[{"volume":321,"publication":"19th International Symposium on Parameterized and Exact Computation","article_number":"2","publication_status":"published","abstract":[{"text":"MaxCut is a classical NP-complete problem and a crucial building block in many combinatorial algorithms. The famous Edwards-Erdős bound states that any connected graph on n vertices with m edges contains a cut of size at least m/2+(n-1)/4. Crowston, Jones and Mnich [Algorithmica, 2015] showed that the MaxCut problem on simple connected graphs admits an FPT algorithm, where the parameter k is the difference between the desired cut size c and the lower bound given by the Edwards-Erdős bound. This was later improved by Etscheid and Mnich [Algorithmica, 2017] to run in parameterized linear time, i.e., f(k)⋅ O(m). We improve upon this result in two ways: Firstly, we extend the algorithm to work also for multigraphs (alternatively, graphs with positive integer weights). Secondly, we change the parameter; instead of the difference to the Edwards-Erdős bound, we use the difference to the Poljak-Turzík bound. The Poljak-Turzík bound states that any weighted graph G has a cut of size at least (w(G))/2+(w_MSF(G))/4, where w(G) denotes the total weight of G, and w_MSF(G) denotes the weight of its minimum spanning forest. In connected simple graphs the two bounds are equivalent, but for multigraphs the Poljak-Turzík bound can be larger and thus yield a smaller parameter k. Our algorithm also runs in parameterized linear time, i.e., f(k)⋅ O(m+n).","lang":"eng"}],"related_material":{"record":[{"relation":"later_version","id":"19603","status":"public"}]},"tmp":{"short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png"},"ddc":["500"],"file":[{"creator":"dernst","content_type":"application/pdf","date_updated":"2025-01-08T09:14:59Z","date_created":"2025-01-08T09:14:59Z","file_size":927326,"success":1,"relation":"main_file","access_level":"open_access","file_id":"18775","checksum":"a64b9a0e41f7b867d25cb155825ccd53","file_name":"2024_LIPIcs_Lill.pdf"}],"type":"conference","date_created":"2025-01-05T23:01:57Z","year":"2024","title":"Linear-time MaxCut in multigraphs parameterized above the Poljak-Turzík bound","ec_funded":1,"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publisher":"Schloss Dagstuhl - Leibniz-Zentrum für Informatik","publication_identifier":{"isbn":["9783959773539"],"issn":["1868-8969"]},"citation":{"ieee":"J. Lill, K. H. Petrova, and S. Weber, “Linear-time MaxCut in multigraphs parameterized above the Poljak-Turzík bound,” in <i>19th International Symposium on Parameterized and Exact Computation</i>, Egham, United Kingdom, 2024, vol. 321.","short":"J. Lill, K.H. Petrova, S. Weber, in:, 19th International Symposium on Parameterized and Exact Computation, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2024.","ista":"Lill J, Petrova KH, Weber S. 2024. Linear-time MaxCut in multigraphs parameterized above the Poljak-Turzík bound. 19th International Symposium on Parameterized and Exact Computation. IPEC: Symposium on Parameterized and Exact Computation, LIPIcs, vol. 321, 2.","mla":"Lill, Jonas, et al. “Linear-Time MaxCut in Multigraphs Parameterized above the Poljak-Turzík Bound.” <i>19th International Symposium on Parameterized and Exact Computation</i>, vol. 321, 2, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2024, doi:<a href=\"https://doi.org/10.4230/LIPIcs.IPEC.2024.2\">10.4230/LIPIcs.IPEC.2024.2</a>.","chicago":"Lill, Jonas, Kalina H Petrova, and Simon Weber. “Linear-Time MaxCut in Multigraphs Parameterized above the Poljak-Turzík Bound.” In <i>19th International Symposium on Parameterized and Exact Computation</i>, Vol. 321. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2024. <a href=\"https://doi.org/10.4230/LIPIcs.IPEC.2024.2\">https://doi.org/10.4230/LIPIcs.IPEC.2024.2</a>.","apa":"Lill, J., Petrova, K. H., &#38; Weber, S. (2024). Linear-time MaxCut in multigraphs parameterized above the Poljak-Turzík bound. In <i>19th International Symposium on Parameterized and Exact Computation</i> (Vol. 321). Egham, United Kingdom: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. <a href=\"https://doi.org/10.4230/LIPIcs.IPEC.2024.2\">https://doi.org/10.4230/LIPIcs.IPEC.2024.2</a>","ama":"Lill J, Petrova KH, Weber S. Linear-time MaxCut in multigraphs parameterized above the Poljak-Turzík bound. In: <i>19th International Symposium on Parameterized and Exact Computation</i>. Vol 321. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2024. doi:<a href=\"https://doi.org/10.4230/LIPIcs.IPEC.2024.2\">10.4230/LIPIcs.IPEC.2024.2</a>"},"_id":"18758","date_updated":"2026-01-05T13:46:07Z","OA_type":"gold","oa":1,"date_published":"2024-12-05T00:00:00Z","external_id":{"arxiv":["2407.01071"],"isi":["001534851900002"]},"project":[{"grant_number":"101034413","_id":"fc2ed2f7-9c52-11eb-aca3-c01059dda49c","name":"IST-BRIDGE: International postdoctoral program","call_identifier":"H2020"}],"conference":{"end_date":"2024-09-06","name":"IPEC: Symposium on Parameterized and Exact Computation","location":"Egham, United Kingdom","start_date":"2024-09-04"},"quality_controlled":"1","status":"public","department":[{"_id":"MaKw"}],"oa_version":"Published Version","arxiv":1,"acknowledgement":"Kalina Petrova: Swiss National Science Foundation, grant no. CRSII5 173721. This project\r\nhas received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No 101034413.\r\nSimon Weber: Swiss National Science Foundation under project no. 204320","corr_author":"1","author":[{"first_name":"Jonas","full_name":"Lill, Jonas","last_name":"Lill"},{"first_name":"Kalina H","last_name":"Petrova","full_name":"Petrova, Kalina H","id":"554ff4e4-f325-11ee-b0c4-a10dbd523381"},{"first_name":"Simon","full_name":"Weber, Simon","last_name":"Weber"}],"intvolume":"       321","isi":1,"alternative_title":["LIPIcs"],"doi":"10.4230/LIPIcs.IPEC.2024.2","month":"12","file_date_updated":"2025-01-08T09:14:59Z","day":"05","scopus_import":"1","article_processing_charge":"Yes","language":[{"iso":"eng"}],"OA_place":"publisher","has_accepted_license":"1"}]