Lacon-和灌木-分解:有界展开类一阶转导的新表征

Jannik Dreier
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引用次数: 7

摘要

有界展开的概念提供了一种健壮的方法来捕获具有有趣算法属性的稀疏图类。最值得注意的是,在有界展开图类上,每一个一阶逻辑可定义的问题都可以在线性时间内得到解决。稀疏图类的一阶解释和转换导致更一般、更密集的图类,这些图类似乎继承了稀疏对应类的许多良好的算法特性。在这项工作中,我们引入lacon分解和灌木分解,并使用它们来表征有界展开图类和其他图类的转换。如果一个人能够有效地计算有界展开类的稀疏灌木分解或lacon分解,那么就可以在线性时间内解决这些类上的每一个一阶逻辑可定义的问题。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Lacon- and Shrub-Decompositions: A New Characterization of First-Order Transductions of Bounded Expansion Classes
The concept of bounded expansion provides a robust way to capture sparse graph classes with interesting algorithmic properties. Most notably, every problem definable in first-order logic can be solved in linear time on bounded expansion graph classes. First-order interpretations and transductions of sparse graph classes lead to more general, dense graph classes that seem to inherit many of the nice algorithmic properties of their sparse counterparts.In this work we introduce lacon- and shrub-decompositions and use them to characterize transductions of bounded expansion graph classes and other graph classes. If one can efficiently compute sparse shrub- or lacon-decompositions of transductions of bounded expansion classes then one can solve every problem definable in first-order logic in linear time on these classes.
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