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Feedback Vertex Set for pseudo-disk graphs in subexponential FPT time
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abstract
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 $2^{O(k^{6/7}\log k)}n^{O(1)}$.
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Layered tree-independence number and clique-based separators
Map graphs, hyperbolic uniform disk graphs, and spherical uniform disk graphs are shown to have bounded or radius-dependent layered tree-independence number, yielding new weighted subexponential algorithms.
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