1996
DOI: 10.1007/bfb0024723
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Submachine locality in the bulk synchronous setting

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Cited by 50 publications
(41 citation statements)
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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%
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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%
“…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%
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