A comparison of sorting algorithms for the connection machine CM-2

Blelloch, Guy E.; Leiserson, Charles E.; Maggs, Bruce M.; Plaxton, C. Greg; Smith, Stephen J. J.; Zagha, Marco

doi:10.1145/113379.113380

Cited by 253 publications

(167 citation statements)

References 28 publications

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“…If the block is accessed in the count array before the another BC steps of the algorithm then a miss is incurred in that access. The probability that block x is accessed in BC steps is 1 , 1 If r divides b then the e ect is 2b=r passes that con ict with a single count array of size 2 r . Expression 9 yields the rst term of equation 7 and the second term is negligible .…”

Section: Discussionmentioning

confidence: 99%

The Influence of Caches on the Performance of Sorting

LaMarca

Ladner

1999

Journal of Algorithms

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We i n vestigate the e ect that caches have on the performance of sorting algorithms both experimentally and analytically. To address the performance problems that high cache miss penalties introduce we restructure mergesort, quicksort, and heapsort in order to improve their cache locality. F or all three algorithms the improvement i n c a c he performance leads to a reduction in total execution time. We also investigate the performance of radix sort. Despite the extremely low instruction count incurred by this linear time sorting algorithm, its relatively poor cache performance results in worse overall performance than the e cient comparison based sorting algorithms. For each algorithm we provide an analysis that closely predicts the number of cache misses incurred by the algorithm.

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Section: Discussionmentioning

confidence: 99%

The Influence of Caches on the Performance of Sorting

LaMarca

Ladner

1999

Journal of Algorithms

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“…We use R/2(1 + ε)k applications of a cache-oblivious selection algorithm [7] to subdivide large bins of size R into bins of size at most 2(1 + ε)k elements using O( R/2(1 + ε)k R/B) memory transfers. 4 Theorem 3. The total number of memory transfers S required to subdivide all m bins to be less than 2(1 + ε)k elements each is O(kn/B), assuming that the largest bin is at most (1 + ε)k ln(kn) elements and n/2 ≤ m ≤ 2n.…”

Section: Finding Splitters For Small Kmentioning

confidence: 99%

“…When k is at least ln 2 n, we use an oversampling technique as used in sample sort [4] to find a set of splitters and bound the size of all bins. In particular, we start by randomly sampling elements as candidate splitters with probability 1/ ln k, which can be accomplished by streaming each list and writing out the samples to a separate candidate list with O(kn/B) memory transfers.…”

Section: Finding Splitters For Large Kmentioning

confidence: 99%

Cache-Oblivious Iterated Predecessor Queries via Range Coalescing

Demaine

Gopal

Hasenplaugh

2015

Lecture Notes in Computer Science

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Abstract. In this paper we develop an optimal cache-oblivious data structure that solves the iterated predecessor problem. Given k static sorted lists L1, L2, . . . , L k of average length n and a query value q, the iterated predecessor problem is to find the largest element in each list which is less than q. Our solution to this problem, called "range coalescing", requires O(log B+1 n + k/B) memory transfers for a query on a cache of block size B, which is information-theoretically optimal. The range-coalescing data structure consumes O(kn) space, and preprocessing requires only O(kn/B) memory transfers with high probability, given a tall cache of size M = Ω B 2 .

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“…Comparing the overheads measured from our experimental evaluation, we can observe that LMW incurs significantly less overhead than ABLSW (by a factor of 2.5-15) or ABSC (by a factor of [4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20]. LSW, despite …”

Section: Validation Of Manual Analysismentioning

confidence: 99%

“…Radix: The radix sort is based on the method described in [5]. The algorithm is iterative, performing one iteration for each radix r digits of the keys.…”

Section: Benchmarksmentioning

confidence: 99%

Performance analysis of methods that overcome false sharing effects in software DSMs

Kudlur

Govindarajan

2004

Journal of Parallel and Distributed Computing

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Page-based software DSMs experience high degrees of false sharing especially in irregular applications with fine grain sharing granularity. The overheads due to false sharing is considered to be a dominant factor limiting the performance of software DSMs. Several approaches have been proposed in the literature to reduce/eliminate false sharing. In this paper, we evaluate two of these approaches, viz., the Multiple Writer approach and the emulated fine grain sharing (EmFiGS) approach. Our evaluation strategy is two pronged. First, we use an implementation-independent analysis that uses overhead counts to compare the different approaches. Our analysis show that the benefits gained by eliminating false sharing are far outweighed by the performance penalty incurred due to the reduced exploitation of spatial locality in the EmFiGS approach. As a consequence, any implementation of the EmFiGS approach is likely to perform significantly worse than the Multiple Writer approach. Second, we use experimental evaluation to validate and complement our analysis. The experimental results match well with our analysis. Also the execution times of the application follow the same trend as in our analysis, reinforcing our conclusions. More specifically, the performance of the EmFiGS approach is significantly worse, by a factor of 1.5 to as much as 90 times, compared to the Multiple Writer approach. In many cases, the EmFiGS approach performs worse than even a single writer lazy release protocol which experiences very high overheads due to false sharing.The performance of the EmFiGS approach remains worse than the Multiple Writer approach even after incorporating Tapeworm-a record and replay technique that fetches pages ahead of demand in an aggregated fashion-to alleviate the spatial locality effect. We next present the effect of asynchronous message handling on the performance of different methods. Finally, we investigate the inter-play between spatial locality exploitation and false sharing elimination with varying sharing granularities in the EmFiGS approach and report the tradeoffs.

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A comparison of sorting algorithms for the connection machine CM-2

Cited by 253 publications

References 28 publications

The Influence of Caches on the Performance of Sorting

The Influence of Caches on the Performance of Sorting

Cache-Oblivious Iterated Predecessor Queries via Range Coalescing

Performance analysis of methods that overcome false sharing effects in software DSMs

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