In this paper, we investigate the existence of parameterized algorithms running in subexponential time for two fundamental cycle-hitting problems: Feedback Vertex Set (FVS) and Triangle Hitting (TH). We focus on the class of pseudo-disk graphs, which forms a common generalization of several graph classes where such results exist, like disk graphs and square graphs. In these graphs, we show that TH can be solved in time $2^{O(k^{3/4}\log k)}n^{O(1)}$, and given a geometric representation FVS can be solved in time $2^{O(k^{6/7}\log k)}n^{O(1)}$.

翻译：本文研究了两个基本的环路命中问题——反馈顶点集（FVS）与三角形命中（TH）——是否存在亚指数时间的参数化算法。我们聚焦于伪圆盘图类，该类是对多个已知存在此类结果的图类（如圆盘图与正方形图）的共同推广。在此类图中，我们证明TH问题可在$2^{O(k^{3/4}\log k)}n^{O(1)}$时间内求解，而在给定几何表示的情况下，FVS问题可在$2^{O(k^{6/7}\log k)}n^{O(1)}$时间内求解。