Sorting with Asymmetric Read and Write Costs

Emerging memory technologies have a significant gap between the cost, both in time and in energy, of writing to memory versus reading from memory. In this paper we present models and algorithms that account for this difference, with a focus on write-efficient sorting algorithms. First, we consider t...

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Bibliographic Details
Published in:arXiv.org
Main Authors: Blelloch, Guy E, Fineman, Jeremy T, Gibbons, Phillip B, Gu, Yan, Shun, Julian
Format: Paper
Language:English
Published: Ithaca Cornell University Library, arXiv.org 11.03.2016
Subjects:
Algorithms
Asymmetry
Classification
Multiplication
Sorting algorithms
ISSN:2331-8422
Online Access:Get full text
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Summary:Emerging memory technologies have a significant gap between the cost, both in time and in energy, of writing to memory versus reading from memory. In this paper we present models and algorithms that account for this difference, with a focus on write-efficient sorting algorithms. First, we consider the PRAM model with asymmetric write cost, and show that sorting can be performed in \(O\left(n\right)\) writes, \(O\left(n \log n\right)\) reads, and logarithmic depth (parallel time). Next, we consider a variant of the External Memory (EM) model that charges \(\omega > 1\) for writing a block of size \(B\) to the secondary memory, and present variants of three EM sorting algorithms (multi-way mergesort, sample sort, and heapsort using buffer trees) that asymptotically reduce the number of writes over the original algorithms, and perform roughly \(\omega\) block reads for every block write. Finally, we define a variant of the Ideal-Cache model with asymmetric write costs, and present write-efficient, cache-oblivious parallel algorithms for sorting, FFTs, and matrix multiplication. Adapting prior bounds for work-stealing and parallel-depth-first schedulers to the asymmetric setting, these yield parallel cache complexity bounds for machines with private caches or with a shared cache, respectively.
Bibliography:SourceType-Working Papers-1
ObjectType-Working Paper/Pre-Print-1
content type line 50
ISSN:2331-8422
DOI:10.48550/arxiv.1603.03505