Hyperlink Web graph with over 3.5 billion vertices and 128 billion edges) can fit in the memory of a single commodity multicore server. Nevertheless, most experimental work in the literature report results on much smaller graphs, and the ones for the Hyperlink graph use distributed or external memory. Therefore, it is natural to ask whether we can efficiently solve a broad class of graph problems on this graph in memory. This paper shows that theoretically-efficient parallel graph algorithms can scale to the largest publicly-available graphs using a single machine with a terabyte of RAM, processing them in minutes. We give implementations of theoretically-efficient parallel algorithms for 13 important graph problems. We also present the optimizations and techniques that we used in our implementations, which were crucial in enabling us to process these large graphs quickly. We show that the running times of our implementations outperform existing state-of-the-art implementations on the largest real-world graphs. For many of the problems that we consider, this is the first time they have been solved on graphs at this scale. We provide a publicly-available benchmark suite containing our implementations.

关键词： work-efficiency multicore graph processing shared-memory parallel graph algorithms

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An Efficient parallel Solver for SDD Linear Systems 14

An Efficient Parallel Solver for SDD Linear Systems

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46th annual acm symposium on Theory of Computing (STOC)

作者： Peng, Richard Spielman, Daniel A. MIT Cambridge MA 02139 USA Yale Univ New Haven CT 06520 USA

ISBN: (纸本)9781450327107

We present the first parallel algorithm for solving systems of linear equations in symmetric, diagonally dominant (SDD) matrices that runs in polylogarithmic time and nearly -linear work. The heart of our algorithm is a construction of a sparse approximate inverse chain for the input matrix: a sequence of sparse matrices whose product approximates its inverse. Whereas other fast algorithms for solving systems of equations in SDD matrices exploit low -stretch spanning trees, our algorithm only requires spectral graph sparsifiers.

关键词： SDD linear systems parallel algorithms linear system solvers

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Sorting with Asymmetric Read and Write Costs 15

Sorting with Asymmetric Read and Write Costs

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

作者： Blelloch, Guy E. Fineman, Jeremy T. Gibbons, Phillip B. Gu, Yan Shun, Julian Carnegie Mellon Univ Pittsburgh PA 15213 USA Georgetown Univ Washington DC 20057 USA Intel Labs Santa Clara CA USA CMU Pittsburgh PA USA

ISBN: (纸本)9781450335881

Emerging memory technologies have a significant gap between the cost, both in time and in energy, of writing to memory versus reading from memory. In this paper we present models and algorithms that account for this difference, with a focus on write-efficient sorting algorithms. First, we consider the PRAM model with asymmetric write cost, and show that sorting can be performed in O(n) writes, O(n log n) reads, and logarithmic depth (parallel time). Next, we consider a variant of the External Memory (EM) model that charges k > 1 for writing a block of size B to the secondary memory, and present variants of three EM sorting algorithms (multi-way mergesort, sample sort, and heapsort using buffer trees) that asymptotically reduce the number of writes over the original algorithms, and perform roughly k block reads for every block write. Finally, we define a variant of the Ideal-Cache model with asymmetric write costs, and present write-efficient, cache-oblivious parallel algorithms for sorting, FFTs, and matrix multiplication. Adapting prior bounds for work-stealing and parallel-depth-first schedulers to the asymmetric setting, these yield parallel cache complexity bounds for machines with private caches or with a shared cache, respectively.

关键词： Sorting asymmetric read-write costs non-volatile memory persistent memory write-efficient write-avoiding parallel algorithms cache-oblivious algorithms external memory model mergesort sample sort I/O buffer tree FFT matrix multiplication

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Fast fault-tolerant parallel communication and on-line maintenance using information dispersal 90

Fast fault-tolerant parallel communication and on-line maint...

