We study properties and applications of various circuit imbalance measures associated with linear spaces. These measures describe possible ratios between nonzero entries of support-minimal nonzero vectors of the space. The fractional circuit imbalance measure turns out to be a crucial parameter in the context of linear programming, and two integer variants can be used to describe integrality properties of associated polyhedra. We give an overview of the properties of these measures, and survey classical and recent applications, in particular, for linear programming algorithms with running time dependence on the constraint matrix only, and for circuit augmentation algorithms. We also present new bounds on the diameter and circuit diameter of polyhedra in terms of the fractional circuit imbalance measure.

翻译：我们研究了与线性空间相关的各种电路不平衡测量的特性和应用,这些措施描述了空间支持-最小非零矢量的非零条目之间的可能比率。在线性编程中,分线性电路不平衡测量结果是一个关键参数,两个整数变量可用于描述相关聚己烷的完整特性。我们概述了这些措施的特性,并考察了典型和近期的应用,特别是仅对制约矩阵有时间依赖的线性编程算法,以及电路增强算法。我们还从分线性电路不平衡测量角度对聚赫德拉的直径和电路直径提出了新的界限。