{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/tight-localizations-of-feedback-sets","title":"Tight Localizations of Feedback Sets","arxiv_id":"2001.01440","date":"2020-01-06","proceeding":null,"authors":["Michael Hecht","Krzysztof Gonciarz","Szabolcs Horvát"],"abstract":"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 $\\nu \\subseteq V$ whose removal $G\\setminus \\varepsilon$, $G\\setminus \\nu$ 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.","url_abs":"http://arxiv.org/abs/2001.01440v2","url_pdf":"http://arxiv.org/pdf/2001.01440v2.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"tight-localizations-of-feedback-sets","repo_url":"https://git.mpi-cbg.de/mosaic/software/math/FaspHeuristic/","is_official":1,"mentioned_in_paper":0,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":"https://app.syntology.ai/?focus=2001.01440","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}