动态网络中检测 Braess 悖论可能性的增量算法
An Incremental Algorithm for Checking the Possibility of Braess Paradox in Dynamic Nets
- Sapienza, University of Rome（罗马第一大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文提出一种增量算法，用于动态图中高效检测 Braess 悖论（脆弱性），通过仅在相关子图上运行检查，使加边总成本达到 O(m²)，与静态算法一致。
AI中文摘要：
Braess 悖论是一种众所周知的现象，它源于在交通网络中移除边后 Wardrop 均衡处的延迟反而降低。这种悖论出现的可能性在 2006 年被 Roughgarden 称为脆弱性，后来在无向图和有向图中都用图论概念进行了刻画。在本文中，我们针对动态演化图，为检查脆弱性的增量情形提供了一种算法。保持每次加边摊还成本为线性的关键思想是，我们无需在整个图上运行脆弱性算法，而只需在一个由所加边确定的、被良好识别的子图上运行。总体而言，添加 m 条边时，我们付出的成本为 O(m²)；这与最先进的静态脆弱性算法的 O(m²) 成本一致。
英文摘要：
Braess paradox is a well-known phenomenon that originates when latency at Wardrop equilibrium in traffic networks decreases because of removing edges. The possibility of having the paradox was called vulnerability by Roughgarden in 2006 and was characterized later on by graph-theoretical notions, both for undirected and for directed graphs. In this paper we provide an algorithm for the incremental case of checking vulnerability for dynamically evolving graphs. The crucial idea to keep the amortized cost linear for every edge addition is that we do not need to run the vulnerability algorithm on the whole graph, but only on a well-identified subgraph, determined by the edge that we are adding. Overall, to add m edges, we pay a cost of O(m2); this aligns with the O(m2) cost of the state-of-the-art static algorithm for vulnerability.
