[{"OA_type":"gold","conference":{"start_date":"2024-09-04","location":"Egham, United Kingdom","end_date":"2024-09-06","name":"IPEC: Symposium on Parameterized and Exact Computation"},"_id":"18758","oa":1,"month":"12","quality_controlled":"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","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"}],"publication":"19th International Symposium on Parameterized and Exact Computation","date_published":"2024-12-05T00:00:00Z","department":[{"_id":"MaKw"}],"file":[{"checksum":"a64b9a0e41f7b867d25cb155825ccd53","file_name":"2024_LIPIcs_Lill.pdf","file_id":"18775","success":1,"content_type":"application/pdf","file_size":927326,"relation":"main_file","date_updated":"2025-01-08T09:14:59Z","date_created":"2025-01-08T09:14:59Z","access_level":"open_access","creator":"dernst"}],"has_accepted_license":"1","scopus_import":"1","doi":"10.4230/LIPIcs.IPEC.2024.2","alternative_title":["LIPIcs"],"citation":{"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.","short":"J. Lill, K.H. Petrova, S. Weber, in:, 19th International Symposium on Parameterized and Exact Computation, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2024.","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>.","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>","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>","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."},"publication_identifier":{"issn":["1868-8969"],"isbn":["9783959773539"]},"day":"05","intvolume":"       321","publication_status":"published","fulldoi":"https://doi.org/10.4230/LIPIcs.IPEC.2024.2","type":"conference","project":[{"_id":"fc2ed2f7-9c52-11eb-aca3-c01059dda49c","name":"IST-BRIDGE: International postdoctoral program","call_identifier":"H2020","grant_number":"101034413"}],"external_id":{"arxiv":["2407.01071"],"isi":["001534851900002"]},"ec_funded":1,"file_date_updated":"2025-01-08T09:14:59Z","arxiv":1,"ddc":["500"],"tmp":{"image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"oa_version":"Published Version","title":"Linear-time MaxCut in multigraphs parameterized above the Poljak-Turzík bound","article_processing_charge":"Yes","publisher":"Schloss Dagstuhl - Leibniz-Zentrum für Informatik","date_created":"2025-01-05T23:01:57Z","OA_place":"publisher","related_material":{"record":[{"id":"19603","relation":"later_version","status":"public"}]},"status":"public","corr_author":"1","author":[{"first_name":"Jonas","last_name":"Lill","full_name":"Lill, Jonas"},{"first_name":"Kalina H","full_name":"Petrova, Kalina H","last_name":"Petrova","id":"554ff4e4-f325-11ee-b0c4-a10dbd523381"},{"full_name":"Weber, Simon","last_name":"Weber","first_name":"Simon"}],"year":"2024","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","isi":1,"volume":321,"date_updated":"2026-01-05T13:46:07Z","language":[{"iso":"eng"}],"article_number":"2"}]