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A New Transference Theorem in the Geometry of Numbers

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Computing and Combinatorics (COCOON 1999)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1627))

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Abstract

We prove a new transference theorem in the geometry of numbers, giving optimal bounds relating the successive minima of a lattice with the minimal length of generating vectors of its dual. It generalizes the transference theorem due to Banaszczyk. The theorem is motivated by our efforts to improve Ajtai's connection factors in the connection of average-case to worst-case complexity of the shortest lattice vector problem. Our proofs are non-constructive, based on methods from harmonic analysis.

Research supported in part by NSF grant CCR-9634665 and a J. S. Guggenheim Fellowship.

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Author information

Authors and Affiliations

  1. Department of Computer Science, State University of New York at Buffalo, Buffalo, NY, 14260

    Jin-Yi Cai

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  1. Jin-Yi Cai
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Editor information

Editors and Affiliations

  1. Department of Information and System Engineering Faculty of Science and Engineering, Chuo University, 1-13-27, Kasuga, Bunkyo-ku, Tokyo, 112-8551, Japan

    Takano Asano

  2. Department of Information Science, University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo, 113-0033, Japan

    Hideki Imai

  3. Academia Sinica, Institute of Information Science, Nankang, Taipei, Taiwan

    D. T. Lee

  4. Department of Computer Science Faculty of Engineering, Gunma University, 1-5-1 Tenjin-cho, Kiryu, Gunma, 376-8515, Japan

    Shin-ichi Nakano

  5. IBM Tokyo Research Laboratory, 1623-14, Shimo-Tsuruma, Yamato Kanagawa, 242-0001, Japan

    Takeshi Tokuyama

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© 1999 Springer-Verlag Berlin Heidelberg

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Cai, JY. (1999). A New Transference Theorem in the Geometry of Numbers. In: Asano, T., Imai, H., Lee, D.T., Nakano, Si., Tokuyama, T. (eds) Computing and Combinatorics. COCOON 1999. Lecture Notes in Computer Science, vol 1627. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48686-0_11

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  • DOI: https://doi.org/10.1007/3-540-48686-0_11

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-66200-6

  • Online ISBN: 978-3-540-48686-2

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