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引用次数: 9
摘要
平面图的\emph{积结构定理}(dujmovovic et al.)\emph{JACM}, \textbf{67}(4):22)指出任何平面图都包含在平面$3$ -tree、路径和$3$ -cycle的强积中。我们给出了一个简单的线性时间算法来找到这个分解，以及几个相关的分解。这改进了以前的$O(n\log n)$时间算法(Morin。\emph{算法}，\textbf{85}(5):1544—1558。
An Optimal Algorithm for Product Structure in Planar Graphs
The \emph{Product Structure Theorem} for planar graphs (Dujmovi\'c et al.\ \emph{JACM}, \textbf{67}(4):22) states that any planar graph is contained in the strong product of a planar $3$-tree, a path, and a $3$-cycle. We give a simple linear-time algorithm for finding this decomposition as well as several related decompositions. This improves on the previous $O(n\log n)$ time algorithm (Morin.\ \emph{Algorithmica}, \textbf{85}(5):1544--1558).
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