Abstract
Let G = 〈S〉 be a solvable subgroup of the symmetric group S n given as input by the generator set S. We give a deterministic polynomial-time algorithm that computes an expanding generator set of size Õ(n 2) for G. As a byproduct of our proof, we obtain a new explicit construction of ε-bias spaces of size Õ\((n{\rm poly}({\rm log} d))({{1}\over{\varepsilon}})^{O(1)}\) for the groups \(\mathbb{Z}_d^n\).
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Arvind, V., Mukhopadhyay, P., Nimbhorkar, P., Vasudev, Y. (2012). Near-Optimal Expanding Generator Sets for Solvable Permutation Groups. In: Rovan, B., Sassone, V., Widmayer, P. (eds) Mathematical Foundations of Computer Science 2012. MFCS 2012. Lecture Notes in Computer Science, vol 7464. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-32589-2_13
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DOI: https://doi.org/10.1007/978-3-642-32589-2_13
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