Revision #1 Authors: Vikraman Arvind, Partha Mukhopadhyay, Prajakta Nimbhorkar, Yadu Vasudev

Accepted on: 25th November 2011 14:36

Downloads: 1946

Keywords:

Let $G=\langle S\rangle$ be a solvable permutation group given as input by generating set $S$. I.e.\ $G$ is a solvable subgroup of the symmetric group $S_n$. We give a deterministic polynomial-time algorithm that computes an expanding generator set for $G$. More precisely, given a constant $\lambda <1$ we can compute an expanding generator set $T$ of size $n^2(\log n)^{O(1)}$ such that the undirected Cayley graph Cay$(G,T)$ is a $\lambda$-spectral expander. In particular, this construction yields $\epsilon$-bias spaces with improved size bounds for the groups $\mathbb{Z}_d^n$ for any constant bias $\epsilon$.

A new subsection (Section 2.2) about general permutation groups is included.

TR11-140 Authors: Vikraman Arvind, Partha Mukhopadhyay, Prajakta Nimbhorkar, Yadu Vasudev

Publication: 31st October 2011 16:01

Downloads: 2518

Keywords:

Let $G=\langle S\rangle$ be a solvable permutation group given as input by generating set $S$. I.e.\ $G$ is a solvable subgroup of the symmetric group $S_n$. We give a deterministic polynomial-time algorithm that computes an expanding generator set for $G$. More precisely, given a constant $\lambda <1$ we can compute an expanding generator set $T$ of size $n^2(\log n)^{O(1)}$ such that the undirected Cayley graph Cay$(G,T)$ is a $\lambda$-spectral expander. In particular, this construction yields $\epsilon$-bias spaces with improved size bounds for the groups $\mathbb{Z}_d^n$ for any constant bias $\epsilon$.