Digraph width measures in parameterized algorithmics
Digraph width measures in parameterized algorithmics
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DOI：
10.1016/j.dam.2013.10.038
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发表时间：
2014-05
期刊：
影响因子：
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通讯作者：
R. Ganian;Petr Hliněný;Joachim Kneis;Alexander Langer;J. Obdržálek;P. Rossmanith
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文献类型：
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作者：
R. Ganian;Petr Hliněný;Joachim Kneis;Alexander Langer;J. Obdržálek;P. Rossmanith
与提供了许多重要算法应用的无向宽度度量（例如树宽度）相比，有向图的类似度量（例如有向树宽度或 DAG 宽度）似乎并不那么成功。最近的几篇论文给出了一些负面的证据。我们通过彻底、详尽地研究一系列关于各种参数的有向问题的复杂性来确认并巩固这一整体情况，并表明即使在受到限制的图类上，它们通常仍然是 NP 难的，而这些图类的限制远远超出了小 DAG 宽度。从积极的一面来看，从参数化复杂性的角度来看，（有向图的）clique-width 在几乎所有考虑的问题上都表现得更好。
In contrast to undirected width measures such as tree-width, which have provided many important algorithmic applications, analogous measures for digraphs such as directed tree-width or DAG-width do not seem so successful. Several recent papers have given some evidence on the negative side. We confirm and consolidate this overall picture by thoroughly and exhaustively studying the complexity of a range of directed problems with respect to various parameters, and by showing that they often remain NP-hard even on graph classes that are restricted very beyond having small DAG-width. On the positive side, it turns out that clique-width (of digraphs) performs much better on virtually all considered problems, from the parameterized complexity point of view.