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

On Circuit Diameter Bounds via Circuit Imbalances