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Deterministic and Low-Span Work-Efficient parallel Batch-Dynamic Trees 24

Deterministic and Low-Span Work-Efficient Parallel Batch-Dyn...

引用

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

作者： Anderson, Daniel Blelloch, Guy E. Carnegie Mellon Univ Pittsburgh PA 15213 USA

ISBN: (纸本)9798400704161

Dynamic trees are a well-studied and fundamental building block of dynamic graph algorithms dating back to the seminal work of Sleator and Tarjan [STOC'81, (1981), pp. 114-122]. the problem is to maintain a tree subject to online edge insertions and deletions while answering queries about the tree, such as the heaviest weight on a path, etc. In the parallel batch-dynamic setting, the goal is to process batches of edge updates work efficiently in low (polylog n) span. Two work-efficient algorithms are known: batch-parallel Euler Tour Trees by Tseng et al. [ALENEX'19, (2019), pp. 92-106] and parallel Rake-Compress (RC) Trees by Acar et al. [ESA'20, (2020), pp. 2:1-2:23]. Both however are randomized and work efficient in expectation. Several downstream results that use these data structures (and indeed to the best of our knowledge, all known workefficient parallel batch-dynamic graph algorithms) are therefore also randomized. In this work, we give the first deterministic work-efficient solution to the problem. Our algorithm maintains a parallel RC-Tree on n vertices subject to batches of k edge updates deterministically in worst-case O(k log(1 + n/k)) work and O(log n log log k) span on the Common-CRCW PRAM. We also show how to improve the span of the randomized algorithm from O(log n log* n) to O(log n). Lastly, as a result of our new deterministic algorithm, we also derandomize several downstream results that make use of parallel batch-dynamic dynamic trees, previously for which the only efficient solutions were randomized.

关键词： dynamic trees parallel graph algorithms batch-dynamic algorithms

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Linear-work parallel algorithm for finding minimum spanning trees

Linear-work parallel algorithm for finding minimum spanning ...

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Proceedings of the 6th annual acm symposium on parallel algorithms and architectures

作者： Cole, Richard Klein, Philip N. Tarjan, Robert E.

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parallel balanced allocations 96

Parallel balanced allocations

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Proceedings of the 1996 8th annual acm symposium on parallel algorithms and architectures

作者： Stemann, Volker Int Computer Science Inst Berkeley CA United States

ISBN: (纸本)9780897918091

We study the well known problem of throwing m balls into n bins. If each ball in the sequential game is allowed to select more than one bin, the maximum load of the bins can be exponentially reduced compared to the `classical balls into bins' game. We consider a static and a dynamic variant of a randomized parallel allocation where each ball can choose a constant number of bins. All results hold with high probability. In the static case all m balls arrive at the same time. We analyze for m = n a very simple optimal class of protocols achieving maximum load O (r√log n/log log n) if r rounds of communication are allowed. this matches the lower bound of [acmR95]. Furthermore, we generalize the protocols to the case of m>n balls. An optimal load of O(m/n) can be achieved using log log n/log(m/n) rounds of communication. Hence, for m = n log log n/log log log n balls this slackness allows to hide the amount of communication. In the `classical balls into bins' game this optimal distribution can only be achieved for m = n log n. In the dynamic variant n of the m balls arrive at the same time and have to be allocated. Each of these initial n balls has a list of m/n successor-balls. As soon as a ball is allocated its successor will be processed. We present an optimal parallel process that allocates all m = n log n balls in O(m/n) rounds. Hence, the expected allocation time is constant. the main contribution of this process is that the maximum allocation time is additionally bounded by O(log log n).

关键词： parallel algorithms

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A parallel block algorithm for exact triangularization of rectangular matrices

A parallel block algorithm for exact triangularization of re...

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13th annual symposium on parallel algorithms and architectures (SPAA 2001)

作者： Dumas, J.-G. Roch, J.-L. Lab. Informatique et Distribution ENSIMAG - antenne de'Montbonnot ZIRST - 51 av. Jean Kuntzmann 38330 Montbonnot Saint-Martin France

A new block algorithm for triangularization of regular or singular matrices with dimension m × n, is proposed. Taking benefit of fast block multiplication algorithms, it achieves the best known sequential complexity O(mω-1n) for any sizes and any rank. Moreover, the block strategy enables to improve locality with respect to previous algorithms as exhibited by practical performances.

关键词： parallel processing systems

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Position paper and brief announcement: Introducing the Hydra parallel programming system

Position paper and brief announcement: Introducing the Hydra...

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SPAA 2006: 18th annual acm symposium on parallelism in algorithms and architectures

作者： Powers Jr., Franklin E. Alaghband, Gita Department of Computer Science and Engineering University of Colorado at Denver Health and Sciences Center Denver CO 80217-3364

ISBN: (纸本)1595934529

Hydra PPS is a collection of annotations, classes, a run-time, and a compiler designed to provide Java programmers with a fairly simple method of producing programs for Symmetric Multiprocessing (SMP) architectures. this paper introduces the basics of this new system including the basic constructs for this new programming language and the relationship between the Java VM, the compiler, the runtime, and the parallel program. Hydra will exploit parallelism when the underlying architecture supports it and will run as normal sequential Java program when the architecture does not have support for parallelism. parallelism is expressed through events in Hydra, it is easy to use, and programs run efficiently on parallel architectures.

关键词： parallel processing systems

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O(n log log n)-work parallel algorithms for straight-line grid embeddings of planar graphs

O(n log log n)-work parallel algorithms for straight-line gr...

