Polynomial Treedepth Bounds in Linear Colorings,Algorithmica

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Polynomial Treedepth Bounds in Linear Colorings
Algorithmica ( IF 0.9 ) Pub Date : 2020-09-03 , DOI: 10.1007/s00453-020-00760-0
Jeremy Kun , Michael P. O’Brien , Marcin Pilipczuk , Blair D. Sullivan

Low-treedepth colorings are an important tool for algorithms that exploit structure in classes of bounded expansion; they guarantee subgraphs that use few colors have bounded treedepth. These colorings have an implicit tradeoff between the total number of colors used and the treedepth bound, and prior empirical work suggests that the former dominates the run time of existing algorithms in practice. We introduce $p$-linear colorings as an alternative to the commonly used $p$-centered colorings. They can be efficiently computed in bounded expansion classes and use at most as many colors as $p$-centered colorings. Although a set of $k

中文翻译：

线性着色中的多项式树深度边界

低树深度着色是利用有界扩展类中的结构的算法的重要工具；它们保证使用很少颜色的子图具有有界的树深度。这些着色在使用的颜色总数和树深度界限之间有一个隐含的权衡，先前的实证工作表明，前者在实践中主导了现有算法的运行时间。我们引入 $p$-linear 着色作为常用的以 $p$ 为中心的着色的替代方案。它们可以在有界扩展类中有效计算，并且最多使用与以 $p$ 为中心的着色一样多的颜色。虽然一组 $k

更新日期：2020-09-03

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