  We study the circuit diameter of polyhedra, introduced by Borgwardt, Finhold,
and Hemmecke (SIDMA 2015) as a relaxation of the combinatorial diameter. We
show that the circuit diameter of a system $\{x \in \mathbb{R}^n: Ax=b, 0\leq
x\leq u\}$ for $A \in \mathbb{R}^{m \times n}$ is bounded by $O(m \min\{m,
n-m\} \log(m+ \kappa_A)+n \log n)$, where $\kappa_A$ is the circuit imbalance
measure of the constraint matrix. This yields a strongly polynomial circuit
diameter bound if e.g., all entries of $A$ have polynomially bounded encoding
length in $n$. Further, we present circuit augmentation algorithms for LPs
using the minimum-ratio circuit cancelling rule. Even though the standard
minimum-ratio circuit cancelling algorithm is not finite in general, our
variant can solve an LP in $O(mn^2\log(n+\kappa_A))$ augmentation steps.
