论文标题
测量集的参数化复杂性
Parameterized Complexity of Geodetic Set
论文作者
论文摘要
如果$ g $的每个顶点都位于$ s $中的两个顶点之间的最短路径上，则图$ g $的顶点$ s $是大地测量的。给定图形$ g $和$ k \ in \ mathbb n $，NP-HARD GEODETIC SET问题询问是否有一组大小的尺寸，最多是$ k $。补充了仅限于特殊图类别的大地测量集的各种作品，我们启动了一项参数化的复杂性研究，对大地测量集进行了参数化的复杂性研究，并在负面显示，当通过反馈顶点数，路径宽度和解决方案大小的参数化时，大地测量集是w [1] - hard。在正面，我们相对于反馈边数，树深度和输入图的模块化宽度开发了固定参数算法。
A vertex set $S$ of a graph $G$ is geodetic if every vertex of $G$ lies on a shortest path between two vertices in $S$. Given a graph $G$ and $k \in \mathbb N$, the NP-hard Geodetic Set problem asks whether there is a geodetic set of size at most $k$. Complementing various works on Geodetic Set restricted to special graph classes, we initiate a parameterized complexity study of Geodetic Set and show, on the negative side, that Geodetic Set is W[1]-hard when parameterized by feedback vertex number, path-width, and solution size, combined. On the positive side, we develop fixed-parameter algorithms with respect to the feedback edge number, the tree-depth, and the modular-width of the input graph.
