论文标题
计算多项式空间和线性fpt时间
Computing treedepth in polynomial space and linear fpt time
论文作者
论文摘要
图$ g $的详细信息是$ g $的消除森林的最小深度：在同一顶点套装上的根森林，其中每对$ g $相邻的顶点都受祖先/后代关系的约束。我们提出了一种算法，该算法给出了$ g $和整数$ d $，要么最多发现$ g $ d $的消除森林，要么得出结论，没有这样的森林；因此，该算法决定了$ g $的超过$ d $。运行时间为$ 2^{o（d^2）} \ cdot n^{o（1）} $，空间用法在$ n $中是多项式。此外，通过允许随机化，可以将时间和空间复杂性提高到$ 2^{o（d^2）} \ cdot n $和$ d^{o（1）} \ cdot n $。这改进了Reidl等人的算法。 [ICALP 2014]，它也有时间复杂性$ 2^{o（d^2）} \ cdot n $，但使用指数空间。
The treedepth of a graph $G$ is the least possible depth of an elimination forest of $G$: a rooted forest on the same vertex set where every pair of vertices adjacent in $G$ is bound by the ancestor/descendant relation. We propose an algorithm that given a graph $G$ and an integer $d$, either finds an elimination forest of $G$ of depth at most $d$ or concludes that no such forest exists; thus the algorithm decides whether the treedepth of $G$ is at most $d$. The running time is $2^{O(d^2)}\cdot n^{O(1)}$ and the space usage is polynomial in $n$. Further, by allowing randomization, the time and space complexities can be improved to $2^{O(d^2)}\cdot n$ and $d^{O(1)}\cdot n$, respectively. This improves upon the algorithm of Reidl et al. [ICALP 2014], which also has time complexity $2^{O(d^2)}\cdot n$, but uses exponential space.
