{"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/designing-practical-ptases-for-minimum","title":"Designing Practical PTASes for Minimum Feedback Vertex Set in Planar Graphs","arxiv_id":"1804.07869","date":"2018-04-21","proceeding":null,"authors":["Glencora Borradaile","Hung Le","Baigong Zheng"],"abstract":"We present two algorithms for the minimum feedback vertex set problem in planar graphs: an $O(n \\log n)$ PTAS using a linear kernel and balanced separator, and a heuristic algorithm using kernelization and local search. We implemented these algorithms and compared their performance with Becker and Geiger's 2-approximation algorithm. We observe that while our PTAS is competitive with the 2-approximation algorithm on large planar graphs, its running time is much longer. And our heuristic algorithm can outperform the 2-approximation algorithm on most large planar graphs and provide a trade-off between running time and solution quality, i.e. a \"PTAS behavior\".","url_abs":"http://arxiv.org/abs/1804.07869v1","url_pdf":"http://arxiv.org/pdf/1804.07869v1.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":"designing-practical-ptases-for-minimum","repo_url":"https://github.com/zbgzbg2007/Practical-FVS-PTASes","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}