## A Novel Deterministic Sampling Scheme with Applications to Broadcast-Efficient Sorting on the Reconfigurable Mesh (1996)

Venue: | Journal of Parallel and Distributed Computing |

Citations: | 13 - 3 self |

### BibTeX

@ARTICLE{Olariu96anovel,

author = {Stephan Olariu and James L. Schwing},

title = {A Novel Deterministic Sampling Scheme with Applications to Broadcast-Efficient Sorting on the Reconfigurable Mesh},

journal = {Journal of Parallel and Distributed Computing},

year = {1996},

volume = {32},

pages = {215--222}

}

### Years of Citing Articles

### OpenURL

### Abstract

The main contribution of this work is to present a simple deterministic sampling strategy that, when used for bucket sorting, yields buckets that are remarkably well balanced, making costly balancing unnecessary. To the best of our knowledge this is the first instance of a deterministic sampling strategy featuring this performance. Although the strategy is perfectly general, we illustrate its power by devising a VLSI-optimal, O(1) time sorting algorithm for the reconfigurable mesh. As a byproduct of the inherent simplicity of our sampling and bucketing scheme we show that our sorting algorithm can be implemented using only 35 broadcast operations, a substantial improvement over the previously best known algorithm that requires 59 broadcasts. Keywords: deterministic sampling, bucket sort, reconfigurable meshes, sorting, VLSI optimal algorithms, constant-time algorithms 1 Introduction Sorting is, unquestionably, one of the fundamental operations in computer science. A natura...

### Citations

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Citation Context ...the resulting buckets are, as a rule, far from being balanced. A standard way around this difficulty is to use randomized sampling -- resulting in buckets that are well balanced with high probability =-=[3, 5, 6, 8, 24, 25]-=-. Typically, by balanced we mean that the buckets differ from the average by at most a constant factor. To date, no deterministic sampling strategy is known to yield balanced buckets. Our main contrib... |

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Citation Context ...the resulting buckets are, as a rule, far from being balanced. A standard way around this difficulty is to use randomized sampling -- resulting in buckets that are well balanced with high probability =-=[3, 5, 6, 8, 24, 25]-=-. Typically, by balanced we mean that the buckets differ from the average by at most a constant factor. To date, no deterministic sampling strategy is known to yield balanced buckets. Our main contrib... |

114 |
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Citation Context ...le interconnection topology and to the fact that many problems feature input data that maps naturally onto the mesh. In addition, the mesh topology is particularly well suited for VLSI implementation =-=[1]-=-. At the same time, due to its large communication diameter, the mesh tends to be slow when it comes to handling data transfer operations over long distances. In an attempt to alleviate this problem, ... |

85 | The Power of Reconfiguration
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Citation Context ...ram control, have been proposed in the literature [10]. Examples include the bus automaton [26], the reconfigurable mesh [18], the content addressable array processor [30], the reconfigurable network =-=[2]-=-, the reconfigurable bus with shift switching [12], the polymorphic torus [9, 17], and the polymorphic processor array [14, 15]. Among these, the reconfigurable mesh has emerged as a very attractive a... |

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Citation Context ...bus automaton [26], the reconfigurable mesh [18], the content addressable array processor [30], the reconfigurable network [2], the reconfigurable bus with shift switching [12], the polymorphic torus =-=[9, 17]-=-, and the polymorphic processor array [14, 15]. Among these, the reconfigurable mesh has emerged as a very attractive and versatile architecture. The reconfigurable mesh combines two desirable feature... |

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Citation Context ...the resulting buckets are, as a rule, far from being balanced. A standard way around this difficulty is to use randomized sampling -- resulting in buckets that are well balanced with high probability =-=[3, 5, 6, 8, 24, 25]-=-. Typically, by balanced we mean that the buckets differ from the average by at most a constant factor. To date, no deterministic sampling strategy is known to yield balanced buckets. Our main contrib... |

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Citation Context ...figuration can change, under program control, have been proposed in the literature [10]. Examples include the bus automaton [26], the reconfigurable mesh [18], the content addressable array processor =-=[30]-=-, the reconfigurable network [2], the reconfigurable bus with shift switching [12], the polymorphic torus [9, 17], and the polymorphic processor array [14, 15]. Among these, the reconfigurable mesh ha... |

