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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11.03.2016
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| Abstract | 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. |
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| AbstractList | 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. |
| Author | Gu, Yan Shun, Julian Fineman, Jeremy T Blelloch, Guy E Gibbons, Phillip B |
| Author_xml | – sequence: 1 givenname: Guy surname: Blelloch middlename: E fullname: Blelloch, Guy E – sequence: 2 givenname: Jeremy surname: Fineman middlename: T fullname: Fineman, Jeremy T – sequence: 3 givenname: Phillip surname: Gibbons middlename: B fullname: Gibbons, Phillip B – sequence: 4 givenname: Yan surname: Gu fullname: Gu, Yan – sequence: 5 givenname: Julian surname: Shun fullname: Shun, Julian |
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| Copyright | 2016. This work is published under http://arxiv.org/licenses/nonexclusive-distrib/1.0/ (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License. |
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| DOI | 10.48550/arxiv.1603.03505 |
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