## Abstract

For the Butterfly of N input/output vertices we present a layout on the square grid of area 1/2 N^{2}+o(N^{2}). A lower bound of the same order is proved. The encompassing rectangle which defines the area is 45° slanted with respect to the grid axes and the input/output vertices are not on the boundary of this rectangle. For the Butterfly of M input/output edges we present a layout of area 1/2 M^{2}+o(M^{2}). In this layout the input edges are on the l.h.s. of the upright encompassing rectangle and the output edges are on its r.h.s. Again this is also a lower bound. Both layouts are scalable, i.e. if one allocates for each switch a square of a×a area, the layouts remain of area 1/2 N^{2}+o(N^{2}) and 1/2 M^{2}+o(M^{2}), respectively, where the value of a affects only the o(N^{2}) and o(M^{2}) terms. Both layouts are free of knock-knees.

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

Pages | 54-63 |

Number of pages | 10 |

DOIs | |

State | Published - 1 Jan 1999 |

Event | Proceedings of the 1999 11th Annual ACM Symposium on Parallel Algorithms and Architectures, SPAA'99 - Saint-Malo Duration: 27 Jun 1999 → 30 Jun 1999 |

### Conference

Conference | Proceedings of the 1999 11th Annual ACM Symposium on Parallel Algorithms and Architectures, SPAA'99 |
---|---|

City | Saint-Malo |

Period | 27/06/99 → 30/06/99 |

## ASJC Scopus subject areas

- Software
- Safety, Risk, Reliability and Quality