Faster Algorithms for Cycle Hitting Problems on Disk Graphs

Abstract

In this paper, we consider three hitting problems on a disk intersection graph: Triangle Hitting Set, Feedback Vertex Set, and Odd Cycle Transversal. Given a disk intersection graph G, our goal is to compute a set of vertices hitting all triangles, all cycles, or all odd cycles, respectively. Our algorithms run in time 2O~(k4/5)nO(1), 2O~(k9/10)nO(1), and 2O~(k19/20)nO(1), respectively, where n denotes the number of vertices of G. These do not require a geometric representation of a disk graph. If a geometric representation of a disk graph is given as input, we can solve these problems more efficiently. In this way, we improve the algorithms for those three problem by Lokshtanov et al. [SODA 2022].