## Optimal parallel prefix on the postal model (2003)

Venue: | J. Information Science and Engineering |

Citations: | 3 - 1 self |

### BibTeX

@ARTICLE{Lin03optimalparallel,

author = {Yen-chun Lin and Ching-sung Yeh},

title = {Optimal parallel prefix on the postal model},

journal = {J. Information Science and Engineering},

year = {2003},

volume = {19},

pages = {75--83}

}

### OpenURL

### Abstract

This paper explores the prefix operation on a message-passing fully connected multicomputer with multiport postal communication. We present an exact communication lower bound for the prefix operation on the model. Two efficient parallel prefix algorithms are also presented; they are optimal in terms of the number of communication steps. For an input of size n, one of the algorithms using n processors is also time-optimal; the other algorithm using p < n processors can be cost-optimal and can achieve linear speedup.

### Citations

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Citation Context ...eration is defined as follows: Given n values v(0), v(1),..., v(n – 1) and an associative binary operation ⊕, compute v(0) ⊕ v(1) ⊕ ... ⊕ v(i), for 0 ≤ i ≤ n – 1. This operation has many applications =-=[1, 6, 9, 10]-=-, and it has been proposed as a primitive operation [4]. Thus, many parallel prefix algorithms on various models have been presented [7-16, 18]. This paper explores the prefix operation on a message-p... |

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Citation Context ...ep 2 (j = 2): S0,2 = {3, 4} ; add edges (0, 3), (0, 4) to T0. Step 3 (j = 3): S0,3 = {5, 6} ; add edges (0, 5), (0, 6) to T0. Step 4 (j = 4): S0,4 = {7} ; add edge (0, 7) to T0. S1,4 = {8} ; add edge =-=(1, 8)-=- to T0. S2,4 = {9} ; add edge (2, 9) to T0. When j ≥ 5, Sx,i = φ for each node x in T0. That is, T0 is completed in four steps. Note that as shown in Fig. 1, a newly added leaf node is white, and it t... |

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Citation Context ...eration is defined as follows: Given n values v(0), v(1),..., v(n – 1) and an associative binary operation ⊕, compute v(0) ⊕ v(1) ⊕ ... ⊕ v(i), for 0 ≤ i ≤ n – 1. This operation has many applications =-=[1, 6, 9, 10]-=-, and it has been proposed as a primitive operation [4]. Thus, many parallel prefix algorithms on various models have been presented [7-16, 18]. This paper explores the prefix operation on a message-p... |

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Citation Context ... – 1) and an associative binary operation ⊕, compute v(0) ⊕ v(1) ⊕ ... ⊕ v(i), for 0 ≤ i ≤ n – 1. This operation has many applications [1, 6, 9, 10], and it has been proposed as a primitive operation =-=[4]-=-. Thus, many parallel prefix algorithms on various models have been presented [7-16, 18]. This paper explores the prefix operation on a message-passing fully connected multicomputer with multiport pos... |

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Citation Context ...ded in step j + λ, where λ ≥ 1. This model, called the k-port postal model, or simply the postal model, in this paper, has been recognized as a trend in multicomputers and in programming environments =-=[2, 3, 5]-=-. In a multicomputer, the time taken to transfer a message between two PEs is significant, and it is desirable to have communication-efficient algorithms. This paper contributes to solving the prefix ... |

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Citation Context ...ded in step j + λ, where λ ≥ 1. This model, called the k-port postal model, or simply the postal model, in this paper, has been recognized as a trend in multicomputers and in programming environments =-=[2, 3, 5]-=-. In a multicomputer, the time taken to transfer a message between two PEs is significant, and it is desirable to have communication-efficient algorithms. This paper contributes to solving the prefix ... |

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Citation Context ...eration is defined as follows: Given n values v(0), v(1),..., v(n – 1) and an associative binary operation ⊕, compute v(0) ⊕ v(1) ⊕ ... ⊕ v(i), for 0 ≤ i ≤ n – 1. This operation has many applications =-=[1, 6, 9, 10]-=-, and it has been proposed as a primitive operation [4]. Thus, many parallel prefix algorithms on various models have been presented [7-16, 18]. This paper explores the prefix operation on a message-p... |

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Citation Context ...ded in step j + λ, where λ ≥ 1. This model, called the k-port postal model, or simply the postal model, in this paper, has been recognized as a trend in multicomputers and in programming environments =-=[2, 3, 5]-=-. In a multicomputer, the time taken to transfer a message between two PEs is significant, and it is desirable to have communication-efficient algorithms. This paper contributes to solving the prefix ... |

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Citation Context ...; add edges (0, 1), (0, 2) to T0. Step 2 (j = 2): S0,2 = {3, 4} ; add edges (0, 3), (0, 4) to T0. Step 3 (j = 3): S0,3 = {5, 6} ; add edges (0, 5), (0, 6) to T0. Step 4 (j = 4): S0,4 = {7} ; add edge =-=(0, 7)-=- to T0. S1,4 = {8} ; add edge (1, 8) to T0. S2,4 = {9} ; add edge (2, 9) to T0. When j ≥ 5, Sx,i = φ for each node x in T0. That is, T0 is completed in four steps. Note that as shown in Fig. 1, a newl... |