Feedback Vertex Set on Geometric Intersection Graphs

In this paper, we present an algorithm for computing a feedback vertex set of a unit disk graph of size k, if it exists, which runs in time 2^O(?k)(n+m), where n and m denote the numbers of vertices and edges, respectively. This improves the 2^O(?klog k) n^O(1)-time algorithm for this problem on unit disk graphs by Fomin et al. [ICALP 2017]. Moreover, our algorithm is optimal assuming the exponential-time hypothesis. Also, our algorithm can be extended to handle geometric intersection graphs of similarly sized fat objects without increasing the running time

Reachability Problems for Transmission Graphs

Let P be a set of n points in the plane where each point p of P is associated with a radius r1