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4th annual acm symposium on parallel algorithms and architectures - SPAA '92

作者： Fuerer, Martin He, Xin Kao, Ming-Yang Raghavachari, Balaji Pennsylvania State Univ University Park United States

ISBN: (纸本)089791483X

A straight-line grid embedding of a planar graph is a drawing of the graph on a plane where the vertices are located at grid points and the edges are represented by nonintersecting segments of straight lines joining their incident vertices. Given an n-vertex planar graph with n ≥ 3, a straight-line embedding on a grid of size (n - 2) × (n - 2) can be computed deterministically in O(log n log log n) time with O(n log log n) work on a parallel random access machine. If randomization is used, the complexity is improved to O(log n) expected time with the same work bound. the parallel random access machine used by these algorithms allows concurrent reads and concurrent writes of the shared memory;in case of a write conflict, an arbitrary processor succeeds.

关键词： Computer graphics

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Don't be too clever: routing BMMC permutations on the MasPar MP-2

Don't be too clever: routing BMMC permutations on the MasPar...

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Proceedings of the 7th annual acm symposium on parallel algorithms and architectures, SPAA'95

作者： Cormen, thomas H. Bruhl, Kristin Dartmouth Coll

We implemented and measured several methods to perform BMMC permutations on the MasPar MP-2. Our results indicate that, except for certain types of permutations or very high virtual processor ratios, the best method overall is the naive method but with virtual-processor numbers computed in Gray-code order. For some permutations, however, the naive method performs very poorly;the best method in these cases is an adaptation of the block BMMC algorithm for parallel disk systems in which the processor elements are treated as independent devices.

关键词： parallel processing systems

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Fundamental parallel algorithms for Private-Cache Chip Multiprocessors 08

Fundamental Parallel Algorithms for Private-Cache Chip Multi...

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20th acm symposium on parallelism in algorithms and architectures

作者： Arge, Lars Goodrich, Michael T. Nelson, Michael Sitchinava, Nodari Univ Aarhus MADALGO Aarhus Denmark Univ Calif Irvine Irvine CA 92697 USA

ISBN: (纸本)9781595939739

In this paper, we study parallel algorithms for private-cache chip multiprocessors (CMPs), focusing on methods for foundational problems that are scalable with the number of cores. By focusing on private-cache CMPs, we show that we can design efficient algorithms that need no additional assumptions about the way cores are interconnected, for we assume that all inter-processor communication occurs through the memory hierarchy. We study several fundamental problems, including prefix sums, selection, and sorting, which often form the building blocks of other parallel algorithms. Indeed, we present two sorting algorithms, a distribution sort and a mergesort. Our algorithms are asymptotically optimal in terms of parallel cache accesses and space complexity under reasonable assumptions about the relationships between the number of processors, the size of memory, and the size of cache blocks. In addition, we study sorting lower bounds in a computational model, which we call the parallel external-memory (PEM) model, that formalizes the essential properties of our algorithms for private-cache CMPs.

关键词： parallel External Memory PEM private-cache CMP

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Optimal parallel algorithms for Dendrogram Computation and Single-Linkage Clustering 24

Optimal Parallel Algorithms for Dendrogram Computation and S...

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

作者： Dhulipala, Laxman Dong, Xiaojun Gowda, Kishen N. Gu, Yan Univ Maryland College Pk MD 20742 USA Univ Calif Riverside Riverside CA 92521 USA

ISBN: (纸本)9798400704161

Computing a Single-Linkage Dendrogram (SLD) is a key step in the classic single-linkage hierarchical clustering algorithm. Given an input edge-weighted tree), the SLD of) is a binary dendrogram that summarizes the n = 1 clusterings obtained by contracting the edges of T in order of weight. Existing algorithms for computing the SLD all require Omega(n log n) work where n = vertical bar T vertical bar. Furthermore, to the best of our knowledge no prior work provides a parallel algorithm obtaining non-trivial speedup for this problem. In this paper, we design faster parallel algorithms for computing SLDs both in theory and in practice based on new structural results about SLDs. In particular, we obtain a deterministic output-sensitive parallel algorithm based on parallel tree contraction that requires O(n log h) work and O(log(2) n log(2) h) depth, where h is the height of the output SLD. We also give a deterministic bottom-up algorithm for the problem inspired by the nearest-neighbor chain algorithm for hierarchical agglomerative clustering, and show that it achieves O(n log h) work and O(h log n) depth. Our results are based on a novel divide-and-conquer framework for building SLDs, inspired by divide-and-conquer algorithms for Cartesian trees. Our new algorithms can quickly compute the SLD on billion-scale trees, and obtain up to 150x speedup over the highly-efficient Union-Find algorithm typically used to compute SLDs in practice.

关键词： Single-Linkage Clustering Hierarchical Graph Clustering HAC Dendrograms parallel algorithms

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Brief Announcement: Distributed Unconstrained Local Search for Multilevel Graph Partitioning 24

Brief Announcement: Distributed Unconstrained Local Search f...

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

作者： Sanders, Peter Seemaier, Daniel Karlsruhe Inst Technol Karlsruhe Germany

ISBN: (纸本)9798400704161

Partitioning a graph into blocks of roughly equal weight while cutting only few edges is a fundamental problem in computer science with numerous practical applications. While shared-memory parallel partitioners have recently matured to achieve the same quality as widely used sequential partitioners, there is still a pronounced quality gap between distributed partitioners and their sequential counterparts. In this work, we shrink this gap considerably by describing the engineering of an unconstrained local search algorithm suitable for distributed partitioners. We integrate the proposed algorithm in a distributed multilevel partitioner. Our extensive experiments show that the resulting algorithm scales to thousands of PEs while computing cuts that are, on average, only 3.5% larger than those of a state-of-the-art high-quality shared-memory partitioner. Compared to previous distributed partitioners, we obtain on average 6.8% smaller cuts than the best-performing competitor while being more than 9 times faster.

关键词： graph partitioning distributed algorithms parallel algorithms

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