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

作者： Lyuu, Yuh-Dauh Harvard Univ Cambridge MA United States

ISBN: (纸本)0897913701

Space-efficient Information Dispersal Algorithm (IDA) [11] is applied to parallel communication in the hypercube. Let N denote the size of the network. Our communication scheme runs in 2·log N + 1 time using constant size buffers. Its probability of successful routing is at least 1 - N-2.419·log N+1.5, proving Rabin's conjecture. The same scheme also tolerates O(N) random link failures with high probability. The scheme runs within the said time bound without long delay. On-line and efficient wire testing and replacement on the hypercube can be realized if our fault-tolerant routing scheme is used. Let α denote the total number of links in the hypercube. It is shown that ≈ α/352 wires can be disabled simultaneously without disrupting the ongoing computation or degrading the routing performance much.

关键词： Computer systems, Digital

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parallel Memory-Independent Communication Bounds for SYRK 23

Parallel Memory-Independent Communication Bounds for SYRK

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

作者： Al Daas, Hussam Ballard, Grey Grigori, Laura Kumar, Suraj Rouse, Kathryn Rutherford Appleton Lab Didcot Oxon England Wake Forest Univ Winston Salem NC 27101 USA Inria Paris Paris France Inria Lyon Lyon France Inmar Intelligence Winston Salem NC USA

ISBN: (纸本)9781450395458

In this paper, we focus on the parallel communication cost of multiplying a matrix with its transpose, known as a symmetric rank-k update (SYRK). SYRK requires half the computation of general matrix multiplication because of the symmetry of the output matrix. Recent work (Beaumont et al., SPAA '22) has demonstrated that the sequential I/O complexity of SYRK is also a constant factor smaller than that of general matrix multiplication. Inspired by this progress, we establish memory-independent parallel communication lower bounds for SYRK with smaller constants than general matrix multiplication, and we show that these constants are tight by presenting communication-optimal algorithms. The crux of the lower bound proof relies on extending a key geometric inequality to symmetric computations and analytically solving a constrained nonlinear optimization problem. The optimal algorithms use a triangular blocking scheme for parallel distribution of the symmetric output matrix and corresponding computation.

关键词： Symmetric matrices Communication costs Convex optimization

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Integrated Model, Batch, and Domain parallelism in Training Neural Networks 18

Integrated Model, Batch, and Domain Parallelism in Training ...

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30th acm symposium on parallelism in algorithms and architectures (SPAA)

作者： Gholami, Amir Azad, Ariful Jin, Peter Keutzer, Kurt Buluc, Aydin Univ Calif Berkeley EECS Dept Berkeley CA 94720 USA Lawrence Berkeley Lab CRD Berkeley CA USA

ISBN: (纸本)9781450357999

We propose a new integrated method of exploiting model, batch and domain parallelism for the training of deep neural networks (DNNs) on large distributed-memory computers using minibatch stochastic gradient descent (SGD). Our goal is to find an efficient parallelization strategy for a fixed batch size using P processes. Our method is inspired by the communication-avoiding algorithms in numerical linear algebra. We see P processes as logically divided into a P-r x P-c grid where the P-r dimension is implicitly responsible for model/domain parallelism and the P-c dimension is implicitly responsible for batch parallelism. In practice, the integrated matrix-based parallel algorithm encapsulates these types of parallelism automatically. We analyze the communication complexity and analytically demonstrate that the lowest communication costs are often achieved neither with pure model nor with pure data parallelism. We also show how the domain parallel approach can help in extending the theoretical scaling limit of the typical batch parallel method.

关键词： communication-avoiding algorithms neural network training model parallelism stochastic gradient descent data parallelism parallel algorithms backpropagation

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Cache-Efficient parallel-Partition algorithms using Exclusive-Read-and-Write Memory 20

Cache-Efficient Parallel-Partition Algorithms using Exclusiv...