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Citation Context ... particular, a number of bus systems whose configuration can change, under program control, have been proposed in the literature [10]. Examples include the bus automaton [26], the reconfigurable mesh =-=[18]-=-, the content addressable array processor [30], the reconfigurable network [2], the reconfigurable bus with shift switching [12], the polymorphic torus [9, 17], and the polymorphic processor array [14... |

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51 |
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Citation Context ...t diameter and a dynamically reconfigurable bus system. It is not surprising, therefore, that the sorting problem has received a great deal of attention in the context of reconfigurable architectures =-=[4, 7, 9, 11, 13, 16, 17, 19, 20, 22, 23, 27, 29]-=-. In an early paper, Wang et al. [29] have proposed a constant-time sorting algorithm on a three-dimensional reconfigurable mesh, using O(n 3 ) processors. Later Nakano et al. [19] have proposed an al... |

50 |
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Citation Context ...18], the content addressable array processor [30], the reconfigurable network [2], the reconfigurable bus with shift switching [12], the polymorphic torus [9, 17], and the polymorphic processor array =-=[14, 15]-=-. Among these, the reconfigurable mesh has emerged as a very attractive and versatile architecture. The reconfigurable mesh combines two desirable features of massively parallel architectures, namely,... |

49 |
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39 |
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Citation Context ...ion of various bus systems. In particular, a number of bus systems whose configuration can change, under program control, have been proposed in the literature [10]. Examples include the bus automaton =-=[26]-=-, the reconfigurable mesh [18], the content addressable array processor [30], the reconfigurable network [2], the reconfigurable bus with shift switching [12], the polymorphic torus [9, 17], and the p... |

25 |
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Citation Context ... machines have been enhanced by the addition of various bus systems. In particular, a number of bus systems whose configuration can change, under program control, have been proposed in the literature =-=[10]-=-. Examples include the bus automaton [26], the reconfigurable mesh [18], the content addressable array processor [30], the reconfigurable network [2], the reconfigurable bus with shift switching [12],... |

24 |
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Citation Context ...t diameter and a dynamically reconfigurable bus system. It is not surprising, therefore, that the sorting problem has received a great deal of attention in the context of reconfigurable architectures =-=[4, 7, 9, 11, 13, 16, 17, 19, 20, 22, 23, 27, 29]-=-. In an early paper, Wang et al. [29] have proposed a constant-time sorting algorithm on a three-dimensional reconfigurable mesh, using O(n 3 ) processors. Later Nakano et al. [19] have proposed an al... |

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Citation Context ...loss of time. It is worth mentioning that at least three recent VLSI implementations have demonstrated the feasibility and benefits of the reconfigurable mesh: these are YUPPIE chip [9, 14], GCN chip =-=[28]-=-, and the PPA [15]. These implementations suggested that the broadcast delay, although not constant, is very small. For example, only 16 machine cycles are required to broadcast on a 10 6 -processor Y... |

19 |
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Citation Context ... [10]. Examples include the bus automaton [26], the reconfigurable mesh [18], the content addressable array processor [30], the reconfigurable network [2], the reconfigurable bus with shift switching =-=[12]-=-, the polymorphic torus [9, 17], and the polymorphic processor array [14, 15]. Among these, the reconfigurable mesh has emerged as a very attractive and versatile architecture. The reconfigurable mesh... |

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Citation Context ...t diameter and a dynamically reconfigurable bus system. It is not surprising, therefore, that the sorting problem has received a great deal of attention in the context of reconfigurable architectures =-=[4, 7, 9, 11, 13, 16, 17, 19, 20, 22, 23, 27, 29]-=-. In an early paper, Wang et al. [29] have proposed a constant-time sorting algorithm on a three-dimensional reconfigurable mesh, using O(n 3 ) processors. Later Nakano et al. [19] have proposed an al... |

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Citation Context ...t diameter and a dynamically reconfigurable bus system. It is not surprising, therefore, that the sorting problem has received a great deal of attention in the context of reconfigurable architectures =-=[4, 7, 9, 11, 13, 16, 17, 19, 20, 22, 23, 27, 29]-=-. In an early paper, Wang et al. [29] have proposed a constant-time sorting algorithm on a three-dimensional reconfigurable mesh, using O(n3) processors. Later Nakano et al. [19] have proposed an algo... |