A linear time algorithm for finding tree-decompositions of small treewidth
A linear time algorithm for finding tree-decompositions of small treewidth
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DOI：
10.1145/167088.167161
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发表时间：
1993-06
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通讯作者：
H. Bodlaender
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文献类型：
--
作者：
H. Bodlaender
在本文中，我们给常数$k$一个线性时间算法，给定一个图$G=（V，E）$，确定是否$G$的树宽是最多$k$，如果是这样，找到一个树分解$G$的树宽最多$k$。一个结果是，不包含所有平面图的图的每一个小闭类都有一个线性时间识别算法。另一个结果是，当我们寻找路径宽度至多为某个常数k的路径分解时，类似的结果也成立。
In this paper, we give for constant $k$ a linear-time algorithm that, given a graph $G=(V,E)$, determines whether the treewidth of $G$ is at most $k$ and, if so, finds a tree-decomposition of $G$ with treewidth at most $k$. A consequence is that every minor-closed class of graphs that does not contain all planar graphs has a linear-time recognition algorithm. Another consequence is that a similar result holds when we look instead for path-decompositions with pathwidth at most some constant $k$.