### Abstract

The author shows that a shortest basis for the 2-dimensional lattice Lambda (u, v) generated by an input pair u, v in Z
^{2}
can be computed in O(M(n) log n) where n is the bit-size of the input numbers and M(n) is the complexity of multiplying two n-bit integers. This generalizes Schonhage's technique (1971) for fast integer GCD to a higher dimension.

Original language | English (US) |
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Title of host publication | Proceedings - 33rd Annual Symposium on Foundations of Computer Science, FOCS 1992 |

Publisher | IEEE Computer Society |

Pages | 437-446 |

Number of pages | 10 |

ISBN (Electronic) | 0818629002 |

DOIs | |

State | Published - Jan 1 1992 |

Event | 33rd Annual Symposium on Foundations of Computer Science, FOCS 1992 - Pittsburgh, United States Duration: Oct 24 1992 → Oct 27 1992 |

### Publication series

Name | Proceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS |
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Volume | 1992-October |

ISSN (Print) | 0272-5428 |

### Conference

Conference | 33rd Annual Symposium on Foundations of Computer Science, FOCS 1992 |
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Country | United States |

City | Pittsburgh |

Period | 10/24/92 → 10/27/92 |

### ASJC Scopus subject areas

- Computer Science(all)

### Cite this

*Proceedings - 33rd Annual Symposium on Foundations of Computer Science, FOCS 1992*(pp. 437-446). [267808] (Proceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS; Vol. 1992-October). IEEE Computer Society. https://doi.org/10.1109/SFCS.1992.267808

**Fast unimodular reduction : Planar integer lattices.** / Yap, Chee.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Proceedings - 33rd Annual Symposium on Foundations of Computer Science, FOCS 1992.*, 267808, Proceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS, vol. 1992-October, IEEE Computer Society, pp. 437-446, 33rd Annual Symposium on Foundations of Computer Science, FOCS 1992, Pittsburgh, United States, 10/24/92. https://doi.org/10.1109/SFCS.1992.267808

}

TY - GEN

T1 - Fast unimodular reduction

T2 - Planar integer lattices

AU - Yap, Chee

PY - 1992/1/1

Y1 - 1992/1/1

N2 - The author shows that a shortest basis for the 2-dimensional lattice Lambda (u, v) generated by an input pair u, v in Z 2 can be computed in O(M(n) log n) where n is the bit-size of the input numbers and M(n) is the complexity of multiplying two n-bit integers. This generalizes Schonhage's technique (1971) for fast integer GCD to a higher dimension.

AB - The author shows that a shortest basis for the 2-dimensional lattice Lambda (u, v) generated by an input pair u, v in Z 2 can be computed in O(M(n) log n) where n is the bit-size of the input numbers and M(n) is the complexity of multiplying two n-bit integers. This generalizes Schonhage's technique (1971) for fast integer GCD to a higher dimension.

UR - http://www.scopus.com/inward/record.url?scp=0004802167&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0004802167&partnerID=8YFLogxK

U2 - 10.1109/SFCS.1992.267808

DO - 10.1109/SFCS.1992.267808

M3 - Conference contribution

AN - SCOPUS:0004802167

T3 - Proceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS

SP - 437

EP - 446

BT - Proceedings - 33rd Annual Symposium on Foundations of Computer Science, FOCS 1992

PB - IEEE Computer Society

ER -