Beyond Binary Search: Parallel In-Place Construction of Implicit Search Tree Layouts

Berney, Kyle; Casanova, Henri; Higuchi, Alyssa; Karsin, Ben; Sitchinava, Nodari

doi:10.1109/ipdps.2018.00116

Cited by 10 publications

(16 citation statements)

References 23 publications

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“…Berney et al present parallel in-place algorithms for constructing implicit search tree layouts from sorted sequences [3]. This research can be used to efficiently generate sorted sequences of integers in-place, which can be used as inputs to their algorithms.…”

Section: Resultsmentioning

confidence: 99%

“…, which creates the dashed edge (3, 2, 1); and (2, 1, 1), (1,3,1), which creates the dashed edge (2,3,1).…”

mentioning

confidence: 99%

“…This results in (f). Finally, in (f), The algorithm processes the single 2-path with vertex 2 as broker, which is (2, 3, 1), (3,2,1), and is left with an empty graph in (h), at which point the array is sorted. .…”

mentioning

confidence: 99%

“…In (d), Regions sort processes all three 2-paths with vertex 1 as broker in parallel. The three 2-paths are (1, 2, 1), (2, 1, 2), which does not add any new edges; (3, 1, 1), (1, 2, 1), which creates the dashed edge (3, 2, 1); and (2, 1, 1),(1,3,1), which creates the dashed edge(2,3,1). This results in (f).…”

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confidence: 99%

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Theoretically-Efficient and Practical Parallel In-Place Radix Sorting

Obeya

Kahssay

Fan

et al. 2019

The 31st ACM Symposium on Parallelism in Algorithms and Architectures

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Radix sort stands out for having a better worse case theoretical bound than any comparison-based sort, for fixed length integers. Despite the fact that radix sort can be implemented either in-place or in parallel, there exists no parallel in-place implementation for radix sort that guarantees a sub-linear worst case span. The challenge arises due to read-write races when reading from and writing to the same array. In this thesis, I introduce Regions sort and use it to implement a parallel work-efficient in-place radix sorting algorithm. To sort integers from a range , and a parameter , the algorithm requires only (log log) auxiliary memory, (log) work and ((/ + log) log) span. Regions sort uses a divide-and-conquer paradigm. It first divides the array into sub-arrays, each of which is sorted independently in parallel. This decreases the irregularity in the input and reorders it into a set of regions, each of which has similar properties. Next, it builds a data structure, called the regions graph to represent the needed data movements to completely sort the array. Finally, Regions sort iteratively plans swaps that satisfies the required data movements. The algorithm then has to recurse on records with so-far equal keys to break ties. I compare two variants of Regions sort with the state-of-the-art sorting integer sort and comparison sort algorithms. Experiments show that the best variant of Regions sort usually outperforms other sorting algorithms. In addition, I perform different experiments showing that Regions sort maintains its superiority regardless input distribution and range. More importantly, the single-threaded implementation of Regions sort outperforms the highly optimized Ska Sort implementation for serial in-place radix sort.

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Section: Resultsmentioning

confidence: 99%

“…, which creates the dashed edge (3, 2, 1); and (2, 1, 1), (1,3,1), which creates the dashed edge (2,3,1).…”

mentioning

confidence: 99%

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confidence: 99%

mentioning

confidence: 99%

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Theoretically-Efficient and Practical Parallel In-Place Radix Sorting

Obeya

Kahssay

Fan

et al. 2019

The 31st ACM Symposium on Parallelism in Algorithms and Architectures

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“…There has been recent work studying theoretically-efficient and practical parallel in-place algorithms for sample sort [3], radix sort [44], partition [41], and constructing implicit search tree layouts [7]. These PIP algorithms achieve better performance than previous algorithms in almost all cases.…”

Section: Introductionmentioning

confidence: 99%

Parallel In-Place Algorithms: Theory and Practice

Gu¹,

Obeya²,

Shun³

2021

Preprint

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Many parallel algorithms use at least linear auxiliary space in the size of the input to enable computations to be done independently without conflicts. Unfortunately, this extra space can be prohibitive for memory-limited machines, preventing large inputs from being processed. Therefore, it is desirable to design parallel in-place algorithms that use sublinear (or even polylogarithmic) auxiliary space.In this paper, we bridge the gap between theory and practice for parallel in-place (PIP) algorithms. We first define two computational models based on fork-join parallelism, which reflect modern parallel programming environments. We then introduce a variety of new parallel in-place algorithms that are simple and efficient, both in theory and in practice. Our algorithmic highlight is the Decomposable Property introduced in this paper, which enables existing non-in-place but highly-optimized parallel algorithms to be converted into parallel in-place algorithms. Using this property, we obtain algorithms for random permutation, list contraction, tree contraction, and merging that take linear work, 𝑂 (𝑛 1−𝜖 ) auxiliary space, and 𝑂 (𝑛 𝜖 • polylog(𝑛)) span for 0 < 𝜖 < 1. We also present new parallel in-place algorithms for scan, filter, merge, connectivity, biconnectivity, and minimum spanning forest using other techniques.In addition to theoretical results, we present experimental results for implementations of many of our parallel in-place algorithms. We show that on a 72-core machine with twoway hyper-threading, the parallel in-place algorithms usually outperform existing parallel algorithms for the same problems that use linear auxiliary space, indicating that the theory developed in this paper indeed leads to practical benefits in terms of both space usage and running time.

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PI-sqrt: novel parallel implementations of in-place sequence rotation on multicore systems

Hashem

Salah

2022

Cluster Comput

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Beyond Binary Search: Parallel In-Place Construction of Implicit Search Tree Layouts

Cited by 10 publications

References 23 publications

Theoretically-Efficient and Practical Parallel In-Place Radix Sorting

Theoretically-Efficient and Practical Parallel In-Place Radix Sorting

Parallel In-Place Algorithms: Theory and Practice

PI-sqrt: novel parallel implementations of in-place sequence rotation on multicore systems

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