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On the hardness of approximating the permanent of structured matrices

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Abstract

We show that for several natural classes of “structured” matrices, including symmetric, circulant, Hankel and Toeplitz matrices, approximating the permanent modulo a prime p is as hard as computing its exact value. Results of this kind are well known for arbitrary matrices. However the techniques used do not seem to apply to “structured” matrices. Our approach is based on recent advances in the hidden number problem introduced by Boneh and Venkatesan in 1996 combined with some bounds of exponential sums motivated by the Waring problem in finite fields.

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Authors and Affiliations

  1. Department of Computer Science, University of Iowa, 14 MacLean Hall, Iowa City, 52240, IA, USA

    Bruno Codenotti

  2. Department of Computer Science, University of Chicago, Ryerson Hall, 1100E 58th Street, Chicago, 60637, IL, USA

    Bruno Codenotti

  3. Department of Computing, Macquarie University, Sydney, 2109, NSW, Australia

    John D. Shparlinski

  4. Temasek Laboratories, National University of Singapore, 10 Kent Ridge Crescent, Singapore, 119260, Singapore

    Arne Winterhof

Authors
  1. Bruno Codenotti
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  2. John D. Shparlinski
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  3. Arne Winterhof
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Correspondence to Bruno Codenotti.

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Codenotti, B., Shparlinski, J. & Winterhof, A. On the hardness of approximating the permanent of structured matrices. comput. complex. 11, 158–170 (2002). https://doi.org/10.1007/s00037-002-0174-3

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  • DOI: https://doi.org/10.1007/s00037-002-0174-3

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