Feedback Vertex Set on Geometric Intersection Graphs

07/08/2021

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by   Shinwoo An, et al.

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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(√(k)log 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.