相互依赖网络的线性输入依赖模型
A linear input dependence model for interdependent networks
摘要：
本文考虑一类具有二元输入依赖的广义最小费用网络流问题的线性松弛。在该模型中，通过某些弧的流由通过其他弧的流的线性（或更一般地，分段线性凹）函数限定。这个公式可以用来模拟相互关联的系统，其中一个系统的组件需要从另一个系统输送材料才能发挥作用（例如，地铁系统的组件可能需要从单独的系统输送电力）。我们提出并研究了随机舍入方案，该模型可以用来近似解相关的混合整数线性规划建模二进制输入依赖。侧约束的引入防止了这个问题被解决使用著名的网络单纯形算法，然而，通过表征其基本结构，我们开发了一个推广的网络单纯形算法，可以用于其{计算}有效解。
英文摘要：
We consider a linear relaxation of a generalized minimum-cost network flow problem with binary input dependencies. In this model the flows through certain arcs are bounded by linear (or more generally, piecewise linear concave) functions of the flows through other arcs. This formulation can be used to model interrelated systems in which the components of one system require the delivery of material from another system in order to function (for example, components of a subway system may require delivery of electrical power from a separate system). We propose and study randomized rounding schemes for how this model can be used to approximate solutions to a related mixed integer linear program for modeling binary input dependencies. The introduction of side constraints prevents this problem from being solved using the well-known network simplex algorithm, however by characterizing its basis structure we develop a generalization of network simplex algorithm that can be used for its {computationally} efficient solution.
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