### Abstract

The grid-area required by a sorting net for input vectors of length N is shown to be at least (N - 1)^{2}/2. Of all sorting nets which use o(N^{2}) comparators, the bitonic sorting net of Batcher has been known to have a layout of O(N^{2}), but the hidden constant factor has not been investigated. A straightforward use of known techniques leads to a layout of grid-area 20.25N^{2}. We present area-efficient layouts of the bitonic sorter. First, we describe a flip-bitonic sorting net - it is isomorphic to Batcher's bitonic sorter but leads naturally to a layout of grid-area less than 4N^{2}. Second, we present a butterfly-based layout of the bitonic sorter with grid-area of 3N^{2} + O(N). The former does not use knock-knees while the latter relies on them and is more compact.

Original language | English (US) |
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Pages | 172-181 |

Number of pages | 10 |

State | Published - Jan 1 1998 |

Event | Proceedings of the 1998 10th Annual ACM Symposium on Parallel Algorithms and Architectures, SPAA - Puerto Vallarta, Mexico Duration: Jun 28 1998 → Jul 2 1998 |

### Conference

Conference | Proceedings of the 1998 10th Annual ACM Symposium on Parallel Algorithms and Architectures, SPAA |
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City | Puerto Vallarta, Mexico |

Period | 6/28/98 → 7/2/98 |

### Fingerprint

### ASJC Scopus subject areas

- Software
- Safety, Risk, Reliability and Quality

### Cite this

*Layout of the Batcher bitonic sorter*. 172-181. Paper presented at Proceedings of the 1998 10th Annual ACM Symposium on Parallel Algorithms and Architectures, SPAA, Puerto Vallarta, Mexico, .

**Layout of the Batcher bitonic sorter.** / Even, Sh; Muthukrishnan, Shanmugavelayutham; Paterson, M. S.; Sahinalp, S. C.

Research output: Contribution to conference › Paper

}

TY - CONF

T1 - Layout of the Batcher bitonic sorter

AU - Even, Sh

AU - Muthukrishnan, Shanmugavelayutham

AU - Paterson, M. S.

AU - Sahinalp, S. C.

PY - 1998/1/1

Y1 - 1998/1/1

N2 - The grid-area required by a sorting net for input vectors of length N is shown to be at least (N - 1)2/2. Of all sorting nets which use o(N2) comparators, the bitonic sorting net of Batcher has been known to have a layout of O(N2), but the hidden constant factor has not been investigated. A straightforward use of known techniques leads to a layout of grid-area 20.25N2. We present area-efficient layouts of the bitonic sorter. First, we describe a flip-bitonic sorting net - it is isomorphic to Batcher's bitonic sorter but leads naturally to a layout of grid-area less than 4N2. Second, we present a butterfly-based layout of the bitonic sorter with grid-area of 3N2 + O(N). The former does not use knock-knees while the latter relies on them and is more compact.

AB - The grid-area required by a sorting net for input vectors of length N is shown to be at least (N - 1)2/2. Of all sorting nets which use o(N2) comparators, the bitonic sorting net of Batcher has been known to have a layout of O(N2), but the hidden constant factor has not been investigated. A straightforward use of known techniques leads to a layout of grid-area 20.25N2. We present area-efficient layouts of the bitonic sorter. First, we describe a flip-bitonic sorting net - it is isomorphic to Batcher's bitonic sorter but leads naturally to a layout of grid-area less than 4N2. Second, we present a butterfly-based layout of the bitonic sorter with grid-area of 3N2 + O(N). The former does not use knock-knees while the latter relies on them and is more compact.

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M3 - Paper

AN - SCOPUS:0031622476

SP - 172

EP - 181

ER -