Parallel sorting by regular sampling

Shi, Hanmao; Schaeffer, Jonathan

doi:10.1016/0743-7315(92)90075-x

Cited by 163 publications

(157 citation statements)

References 11 publications

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“…Sorting by deterministic oversampling and splitting into smaller subsets of about equal size is known to be achievable using the following idea [13,30,37]: Lemma 6.1 For numbers N, S, G and t one can find a set of S splitters in any ordered set X of N elements such that in the ordering on X the number of elements between two successive splitters is N/S ± 2tG by using the following procedure: Partition X into G sets of N/G elements each, sort each such set, pick out every t th element from each such sorted list, sort the resulting N/t elements, and finally pick every N/(tS) th element of that.…”

Section: Sortingmentioning

confidence: 99%

A Bridging Model for Multi-core Computing

Valiant

2008

Algorithms - ESA 2008

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Writing software for one parallel system is a feasible though arduous task. Reusing the substantial intellectual effort so expended for programming a second system has proved much more challenging. In sequential computing algorithms textbooks and portable software are resources that enable software systems to be written that are efficiently portable across changing hardware platforms. These resources are currently lacking in the area of multi-core architectures, where a programmer seeking high performance has no comparable opportunity to build on the intellectual efforts of others.In order to address this problem we propose a bridging model aimed at capturing the most basic resource parameters of multi-core architectures. We suggest that the considerable intellectual effort needed for designing efficient algorithms for such architectures may be most fruitfully expended in designing portable algorithms, once and for all, for such a bridging model. Portable algorithms would contain efficient designs for all reasonable combinations of the basic resource parameters and input sizes, and would form the basis for implementation or compilation for particular machines.Our Multi-BSP model is a multi-level model that has explicit parameters for processor numbers, memory/cache sizes, communication costs, and synchronization costs. The lowest level corresponds to shared memory or the PRAM, acknowledging the relevance of that model for whatever limitations on memory and processor numbers it may be efficacious to emulate it.We propose parameter-aware portable algorithms that run efficiently on * This work was supported in part by NSF-CCF-04-27129. A preliminary version appeared in Proc. 16th Annual European Symposium on Algorithms, Sept 15-17, 2008, Karlsruhe Germany, LNCS Vol 5193, pp. 13-28, and had also been presented at SPAA, June [14][15][16] 2008.Email addresses: valiant@seas.harvard.edu (Leslie G. Valiant) January 15, 2010 all relevant architectures with any number of levels and any combination of parameters. For these algorithms we define a parameter-free notion of optimality. We show that for several fundamental problems, including standard matrix multiplication, the Fast Fourier Transform, and comparison sorting, there exist optimal portable algorithms in that sense, for all combinations of machine parameters. Thus some algorithmic generality and elegance can be found in this many parameter setting. Preprint submitted to Elsevier

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Section: Sortingmentioning

confidence: 99%

A Bridging Model for Multi-core Computing

Valiant

2008

Algorithms - ESA 2008

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“…This algorithm is based on the standard sample sort algorithm that uses 'over-sampling' and then picks pivots evenly from the chosen samples arranged in sorted order [7,8,10,11,16,22,23]. Proof.…”

Section: Sample Sort Algorithmmentioning

confidence: 99%

Emulations between QSM, BSP and LogP: a framework for general-purpose parallel algorithm design

Ramachandran

Grayson

Dahlin

2003

Journal of Parallel and Distributed Computing

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We present work-preserving emulations with small slowdown between LogP and two other parallel models: BSP and QSM. In conjunction with earlier work-preserving emulations between QSM and BSP, these results establish a close correspondence between these three general-purpose parallel models. Our results also correct and improve on results reported earlier on emulations between BSP and LogP. In particular we shed new light on the relative power of stalling and non-stalling LogP models.The QSM is a shared-memory model with only two parameters-p; the number of processors, and g; a bandwidth parameter. The simplicity of the QSM parameters makes QSM a convenient model for parallel algorithm design, and simple work-preserving emulations of QSM on BSP and QSM on LogP show that algorithms designed for the QSM will also map quite well to these other models. The simplicity and generality of QSM present a strong case for the use of QSM as the model of choice for parallel algorithm design.We present QSM algorithms for three basic problems-prefix sums, sample sort and list ranking. We show that these algorithms are optimal in terms of both the total work performed and the number of 'phases' for input sizes of practical interest. For prefix sums, we present a matching lower bound that shows our algorithm to be optimal over the complete range of these parameters. We then examine the predicted and simulated performance of these algorithms. These results suggest that QSM analysis will predict algorithm performance quite accurately for problem sizes that arise in practice. r

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“…In our experiments we have simulated parallel sample sort [12] as an external memory algorithm. For comparison, we include timings from TPIE's [5] test sort and STXXL's [6] test sort1.…”

Section: Methodsmentioning

confidence: 99%

Experiments with a Parallel External Memory System

Nikseresht

Hutchinson

Maheshwari

High Performance Computing – HiPC 2007

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Abstract. The theory of bulk-synchronous parallel computing has produced a large number of attractive algorithms, which are provably optimal in some sense, but typically require that the aggregate random access memory (RAM) of the processors be sufficient to hold the entire data set of the parallel problem instance. In this work we investigate the performance of parallel algorithms for extremely large problem instances relative to the available RAM. We describe a system, Parallel External Memory System (PEMS), which allows existing parallel programs designed for a large number of processors without disks to be adapted easily to smaller, realistic numbers of processors, each with its own disk system. Our experiments with PEMS show that this approach is practical and promising and the run times scale predictable with the number of processors and with the problem size.

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Parallel sorting by regular sampling

Cited by 163 publications

References 11 publications

A Bridging Model for Multi-core Computing

A Bridging Model for Multi-core Computing

Emulations between QSM, BSP and LogP: a framework for general-purpose parallel algorithm design

Experiments with a Parallel External Memory System

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