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Essentially Every Unimodular Matrix Defines an Expander

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Algorithms and Computation (ISAAC 2000)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1969))

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Abstract

We generalize the construction of Gabber and Galil to essentially every unimodular matrix in SL 2(Z). It is shown that every parabolic or hyperbolic fractional linear transformation explicitly defines an expander of bounded degree and constant expansion. Thus all but a vanishingly small fraction of unimodular matrices define expanders.

Research supported in part by NSF grant CCR-9820806 and by a Guggenheim Fellowship.

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Author information

Authors and Affiliations

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

    Jin-Yi Cai

  2. Computer Sciences Department, University of Wisconsin, 53706, Madison, WI

    Jin-Yi Cai

Authors
  1. Jin-Yi Cai
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Editor information

Editors and Affiliations

  1. Karlsruhe University, Germany

    Gerhard Goos

  2. Cornell University, NY, USA

    Juris Hartmanis

  3. Utrecht University, The Netherlands

    Jan van Leeuwen

  4. Academia Sinica, Institute of Information Science, 128 Academia Road, Section 2, Nankang, 115, Taipei, Taiwan, R.O.C.

    D. T. Lee

  5. Department of Computer Science and Akamai Technologies, University of Illinois at Urbana Champaign, 500 Technology Square, 02139, Cambridge, MA, USA

    Shang-Hua Teng

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© 2000 Springer-Verlag Berlin Heidelberg

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Cai, JY. (2000). Essentially Every Unimodular Matrix Defines an Expander. In: Goos, G., Hartmanis, J., van Leeuwen, J., Lee, D.T., Teng, SH. (eds) Algorithms and Computation. ISAAC 2000. Lecture Notes in Computer Science, vol 1969. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-40996-3_2

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  • DOI: https://doi.org/10.1007/3-540-40996-3_2

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-41255-7

  • Online ISBN: 978-3-540-40996-0

  • eBook Packages: Springer Book Archive

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