Under the auspices of the Computational Complexity Foundation (CCF)

REPORTS > DETAIL:

### Revision(s):

Revision #1 to TR11-140 | 25th November 2011 14:36

#### Expanding Generator Sets for Solvable Permutation Groups

Revision #1
Accepted on: 25th November 2011 14:36
Keywords:

Abstract:

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 $\epsilon$.

Changes to previous version:

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

### Paper:

TR11-140 | 31st October 2011 15:09

#### Expanding Generator Sets for Solvable Permutation Groups

TR11-140
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 $\epsilon$.