Tight Localizations of Feedback Sets
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
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2020
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| _version_ | 1866908323935158272 |
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| author | Hecht, Michael Gonciarz, Krzysztof Horvát, Szabolcs |
| author_facet | Hecht, Michael Gonciarz, Krzysztof Horvát, Szabolcs |
| contents | The classical NP-hard feedback arc set problem (FASP) and feedback vertex set problem (FVSP) ask for a minimum set of arcs $\varepsilon \subseteq E$ or vertices $ν\subseteq V$ whose removal $G\setminus \varepsilon$, $G\setminus ν$ makes a given multi-digraph $G=(V,E)$ acyclic, respectively. Though both problems are known to be APX-hard, approximation algorithms or proofs of inapproximability are unknown. We propose a new $\mathcal{O}(|V||E|^4)$-heuristic for the directed FASP. While a ratio of $r \approx 1.3606$ is known to be a lower bound for the APX-hardness, at least by empirical validation we achieve an approximation of $r \leq 2$. The most relevant applications, such as circuit testing, ask for solving the FASP on large sparse graphs, which can be done efficiently within tight error bounds due to our approach. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2001_01440 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Tight Localizations of Feedback Sets Hecht, Michael Gonciarz, Krzysztof Horvát, Szabolcs Discrete Mathematics Data Structures and Algorithms The classical NP-hard feedback arc set problem (FASP) and feedback vertex set problem (FVSP) ask for a minimum set of arcs $\varepsilon \subseteq E$ or vertices $ν\subseteq V$ whose removal $G\setminus \varepsilon$, $G\setminus ν$ makes a given multi-digraph $G=(V,E)$ acyclic, respectively. Though both problems are known to be APX-hard, approximation algorithms or proofs of inapproximability are unknown. We propose a new $\mathcal{O}(|V||E|^4)$-heuristic for the directed FASP. While a ratio of $r \approx 1.3606$ is known to be a lower bound for the APX-hardness, at least by empirical validation we achieve an approximation of $r \leq 2$. The most relevant applications, such as circuit testing, ask for solving the FASP on large sparse graphs, which can be done efficiently within tight error bounds due to our approach. |
| title | Tight Localizations of Feedback Sets |
| topic | Discrete Mathematics Data Structures and Algorithms |
| url | https://arxiv.org/abs/2001.01440 |