{"url":"/task/feedback-vertex-set-fvs","name":"Feedback Vertex Set (FVS)","slug":"feedback-vertex-set-fvs","description_markdown":"The **Feedback Vertex Set (FVS)** problem is a computational problem in computer science and graph theory that involves finding the smallest possible subset of vertices in an undirected graph such that removing those vertices results in a graph that is acyclic, i.e., a forest. The goal of the FVS problem is to minimize the size of the feedback vertex set, and is considered NP-hard, meaning that finding the optimal solution is computationally difficult. For directed graphs, a feedback vertex set is instead a subset of vertices whose removal results in directed acyclic graph (DAG), not necessarily a forest. This task can refer to either looking for a set of provably minimal size (in as little time as possible), or a heuristic algorithm that produces small solutions quickly (but which may have even smaller sets).","categories":[{"name":"Graphs","url":"/area/graphs"}],"source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","slug_source":"archive_url"},"counts":{"papers_tagged":4,"papers_with_code":1,"benchmarks":0,"benchmark_tables_in_archive":0,"benchmark_tables_shown":0,"benchmark_tables_withheld_as_spam":0,"benchmark_definition":"a leaderboard table with at least one row; benchmark_tables_shown also counts the zero-row tables; benchmark_tables_in_archive adds the tables withheld as spam","datasets":3,"subtasks":0,"parent_tasks":0},"benchmarks":[],"datasets":[{"url":"/dataset/pace-2016-feedback-vertex-set","name":"PACE 2016 Feedback Vertex Set","full_name":"PACE 2016 Track B, Feedback Vertex Set","num_papers_in_archive":2},{"url":"/dataset/pace-2022-exact","name":"PACE 2022 Exact","full_name":"PACE 2022 Directed Feedback Vertex Set, Exact Track","num_papers_in_archive":2},{"url":"/dataset/pace-2022-heuristic","name":"PACE 2022 Heuristic","full_name":"PACE 2022 Directed Feedback Vertex Set, HeuristicTrack","num_papers_in_archive":1}],"subtasks":[],"parent_tasks":[],"papers":{"order":"repositories listed in the archive (desc), then date (desc); the archive holds no stars","population":"papers tagged with this task that list at least one repository in the archive","shown":1,"of":1,"tagged_in_all":4,"items":[{"url":"/paper/structure-based-approach-to-identifying-small","title":"Structure-based approach to identifying small sets of driver nodes in biological networks","date":"2021-11-22","arxiv_id":"2111.11558","repositories_listed":1,"syntology":{"n":4,"n_ran":0,"n_unverified":4,"n_pointer_only":0}}],"syntology_records":1,"syntology_note":"a paper without a record is not a recorded non-run: it may lack an arXiv id or simply be absent from the graph layer"},"description_links":{"kept":0,"unwrapped_to_text":0,"bare_urls_linked":0,"relative_images_dropped":0,"rule":"internal links are kept only when the target slug exists in the catalog"},"syntology":{"read_at":"2026-09-24T18:15:14+00:00","claim":"Per-sample execution status on synthesized fixtures ('ran N of M samples'); not a correctness claim and not a ranking signal.","status_vocabulary":{"ran_honours":"ran, honoured the contract we drafted","ran_violates":"ran, violated the contract we drafted","ran_draft_wrong":"ran; our contract draft was wrong, not the code","ran_fixture":"ran; our fixture could not drive it","ran":"ran on a synthesized input","unverified":"unverified (harvested, no recorded run)"}},"not_shown":{"libraries":"the archive has no per-task library table","trend_sparklines":"the Trend column of the benchmarks table was a rendered image; it is not in the archive","social_and_latest_sorts":"stars and social signals are not in the archive"}}