Quick-Sort Style Approximation Algorithms for Generalizations of Feedback Vertex Set in Tournaments
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866911774160191488 |
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| author | Gupta, Sushmita Modak, Sounak Saurabh, Saket Seetharaman, Sanjay |
| author_facet | Gupta, Sushmita Modak, Sounak Saurabh, Saket Seetharaman, Sanjay |
| contents | A feedback vertex set (FVS) in a digraph is a subset of vertices whose removal makes the digraph acyclic. In other words, it hits all cycles in the digraph. Lokshtanov et al. [TALG '21] gave a factor 2 randomized approximation algorithm for finding a minimum weight FVS in tournaments. We generalize the result by presenting a factor $2α$ randomized approximation algorithm for finding a minimum weight FVS in digraphs of independence number $α$; a generalization of tournaments which are digraphs with independence number $1$. Using the same framework, we present a factor $2$ randomized approximation algorithm for finding a minimum weight Subset FVS in tournaments: given a vertex subset $S$ in addition to the graph, find a subset of vertices that hits all cycles containing at least one vertex in $S$. Note that FVS in tournaments is a special case of Subset FVS in tournaments in which $S = V(T)$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2402_06407 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Quick-Sort Style Approximation Algorithms for Generalizations of Feedback Vertex Set in Tournaments Gupta, Sushmita Modak, Sounak Saurabh, Saket Seetharaman, Sanjay Data Structures and Algorithms A feedback vertex set (FVS) in a digraph is a subset of vertices whose removal makes the digraph acyclic. In other words, it hits all cycles in the digraph. Lokshtanov et al. [TALG '21] gave a factor 2 randomized approximation algorithm for finding a minimum weight FVS in tournaments. We generalize the result by presenting a factor $2α$ randomized approximation algorithm for finding a minimum weight FVS in digraphs of independence number $α$; a generalization of tournaments which are digraphs with independence number $1$. Using the same framework, we present a factor $2$ randomized approximation algorithm for finding a minimum weight Subset FVS in tournaments: given a vertex subset $S$ in addition to the graph, find a subset of vertices that hits all cycles containing at least one vertex in $S$. Note that FVS in tournaments is a special case of Subset FVS in tournaments in which $S = V(T)$. |
| title | Quick-Sort Style Approximation Algorithms for Generalizations of Feedback Vertex Set in Tournaments |
| topic | Data Structures and Algorithms |
| url | https://arxiv.org/abs/2402.06407 |