### Abstract

This paper presents a new parallel architecture having p processors and N = n2 memory locations, each consisting of 2s bits. The proposed organization can sort N s -bit numbers, where s = O((1+ ε) logN), e > 0, in time t = O for p in the range 1 to √Nlog √N. This result is optimal in the sense that the product of the number of processors and the parallel sorting time is equal to the sequential complexity of sorting. Also, the constant factors involved in the algorithm complexity are relatively small. When p = √Nlog√N, the time required for sorting N numbers on the proposed organization is O(√N), which is the same time required by a two-dimensional mesh array, a mesh of trees organization, or a pyramid computer, all with O(N) processors, to sort N numbers.

Original language | English |
---|---|

Pages (from-to) | 105-110 |

Number of pages | 6 |

Journal | IEEE Transactions on Computers |

Volume | 40 |

Issue number | 1 |

DOIs | |

Publication status | Published - 1 Jan 1991 |

Externally published | Yes |

### Fingerprint

### Keywords

- Optimal parallel algorithms
- optimal sorting
- proces-
- reduced VLSI architectures
- row-column sorting
- sor-time tradeoffs
- techniques

### ASJC Scopus subject areas

- Theoretical Computer Science
- Software
- Hardware and Architecture
- Computational Theory and Mathematics

### Cite this

**Optimal VLSI Sorting with Reduced Number of Processors.** / Alnuweiri, Hussein.

Research output: Contribution to journal › Article

*IEEE Transactions on Computers*, vol. 40, no. 1, pp. 105-110. https://doi.org/10.1109/12.67326

}

TY - JOUR

T1 - Optimal VLSI Sorting with Reduced Number of Processors

AU - Alnuweiri, Hussein

PY - 1991/1/1

Y1 - 1991/1/1

N2 - This paper presents a new parallel architecture having p processors and N = n2 memory locations, each consisting of 2s bits. The proposed organization can sort N s -bit numbers, where s = O((1+ ε) logN), e > 0, in time t = O for p in the range 1 to √Nlog √N. This result is optimal in the sense that the product of the number of processors and the parallel sorting time is equal to the sequential complexity of sorting. Also, the constant factors involved in the algorithm complexity are relatively small. When p = √Nlog√N, the time required for sorting N numbers on the proposed organization is O(√N), which is the same time required by a two-dimensional mesh array, a mesh of trees organization, or a pyramid computer, all with O(N) processors, to sort N numbers.

AB - This paper presents a new parallel architecture having p processors and N = n2 memory locations, each consisting of 2s bits. The proposed organization can sort N s -bit numbers, where s = O((1+ ε) logN), e > 0, in time t = O for p in the range 1 to √Nlog √N. This result is optimal in the sense that the product of the number of processors and the parallel sorting time is equal to the sequential complexity of sorting. Also, the constant factors involved in the algorithm complexity are relatively small. When p = √Nlog√N, the time required for sorting N numbers on the proposed organization is O(√N), which is the same time required by a two-dimensional mesh array, a mesh of trees organization, or a pyramid computer, all with O(N) processors, to sort N numbers.

KW - Optimal parallel algorithms

KW - optimal sorting

KW - proces-

KW - reduced VLSI architectures

KW - row-column sorting

KW - sor-time tradeoffs

KW - techniques

UR - http://www.scopus.com/inward/record.url?scp=0025786392&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0025786392&partnerID=8YFLogxK

U2 - 10.1109/12.67326

DO - 10.1109/12.67326

M3 - Article

AN - SCOPUS:0025786392

VL - 40

SP - 105

EP - 110

JO - IEEE Transactions on Computers

JF - IEEE Transactions on Computers

SN - 0018-9340

IS - 1

ER -