Fast unimodular reduction

Planar integer lattices

Research output: Chapter in Book/Report/Conference proceedingConference contribution

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 languageEnglish (US)
Title of host publicationProceedings - 33rd Annual Symposium on Foundations of Computer Science, FOCS 1992
PublisherIEEE Computer Society
Pages437-446
Number of pages10
ISBN (Electronic)0818629002
DOIs
StatePublished - Jan 1 1992
Event33rd Annual Symposium on Foundations of Computer Science, FOCS 1992 - Pittsburgh, United States
Duration: Oct 24 1992Oct 27 1992

Publication series

NameProceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS
Volume1992-October
ISSN (Print)0272-5428

Conference

Conference33rd Annual Symposium on Foundations of Computer Science, FOCS 1992
CountryUnited States
CityPittsburgh
Period10/24/9210/27/92

ASJC Scopus subject areas

  • Computer Science(all)

Cite this

Yap, C. (1992). Fast unimodular reduction: Planar integer lattices. In 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.

Proceedings - 33rd Annual Symposium on Foundations of Computer Science, FOCS 1992. IEEE Computer Society, 1992. p. 437-446 267808 (Proceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS; Vol. 1992-October).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Yap, C 1992, Fast unimodular reduction: Planar integer lattices. in 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
Yap C. Fast unimodular reduction: Planar integer lattices. In Proceedings - 33rd Annual Symposium on Foundations of Computer Science, FOCS 1992. IEEE Computer Society. 1992. p. 437-446. 267808. (Proceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS). https://doi.org/10.1109/SFCS.1992.267808
Yap, Chee. / Fast unimodular reduction : Planar integer lattices. Proceedings - 33rd Annual Symposium on Foundations of Computer Science, FOCS 1992. IEEE Computer Society, 1992. pp. 437-446 (Proceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS).
@inproceedings{c4f8d880a01d456c96da359d37710ec8,
title = "Fast unimodular reduction: Planar integer lattices",
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.",
author = "Chee Yap",
year = "1992",
month = "1",
day = "1",
doi = "10.1109/SFCS.1992.267808",
language = "English (US)",
series = "Proceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS",
publisher = "IEEE Computer Society",
pages = "437--446",
booktitle = "Proceedings - 33rd Annual Symposium on Foundations of Computer Science, FOCS 1992",

}

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

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 -