Analysis of swaps in radix selection

Elmasry, Amr; Mahmoud, Hosam M.

doi:10.1239/aap/1308662491

Cited by 3 publications

(1 citation statement)

References 23 publications

(9 reference statements)

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“…The methodology can be extended, with some adaptation, to other one-sided algorithms of similar structure; see, e.g. [3], [10], [14], and [19]. A variety of other one-sided algorithms may be approached by the methods we discuss in the present paper, such as the random walk on interval trees [6], which have a continuous flavor.…”

Section: Introductionmentioning

confidence: 99%

Perpetuities in Fair Leader Election Algorithms

Kalpathy

Mahmoud

2014

Advances in Applied Probability

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We consider a broad class of fair leader election algorithms, and study the duration of contestants (the number of rounds a randomly selected contestant stays in the competition) and the overall cost of the algorithm. We give sufficient conditions for the duration to have a geometric limit distribution (a perpetuity built from Bernoulli random variables), and for the limiting distribution of the total cost (after suitable normalization) to be a perpetuity. For the duration, the proof is established via convergence (to 0) of the first-order Wasserstein distance from the geometric limit. For the normalized overall cost, the method of proof is also convergence of the first-order Wasserstein distance, augmented with an argument based on a contraction mapping in the first-order Wasserstein metric space to show that the limit approaches a unique fixed-point solution of a perpetuity distributional equation. The use of these two steps is commonly referred to as the contraction method.

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Section: Introductionmentioning

confidence: 99%

Perpetuities in Fair Leader Election Algorithms

Kalpathy

Mahmoud

2014

Advances in Applied Probability

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A radix sorting parallel algorithm suitable for graphic processing unit computing

Xiao

Guo

et al. 2020

Concurrency and Computation

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Radix sorting is an essential basic data processing operation in many computer fields. It has important practical significance to accelerate its performance through Graphic Processing Unit (GPU). The heterogeneous parallel computing technology attracts much attention and is widely applied for its effective computation efficiency and parallel real-time data processing capability. Taking advantage of the parallelism of GPU in numerical computation processing, a parallelization design method of the Binary_Least Significant Digit (LSD) first Radix Sorting (B_LSD_RS) algorithm based on Open Computing Language (OpenCL) is proposed. The radix sorting algorithm is divided into multiple kernel tasks, and the kernels are sequentially controlled by the event information transfer. The parallel algorithm is implemented and verified on the GPU + CPU heterogeneous platform. The experimental results show that compared with the performance of the B_LSD_RS sequential algorithm based on AMD Ryzen5 1600X CPU, B_LSD_RS parallel algorithm based on Open Multi-Processing (OpenMP) and B_LSD_RS parallel algorithm based on Compute Unified Device Architecture (CUDA), the B_LSD_RS parallel algorithm based on OpenCL obtained 28.86 times, 11.01 times and 2.14 times speedup in the NVIDIA GTX 1070 computing platform respectively, not only achieves high performance but also achieves performance portability among different GPU computing platforms.

show abstract

Perpetuities in Fair Leader Election Algorithms

Kalpathy

Mahmoud

2014

Adv. Appl. Probab.

Self Cite

View full text Add to dashboard Cite

We consider a broad class of fair leader election algorithms, and study the duration of contestants (the number of rounds a randomly selected contestant stays in the competition) and the overall cost of the algorithm. We give sufficient conditions for the duration to have a geometric limit distribution (a perpetuity built from Bernoulli random variables), and for the limiting distribution of the total cost (after suitable normalization) to be a perpetuity. For the duration, the proof is established via convergence (to 0) of the firstorder Wasserstein distance from the geometric limit. For the normalized overall cost, the method of proof is also convergence of the first-order Wasserstein distance, augmented with an argument based on a contraction mapping in the first-order Wasserstein metric space to show that the limit approaches a unique fixed-point solution of a perpetuity distributional equation. The use of these two steps is commonly referred to as the contraction method.

show abstract

Analysis of swaps in radix selection

Cited by 3 publications

References 23 publications

Perpetuities in Fair Leader Election Algorithms

Perpetuities in Fair Leader Election Algorithms

A radix sorting parallel algorithm suitable for graphic processing unit computing

Perpetuities in Fair Leader Election Algorithms

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