发表机构
Sapienza, University of Rome（罗马智慧大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出一种线性摊销复杂度的递减算法，用于动态网络中Braess悖论脆弱性的检查，通过静态算法标记无关边并改进复杂度至O(m^2)。
AI 中文摘要
Braess悖论源于在交通网络中移除边导致Wardrop均衡下的延迟减少。遭受Braess悖论的网络的图论性质在2006年被Roughgarden称为脆弱性；随后，该性质在无向网络和有向网络中均被刻画并进行了算法检查。在本文中，我们提供了一种线性摊销复杂度的递减算法，用于检查动态演化网络的脆弱性。我们动态算法的基本思想是使用一种静态算法，该算法将某些边标记为对图的脆弱性无关，并在后续所有递减过程的运行中忽略这些边。为了在每次边移除时获得线性摊销成本，我们还提供了这种静态算法的一个新版本，将其复杂度从O(n m^2)改进到O(m^2)，这反过来与最先进的静态脆弱性算法的成本一致。
英文摘要
Braess paradox originates when latency at Wardrop equilibrium in traffic networks decreases because of removing edges. The graph-theoretic property of networks suffering from the Braess paradox was called vulnerability by Roughgarden in 2006; it was then characterized and algorithmically checked both for undirected and for directed nets. In this paper, we provide a decremental algorithm of linear amortized complexity to check vulnerability for dynamically evolving networks. The basic idea of our dynamic algorithm is to use a static algorithm that marks some edges as irrelevant for the vulnerability of the graph and ignore those edges for all subsequent runs of the decremental procedure. To get a linear amortized cost for every edge remotion, we also provide a new version of such a static algorithm that improves its complexity from O(n m^2) to O(m^2), that is in turn aligned with the cost of the best state-of-the-art static algorithm for vulnerability.
