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- W3011879093 abstract "In the Directed Long Cycle Hitting Set} problem we are given a directed graph $G$, and the task is to find a set $S$ of at most $k$ vertices/arcs such that $G-S$ has no cycle of length longer than $ell$. We show that the problem can be solved in time $2^{mathcal O(ell k^3log k + k^5log klogell)}cdot n^{mathcal O(1)}$, that is, it is fixed-parameter tractable (FPT) parameterized by $k$ and $ell$. This algorithm can be seen as a far-reaching generalization of the fixed-parameter tractability of {sc Mixed Graph Feedback Vertex Set} [Bonsma and Lokshtanov WADS 2011], which is already a common generalization of the fixed-parameter tractability of (undirected) {sc Feedback Vertex Set} and the {sc Directed Feedback Vertex Set} problems, two classic results in parameterized algorithms. The algorithm requires significant insights into the structure of graphs without directed cycles length longer than $ell$ and can be seen as an exact version of the approximation algorithm following from the Erd{ő}s-P{o}sa property for long cycles in directed graphs proved by Kreutzer and Kawarabayashi [STOC 2015]." @default.
- W3011879093 created "2020-03-23" @default.
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- W3011879093 date "2020-03-11" @default.
- W3011879093 modified "2023-09-23" @default.
- W3011879093 title "Hitting Long Directed Cycles is Fixed-Parameter Tractable" @default.
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