## GPU-ABiSort: Optimal parallel sorting on stream architectures (2006)

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Venue: | IN PROCEEDINGS OF THE 20TH IEEE INTERNATIONAL PARALLEL AND DISTRIBUTED PROCESSING SYMPOSIUM (IPDPS ’06) (APR |

Citations: | 36 - 0 self |

### BibTeX

@INPROCEEDINGS{Greß06gpu-abisort:optimal,

author = {Alexander Greß and Gabriel Zachmann},

title = {GPU-ABiSort: Optimal parallel sorting on stream architectures},

booktitle = {IN PROCEEDINGS OF THE 20TH IEEE INTERNATIONAL PARALLEL AND DISTRIBUTED PROCESSING SYMPOSIUM (IPDPS ’06) (APR},

year = {2006},

pages = {45},

publisher = {}

}

### Years of Citing Articles

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### Abstract

In this paper, we present a novel approach for parallel sorting on stream processing architectures. It is based on adaptive bitonic sorting. For sorting n values utilizing p stream processor units, this approach achieves the optimal time complexity O((n log n)/p). While this makes our approach competitive with common sequential sorting algorithms not only from a theoretical viewpoint, it is also very fast from a practical viewpoint. This is achieved by using efficient linear stream memory accesses and by combining the optimal time approach with algorithms optimized for small input sequences. We present an implementation on modern programmable graphics hardware (GPUs). On recent GPUs, our optimal parallel sorting approach has shown to be remarkably faster than sequential sorting on the CPU, and it is also faster than previous non-optimal sorting approaches on the GPU for sufficiently large input sequences. Because of the excellent scalability of our algorithm with the number of stream processor units p (up to n / log 2 n or even n / log n units, depending on the stream architecture), our approach profits heavily from the trend of increasing number of fragment processor units on GPUs, so that we can expect further speed improvement with upcoming GPU generations.

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Citation Context ...ng can be adapted to a stream processor, which does not have the ability of random-access writes, as we will show in this paper. Adaptive bitonic sorting is based on Batcher’s bitonic sorting network =-=[4]-=-, which is a conceptually simpler approach that achieves only the non-optimal parallel running time O(log 2 n) for a sorting network of n nodes. 2.2. GPU-based sorting Several sorting approaches on st... |

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Citation Context ...s achieve only the non-optimal time complexity O((n log 2 n)/p) on a stream architecture with p processor units (in worst and average case since sorting networks are data-independent). Purcell et al. =-=[18]-=- presented a bitonic sorting network implementation for the GPU which is based on an equivalent implementation for the Imagine stream processor by Kapasi et al. [12]. Kipfer et al. [13, 14] implemente... |

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Citation Context ... [12]. Kipfer et al. [13, 14] implemented a bitonic as well as an odd-even merge sort network on the GPU. Govindaraju et al. presented an implementation based on the periodic balanced sorting network =-=[10]-=- and, more recently, also an implementation based on the bitonic sorting network [9]. The latter has been highly optimized for cache efficiency and is the fastest of the approaches above. On an NVIDIA... |

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27 |
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22 |
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Citation Context ...Purcell et al. [18] presented a bitonic sorting network implementation for the GPU which is based on an equivalent implementation for the Imagine stream processor by Kapasi et al. [12]. Kipfer et al. =-=[13, 14]-=- implemented a bitonic as well as an odd-even merge sort network on the GPU. Govindaraju et al. presented an implementation based on the periodic balanced sorting network [10] and, more recently, also... |

19 | Computer Graphics on a Stream Architecture
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Citation Context ...tonic sorting network based approaches, their implementation is restricted to sequence lengths that are a power of two. 3. The stream programming model 3.1. The basics In the stream programming model =-=[12, 17, 6, 16]-=-, the basic program structure is described by streams of data passing through computation kernels. A stream is an ordered set of data of an arbitrary (simple or complex) datatype. Kernels perform comp... |

14 | Logarithmic Time Cost Optimal Parallel Sorting is Not Yet Fast
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Citation Context ...itecture. However, although asymptotically optimal, it has been show, that neither the AKS sorting network nor Cole’s parallel merge sort are fast in practice for reasonable numbers of values to sort =-=[8, 15]-=-. Adaptive bitonic sorting [5] is another optimal parallel sorting approach for a shared-memory EREWPRAM architecture (also called PRAC for parallel random access computer). It requires a smaller numb... |

8 |
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Citation Context ...e parallelism of an algorithm more effectively. For developing efficient applications on such architectures with maximum programmer productivity, alternative programming paradigms seem to be required =-=[3]-=-. The stream programming model has shown to be a promising approach going in this direction. Furthermore, the stream programming model provided the foundations for the architecture of modern programma... |

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Citation Context ...e reader to [Akl90]. Especially parallel sorting using sorting networks as well as algorithms for sorting on a CREW-PRAM or EREW-PRAM model have been extensively studied. Ajtai, Komlos, and Szemeredi =-=[AKS83]-=- showed how optimal asymptotic complexity can be achieved with a sorting network. Cole [Col88] presented a parallel merge sort approach for the CREW-PRAM as well as for the EREW-PRAM, which achieves o... |

5 |
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Citation Context ...ed above, we propose the usage of an alternative, GPU-cache-optimized mapping between 1D and 2D streams where the 2D space is mapped to 1D along a space-filling curve known as Z-order or Morton order =-=[Mor66]-=-: Assuming that a 1D integer index a is given, which has the bit representation (a31, . . . , a1, a0). Then this index is mapped to the 2D index (ax, ay) where ax has the bit representation (a30, . . ... |

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