AI 中文总结
本文针对平面图连通性增强问题，在Gutwenger与Mutzel的研究基础上，提出一种时间复杂度为O(|V|(1+α(|V|)))的算法，可计算使连通平面图变为2边连通的最小边集，同时保留平面性。
AI 中文摘要
我们研究平面图的连通性增强问题，同时保留其平面性。该问题的现实动机来自道路网络、电力网络等场景，这些场景中增强后保留原始平面嵌入至关重要。2009年，Gutwenger与Mutzel提出构造性算法，证明具有固定嵌入的连通平面图（即平面 graph）可在保留嵌入的同时，最优地增强为无交叉的双连通图。我们推进该方向研究，提出一种算法，可计算使连通平面 graph 变为2边连通的最小边集，时间复杂度为O(|V|(1+α(|V|)))，空间为线性，其中α为逆阿克曼函数。
英文摘要
We study the problem of connectivity augmentation of a planar graph, while preserving planarity. This problem is motivated by many real-world settings such as road-networks, power-networks etc. In these settings, it is crucial to preserve the original planar embedding after augmentation. In 2009, Gutwenger and Mutzel gave a constructive algorithm showing that a connected planar graph with a fixed embedding (a plane graph) can be optimally augmented to a biconnected graph without crossings while preserving the embedding. We further this line of research, by giving an algorithm that computes a minimum set of edges that makes a connected plane graph 2-edge-connected in \(O(|V|(1+α(|V|)))\) time and linear space, where \(α\) is the inverse Ackermann function.
CommentsAccepted for publication in MFCS 2026. 29 pages, 4 figures
