Adapting Parallel Algorithms to the W-Stream Model, with Applications to Graph Problems

Demetrescu, Camil; Escoffier, Bruno; Moruz, Gabriel; Ribichini, Andrea

doi:10.1007/978-3-540-74456-6_19

Cited by 12 publications

(17 citation statements)

References 13 publications

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“…In this section we list the main contributions of the present dissertation. We give detailed description of our results in Chapters 4-10, which present the work published in [24,[28][29][30][31]36, 70] 1 .…”

Section: Contributionsmentioning

confidence: 99%

“…Parallel algorithms are good for streaming (Chapter 8, [36]). We show in [36] how to simulate parallel algorithms to obtain efficient algorithms in the W-Stream model.…”

Section: Contributionsmentioning

confidence: 99%

“…Parallel algorithms are good for streaming (Chapter 8, [36]). We show in [36] how to simulate parallel algorithms to obtain efficient algorithms in the W-Stream model. Motivated by the fact that simulating classical PRAM algorithms does not always help in achieving good results in the W-Stream model, we introduce a new model of computation denoted RPRAM (Relaxed PRAM).…”

Section: Contributionsmentioning

confidence: 99%

“…In this chapter we introduce the results in [36]. In Section 8.1 we show how to turn parallel algorithms into efficient algorithm in the W-Stream model.…”

Section: Chaptermentioning

confidence: 99%

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Algorithms and Data Structures

Vegter¹

2013

Lecture Notes in Computer Science

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Various computer hardware components are affecting the running time of algorithms in different proportions, or may have severe implications on the accuracy of algorithms. In this dissertation we propose algorithms and data structures that are efficient and robust with respect to different hardware factors. The hardware factors affecting the running time that we consider include branch mispredictions occurring in the processor, memory transfers occurring between consecutive levels of the memory hierarchy in modern computers, as well as the high rate sequential access on modern hard-disks which is a major motivation for developing streaming algorithms. Regarding the factors affecting the accuracy of algorithms, we consider soft memory errors which determine corruptions in RAM memories.Branch mispredictions incur significant performance losses for algorithms. First, we show that the running time of randomized Quicksort is adaptive, i.e. it depends on the presortedness of the input. We prove theoretically that the number of element swaps performed by Quicksort depends on the number Inv of inversions in the input and show experimentally that the number of element swaps is closely correlated to the number of branch mispredictions. We then give lower bound trade-offs between comparisons and branch mispredictions for sorting and adaptive sorting, and propose sorting and adaptive sorting algorithms matching these bounds. Finally, we show experimentally that for random queries perfectly balanced binary search trees can be outperformed by skewed binary search trees, i.e. trees for which at any given node there is a fixed ratio between the nodes in the left and right subtrees. This happens because the skewed binary search trees perform more comparisons, but fewer branch mispredictions, compared to perfectly binary search trees for random queries.Memory transfers occurring between consecutive levels of the memory hierarchy in modern computers are modeled in the I/O model and cache oblivious model, and the complexity of algorithms is given by the number of memory transfers performed. We introduce I/O lower bounds for adaptive sorting algorithms and give two algorithms that are optimal and I/O optimal with respect to Inv .In a streaming setting, algorithms are restricted to access data sequentially, while having at their disposal a working memory that can be accessed for free, but which is usually much smaller than the problem size. We give general reductions from parallel algorithms to streaming algorithms, and show that we can obtain optimal algorithms (up to poly-log factors) for several combinatorial problems, such as sorting, connected components, minimum spanning tree, v biconnected components, or maximal independent set.To analyze memory corruptions, we use the faulty-memory RAM model proposed by Finocchi and Italiano. In this model, any memory cell can get corrupted at any time during the execution of an algorithm, with no possibility of distinguishing between corrupted and uncorrupted cells. The number of corr...

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Section: Contributionsmentioning

confidence: 99%

“…Parallel algorithms are good for streaming (Chapter 8, [36]). We show in [36] how to simulate parallel algorithms to obtain efficient algorithms in the W-Stream model.…”

Section: Contributionsmentioning

confidence: 99%

Section: Contributionsmentioning

confidence: 99%

“…In this chapter we introduce the results in [36]. In Section 8.1 we show how to turn parallel algorithms into efficient algorithm in the W-Stream model.…”

Section: Chaptermentioning

confidence: 99%

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Algorithms and Data Structures

Vegter¹

2013

Lecture Notes in Computer Science

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“…Massive data sets and the large disparity in access times between internal main memory and disks moti-vated the study of out-of-core or external memory algorithms that leverage the effectiveness of sequential disk access, originating in 1980 [16] and later exemplified by the parallel disk model (PDM) introduced in 1994 [18] and the streaming computation model in 1998 [9] with improvements to the streaming model introduced more recently [6]. This body of work laid the foundation for effective disk-based processing for graph algorithms but these approaches are sequential or require multiple passes over the graph data which is impractical for graphs at the petabyte scale and beyond.…”

Section: Related Workmentioning

confidence: 99%

A cloud-based approach to big graphs

Burkhardt¹,

Waring²

2015

2015 IEEE High Performance Extreme Computing Conference (HPEC)

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Data sizes in today's Big Data age presents a profound scalability challenge to modeling networks as graphs. Historically, memory-based solutions were utilized to cope with high latency incurred by irregular data access common in many natural networks. But current data rates impose both economic and environmental challenges to continually expand the total aggregate system memory to "fit" the graph. Graph scalability has wide-reaching impact since network analysis has expanded beyond its traditional fields into many areas of research including neuroscience, genomics, bioinformatics, and social network analysis. We present a Cloud-based approach that scales with Big Data while being fault-tolerant, applying it on the largest problem size in the Graph500 benchmark to traverse a Petabyte graph consisting of over 4 trillion vertices and 70 trillion edges, a size nearly twenty times the physical memory capacity of our computing platform.

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Graph Mining on Streams

McGregor¹

2009

Encyclopedia of Database Systems

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Adapting Parallel Algorithms to the W-Stream Model, with Applications to Graph Problems

Cited by 12 publications

References 13 publications

Algorithms and Data Structures

Algorithms and Data Structures

A cloud-based approach to big graphs

Graph Mining on Streams

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