通过路由优化进行网络提取
Network extraction by routing optimization
摘要：
路由优化在许多情况下都是一个相关的问题。直接求解这种类型的优化问题通常在计算上是不可行的。最近的研究表明，人们可以把这个问题转化为求解一个动力学方程组，而这个方程组可以用数值方法有效地求解。这导致能够从各种路由问题中获取最佳网络拓扑。然而，在最终网络拓扑结构方面的解决方案的实际提取依赖于数值细节，这可能会妨碍对其拓扑性质的准确调查。在这种情况下，理论结果只有专家才能完全访问，而非专家的现成实现很少可用或没有充分的文档记录。特别是，在这个框架中，最终的图形获取本身就是一个具有挑战性的问题。本文介绍了一种在不同参数设置下，从路由优化的动力学方程中提取网络拓扑的方法。我们的方法由三个步骤组成：首先，通过求解动力系统提取最佳轨迹，然后预提取网络，最后过滤掉潜在的冗余。值得注意的是，我们提出了一个原则性的模型来解决过滤的最后一步，并给出了定量的解释，在运输相关的成本函数。这种原则性的过滤可以应用于更一般的问题，例如从图像中提取网络，从而超越了第一步中设想的场景。总的来说，这种新的算法允许从业者通过结合数值方法，优化和网络理论的基本工具，轻松地提取最佳网络拓扑结构。因此，我们提供了一种替代手动图形提取，允许接地提取各种各样的最佳拓扑结构。
英文摘要：
Routing optimization is a relevant problem in many contexts. Solving directly this type of optimization problem is often computationally unfeasible. Recent studies suggest that one can instead turn this problem into one of solving a dynamical system of equations, which can instead be solved efficiently using numerical methods. This results in enabling the acquisition of optimal network topologies from a variety of routing problems. However, the actual extraction of the solution in terms of a final network topology relies on numerical details which can prevent an accurate investigation of their topological properties. In this context, theoretical results are fully accessible only to an expert audience and ready-to-use implementations for non-experts are rarely available or insufficiently documented. In particular, in this framework, final graph acquisition is a challenging problem in-and-of-itself. Here we introduce a method to extract networks topologies from dynamical equations related to routing optimization under various parameters' settings. Our method is made of three steps: first, it extracts an optimal trajectory by solving a dynamical system, then it pre-extracts a network and finally, it filters out potential redundancies. Remarkably, we propose a principled model to address the filtering in the last step, and give a quantitative interpretation in terms of a transport-related cost function. This principled filtering can be applied to more general problems such as network extraction from images, thus going beyond the scenarios envisioned in the first step. Overall, this novel algorithm allows practitioners to easily extract optimal network topologies by combining basic tools from numerical methods, optimization and network theory. Thus, we provide an alternative to manual graph extraction which allows a grounded extraction from a large variety of optimal topologies.
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