无向图无弦圈表的摊销$\tilde{O}(|V|)$ -延迟算法
Amortized $\tilde{O}(|V|)$-Delay Algorithm for Listing Chordless Cycles in Undirected Graphs
摘要：
无弦圈是无向图中非常自然的结构，在图论中有着重要的历史和杰出的作用。动机也由以前的工作上市周期的经典问题，我们研究如何列出弦周期。列出无向图$G = (V,E)$中包含的所有$C$无弦循环的最佳已知解决方案需要$O(|E|^2 +|E|\cdot C)$时间。在本文中，我们提供了一个算法采取$\tilde{O}(|E| + |V |\cdot C)$时间。我们还展示了如何获得相同的复杂性，列出所有的$P$无弦$st$ -路径在$G$（其中$C$被替换为$P$）。
英文摘要：
Chordless cycles are very natural structures in undirected graphs, with an important history and distinguished role in graph theory. Motivated also by previous work on the classical problem of listing cycles, we study how to list chordless cycles. The best known solution to list all the $C$ chordless cycles contained in an undirected graph $G = (V,E)$ takes $O(|E|^2 +|E|\cdot C)$ time. In this paper we provide an algorithm taking $\tilde{O}(|E| + |V |\cdot C)$ time. We also show how to obtain the same complexity for listing all the $P$ chordless $st$-paths in $G$ (where $C$ is replaced by $P$ ).
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
