Submachine locality in the bulk synchronous setting

Torre, Pilar de la; Kruskal, Clyde P.

doi:10.1007/bfb0024723

Cited by 50 publications

(41 citation statements)

References 8 publications

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“…Using memory size as a fourth BSP parameter was proposed and investigated by Tiskin [38] and by McColl and Tiskin [29]. In a different direction a variety of hierarchical versions of BSP have been proposed such as the D-BSP of de la Torre and Kruskal [13], which has been further investigated by Bilardi et al [6,8]. In [8] a network-oblivious result is proved in this communication hierarchical context that, like our analyses, allows for arbitrary parameters at each level.…”

Section: Introductionmentioning

confidence: 63%

“…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%

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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: Introductionmentioning

confidence: 63%

Section: Sortingmentioning

confidence: 99%

A Bridging Model for Multi-core Computing

Valiant

2008

Algorithms - ESA 2008

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“…For concreteness, consider the case of matrix multiplication. On D-BSP (v, O (1) , g(x)), the algorithm of [9,13] multiplies two √ v × √ v matrices by using 2 i 2i-supersteps, for every 0 ≤ i < log(v)/2, performing constant local computation per superstep. It is easy to see that our simulation of this algorithm yields an optimal O v 3/2 algorithm for f (x)-BT, while a trivial step-by-step D-BSP simulation would have required at least time Ω v 3/2 log * v for f (x) = log x, and time Ω v 3/2 log log v for f (x) = x α .…”

Section: Discussion and Applicationsmentioning

confidence: 99%

“…(D-BSP) model was introduced in [9] to capture submachine locality in a structured way through submachine decomposition, and was further investigated in [6,7,14].…”

Section: D-bsp the Decomposable Bulk Synchronous Parallelmentioning

confidence: 99%

“…A more general study on the relation between parallelism and locality of reference has been initiated in [13], where we have shown how a more structured form of parallelism, such as the one exhibited by the Decomposable BSP (a clustered variant of BSP defined in [9]) can lead to the design of sequential algorithms that feature an optimal exploitation of temporal locality on arbitrarily deep memory hierarchies. More precisely, the main contribution of that work is a strategy that simulates a D-BSP algorithm on HMM with a slowdown which is merely proportional to the loss of parallelism, thus proving that no extra cost is incurred in accessing the much larger memory of the sequential machine.…”

Section: Introductionmentioning

confidence: 99%

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Translating submachine locality into locality of reference

Fantozzi¹,

Pietracaprina²,

Pucci³

2006

Journal of Parallel and Distributed Computing

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Algorithm Engineering for Parallel Computation

Bader

Moret

Sanders

2002

Experimental Algorithmics

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The emerging discipline of algorithm engineering has primarily focused on transforming pencil-and-paper sequential algorithms into robust, efficient, well tested, and easily used implementations. As parallel computing becomes ubiquitous, we need to extend algorithm engineering techniques to parallel computation. Such an extension adds significant complications. After a short review of algorithm engineering achievements for sequential computing, we review the various complications caused by parallel computing, present some examples of successful efforts, and give a personal view of possible future research.

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Submachine locality in the bulk synchronous setting

Cited by 50 publications

References 8 publications

A Bridging Model for Multi-core Computing

A Bridging Model for Multi-core Computing

Translating submachine locality into locality of reference

Algorithm Engineering for Parallel Computation

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