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32nd acm symposium on parallelism in algorithms and architectures, SPAA 2020

作者： Kuszmaul, William Westover, Alek Massachusetts Institute of Technology BostonMA United States Belmont High School BostonMA United States

ISBN: (纸本)9781450369350

We present an in-place algorithm for the parallel-partition problem with linear work and polylogarithmic span. The algorithm uses only exclusive read/write shared variables and can be implemented using parallel-for-loops without any additional concurrency considerations (i.e., the algorithm is EREW). A key feature of the algorithm is that it exhibits provably optimal cache behavior up to small-order factors. We also present a second in-place EREW algorithm with work O(n) and span O(log n · log log n), which is within an O(log log n) factor of the optimal span. By using this low-span algorithm as a subroutine within the cache-friendly algorithm, we obtain a single EREW algorithm that combines their theoretical guarantees: the algorithm achieves span O(log n · log log n) and exhibits optimal cache behavior. As an immediate consequence, we also get an in-place EREW Quicksort algorithm with work O(n log n) and span O(log2 n · log log n). Whereas the standard EREW algorithm for parallel-partition is memory-bandwidth bound on large numbers of cores, our cache-friendly algorithm is able to achieve near-ideal scaling in practice by avoiding the memory-bandwidth bottleneck. Our algorithm's performance is comparable to that of the Blocked Strided Algorithm of Francis, Pannan, Frias, and Petit, which is the previous state-of-the-art for parallel EREW sorting algorithms, but which lacks theoretical guarantees on its span and cache behavior. © 2020 Owner/Author.

关键词： Bandwidth

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Practical parallel Hypergraph algorithms 20

Practical Parallel Hypergraph Algorithms

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25th acm SIGPLAN symposium on Principles and Practice of parallel Programming (PPoPP)

作者： Shun, Julian MIT CSAIL Cambridge MA 02139 USA

ISBN: (纸本)9781450368186

While there has been significant work on parallel graph processing, there has been very surprisingly little work on high-performance hypergraph processing. This paper presents a collection of efficient parallel algorithms for hypergraph processing, including algorithms for betweenness centrality, maximal independent set, k-core decomposition, hyper-trees, hyperpaths, connected components, PageRank, and single-source shortest paths. For these problems, we either provide new parallel algorithms or more efficient implementations than prior work. Furthermore, our algorithms are theoretically-efficient in terms of work and depth. To implement our algorithms, we extend the Ligra graph processing framework to support hypergraphs, and our implementations benefit from graph optimizations including switching between sparse and dense traversals based on the frontier size, edge-aware parallelization, using buckets to prioritize processing of vertices, and compression. Our experiments on a 72-core machine and show that our algorithms obtain excellent parallel speedups, and are *** faster than algorithms in existing hypergraph processing frameworks.

关键词： parallel algorithms

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Communication-Avoiding parallel Minimum Cuts and Connected Components 18

Communication-Avoiding Parallel Minimum Cuts and Connected C...

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23rd acm SIGPLAN symposium on Principles and Practice of parallel Programming (PPoPP)

作者： Gianinazzi, Lukas Kalvoda, Pavel De Palma, Alessandro Besta, Maciej Hoefler, Torsten Swiss Fed Inst Technol Dept Comp Sci Zurich Switzerland Google Inc Mountain View CA USA

ISBN: (纸本)9781450349826

We present novel scalable parallel algorithms for finding global minimum cuts and connected components, which are important and fundamental problems in graph processing. To take advantage of future massively parallel architectures, our algorithms are communication-avoiding: they reduce the costs of communication across the network and the cache hierarchy. The fundamental technique underlying our work is the randomized sparsification of a graph: removing a fraction of graph edges, deriving a solution for such a sparsified graph, and using the result to obtain a solution for the original input. We design and implement sparsification with O(1) synchronization steps. Our global minimum cut algorithm decreases communication costs and computation compared to the state-of-the-art, while our connected components algorithm incurs few cache misses and synchronization steps. We validate our approach by evaluating MPI implementations of the algorithms on a petascale supercomputer. We also provide an approximate variant of the minimum cut algorithm and show that it approximates the exact solutions well while using a fraction of cores in a fraction of time.

关键词： parallel Computing Minimum cuts Randomized algorithms Graph algorithms

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