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|Title:||On the hardness of approximating the permanent of structured matrices|
|Keywords:||Approximation of the permanent|
Hidden number problem
|Source:||Codenotti, B., Shparlinski, I.E., Winterhof, A. (2002). On the hardness of approximating the permanent of structured matrices. Computational Complexity 11 (3-4) : 158-170. ScholarBank@NUS Repository. https://doi.org/10.1007/s00037-002-0174-3|
|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.|
|Source Title:||Computational Complexity|
|Appears in Collections:||Staff Publications|
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