## Optimal and Sublogarithmic Time Randomized Parallel Sorting Algorithms (1989)

Venue: | SIAM JOURNAL ON COMPUTING |

Citations: | 61 - 12 self |

### BibTeX

@ARTICLE{Rajasekaran89optimaland,

author = {Sanguthevar Rajasekaran and John H. Reif},

title = {Optimal and Sublogarithmic Time Randomized Parallel Sorting Algorithms},

journal = {SIAM JOURNAL ON COMPUTING},

year = {1989},

volume = {18},

pages = {594--607}

}

### Years of Citing Articles

### OpenURL

### Abstract

We assume a parallel RAM model which allows both concurrent reads and concurrent writes of a global memory. Our main result is an optimal randomized parallel algorithm for INTEGER SORT (i.e., for sorting n integers in the range [1; n]). Our algorithm costs only logarithmic time and is the first known that is optimal: the product of its time and processor bounds is upper bounded by a linear function of the input size. We also give a deterministic sub-logarithmic time algorithm for prefix sum. In addition we present a sub-logarithmic time algorithm for obtaining a random permutation of n elements in parallel. And finally, we present sub-logarithmic time algorithms for GENERAL SORT and INTEGER SORT. Our sublogarithmic GENERAL SORT algorithm is also optimal.

### Citations

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Citation Context ...esent an optimal algorithm for INTEGER SORT. This algorithm employs n= log n processors and runs in time e O(log n). 8s3.1 Summary of the Algorithm The main idea behind our algorithm is radix sorting =-=[15]-=-. As an example of radix sorting, consider the problem of sorting a sequence of two-bit decimal integers. One way of doing this is to sort the sequence with respect the least signi cant bits (LSB) of ... |

290 | Parallel merge sort - Cole - 1988 |

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(Show Context)
Citation Context ...2 It should be mentioned here that when the number of groups, m, is 1 the above algorithm outputs a random permutation of (1; 2;:::;n). An algorithm for this special case was given by Miller and Reif =-=[19]-=-. 2.3 Some Known Results We state here the existence of optimal sequential algorithms for INTEGER SORT and optimal parallel algorithms for GENERAL SORT. Lemma 2.4 Stable INTEGER SORT ofnkeys can be do... |

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Parallel Pre x
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(Show Context)
Citation Context ...ut (X(1); X(1) X(2); :::; X(1) X(2) ::: X(n)). The special case of pre x computation when is the set of all natural numbers and is integer addition is called pre x sum computation. Ladner and Fischer =-=[18]-=- show that pre x computation can be done by a circuit of depth O(log n) and size n. The processor bound of this algorithm can be improved as follows. Lemma 2.1 Pre x computation can be done in time O(... |

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4 |
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(Show Context)
Citation Context ...parallel algorithm that used n synchronous PRAM processors to sort n general keys in O(log n) time. This algorithm however is impractical owing to its large word-length requirements. Reif and Valiant =-=[24]-=- presented a random3sized sorting algorithm that ran on a xed connection network called cube connected cycles (CCC). This algorithm employed n processors to sort n general keys in time O(log n). Since... |

3 | Randomness in computability - Ambos-Spies, Kucera - 1999 |

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3 |
SZEMEREDI,An O(n log n) Sorting Network
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(Show Context)
Citation Context ...s (CCC). This algorithm employed n processors to sort n general keys in time O(log n). Since (n log n) is a sequential lower bound for this problem, their algorithm is indeed optimal. Simultaneously, =-=[4]-=- discovered a deterministic parallel algorithm for sorting n general keys in time O(log n) using a sorting network of O(n log n) processors. Later Leighton [17] showed that this algorithm could be mod... |

1 | Parallel Computation and Con icts - KUCERA - 1982 |