Lacon- and Shrub-Decompositions: A New Characterization of First-Order Transductions of Bounded Expansion Classes
Lacon- and Shrub-Decompositions: A New Characterization of First-Order Transductions of Bounded Expansion Classes
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DOI：
10.1109/lics52264.2021.9470680
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发表时间：
2021-06
期刊：
影响因子：
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通讯作者：
Jannik Dreier
中科院分区：
文献类型：
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作者：
Jannik Dreier
有界扩展的概念提供了一种鲁棒的方法来捕获具有有趣算法特性的稀疏图类。最值得注意的是，在一阶逻辑中可定义的每个问题都可以在有界扩展图类上在线性时间内解决。稀疏图类的一阶解释和转换导致更一般的，密集的图类，似乎继承了许多很好的算法属性的稀疏people.In这项工作中，我们引入了lacon和灌木分解，并用它们来表征有界扩展图类和其他图类的转换。如果一个人可以有效地计算稀疏灌木或花边分解的有界扩展类的转换，然后可以解决每一个问题定义在一阶逻辑在线性时间对这些类。
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.