Faster Exact and Parameterized Algorithm for Feedback Vertex Set in Bipartite Tournaments
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866917828893868032 |
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| author | Kumar, Mithilesh Lokshtanov, Daniel |
| author_facet | Kumar, Mithilesh Lokshtanov, Daniel |
| contents | A {\em bipartite tournament} is a directed graph $T:=(A \cup B, E)$ such that every pair of vertices $(a,b), a\in A,b\in B$ are connected by an arc, and no arc connects two vertices of $A$ or two vertices of $B$. A {\em feedback vertex set} is a set $S$ of vertices in $T$ such that $T - S$ is acyclic. In this article we consider the {\sc Feedback Vertex Set} problem in bipartite tournaments. Here the input is a bipartite tournament $T$ on $n$ vertices together with an integer $k$, and the task is to determine whether $T$ has a feedback vertex set of size at most $k$. We give a new algorithm for {\sc Feedback Vertex Set in Bipartite Tournaments}. The running time of our algorithm is upper-bounded by $O(1.6181^k + n^{O(1)})$, improving over the previously best known algorithm with running time $2^kk^{O(1)} + n^{O(1)}$ [Hsiao, ISAAC 2011]. As a by-product, we also obtain the fastest currently known exact exponential-time algorithm for the problem, with running time $O(1.3820^n)$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2411_02821 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Faster Exact and Parameterized Algorithm for Feedback Vertex Set in Bipartite Tournaments Kumar, Mithilesh Lokshtanov, Daniel Data Structures and Algorithms A {\em bipartite tournament} is a directed graph $T:=(A \cup B, E)$ such that every pair of vertices $(a,b), a\in A,b\in B$ are connected by an arc, and no arc connects two vertices of $A$ or two vertices of $B$. A {\em feedback vertex set} is a set $S$ of vertices in $T$ such that $T - S$ is acyclic. In this article we consider the {\sc Feedback Vertex Set} problem in bipartite tournaments. Here the input is a bipartite tournament $T$ on $n$ vertices together with an integer $k$, and the task is to determine whether $T$ has a feedback vertex set of size at most $k$. We give a new algorithm for {\sc Feedback Vertex Set in Bipartite Tournaments}. The running time of our algorithm is upper-bounded by $O(1.6181^k + n^{O(1)})$, improving over the previously best known algorithm with running time $2^kk^{O(1)} + n^{O(1)}$ [Hsiao, ISAAC 2011]. As a by-product, we also obtain the fastest currently known exact exponential-time algorithm for the problem, with running time $O(1.3820^n)$. |
| title | Faster Exact and Parameterized Algorithm for Feedback Vertex Set in Bipartite Tournaments |
| topic | Data Structures and Algorithms |
| url | https://arxiv.org/abs/2411.02821 |