Feedback Vertex Set on Geometric Intersection Graphs
Shinwoo An, Eunjin Oh

TL;DR
This paper introduces an optimized algorithm for finding feedback vertex sets in unit disk graphs that improves previous methods and is optimal under the exponential-time hypothesis, with extensions to other geometric intersection graphs.
Contribution
It presents a faster, optimal algorithm for feedback vertex set on unit disk graphs, extending to fat objects without increasing complexity.
Findings
Runs in 2^{O(√k)}(n+m) time, improving previous algorithms.
Proves optimality assuming the exponential-time hypothesis.
Extends to geometric intersection graphs of fat objects.
Abstract
In this paper, we present an algorithm for computing a feedback vertex set of a unit disk graph of size , if it exists, which runs in time , where and denote the numbers of vertices and edges, respectively. This improves the -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.
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