{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,8]],"date-time":"2026-05-08T06:06:40Z","timestamp":1778220400695,"version":"3.51.4"},"reference-count":22,"publisher":"Association for Computing Machinery (ACM)","issue":"1","license":[{"start":{"date-parts":[[2013,5,1]],"date-time":"2013-05-01T00:00:00Z","timestamp":1367366400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.acm.org\/publications\/policies\/copyright_policy#Background"}],"funder":[{"DOI":"10.13039\/501100001870","name":"Foundation For Polish Science","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100001870","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100004281","name":"Narodowe Centrum Nauki","doi-asserted-by":"publisher","award":["N206 567140"],"award-info":[{"award-number":["N206 567140"]}],"id":[{"id":"10.13039\/501100004281","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100000781","name":"European Research Council","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100000781","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":["ACM Trans. Comput. Theory"],"published-print":{"date-parts":[[2013,5]]},"abstract":"<jats:p>\n            We introduce a concept of parameterizing a problem above the optimum solution of its natural linear programming relaxation and prove that the\n            <jats:italic>node multiway cut<\/jats:italic>\n            problem is fixed-parameter tractable (FPT) in this setting. As a consequence we prove that node multiway cut is FPT, when parameterized above the maximum separating cut, resolving an open problem of Razgon.\n          <\/jats:p>\n          <jats:p>\n            Our results imply\n            <jats:italic>O<\/jats:italic>\n            <jats:sup>*<\/jats:sup>\n            (4\n            <jats:italic>\n              <jats:sup>k<\/jats:sup>\n            <\/jats:italic>\n            ) algorithms for vertex cover above maximum matching and almost 2-SAT as well as an\n            <jats:italic>O<\/jats:italic>\n            <jats:sup>*<\/jats:sup>\n            (2\n            <jats:italic>\n              <jats:sup>k<\/jats:sup>\n            <\/jats:italic>\n            ) algorithm for node multiway cut with a standard parameterization by the solution size, improving previous bounds for these problems.\n          <\/jats:p>","DOI":"10.1145\/2462896.2462899","type":"journal-article","created":{"date-parts":[[2013,5,28]],"date-time":"2013-05-28T16:35:32Z","timestamp":1369758932000},"page":"1-11","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":54,"title":["On multiway cut parameterized above lower bounds"],"prefix":"10.1145","volume":"5","author":[{"given":"Marek","family":"Cygan","sequence":"first","affiliation":[{"name":"University of Warsaw, Poland"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Marcin","family":"Pilipczuk","sequence":"additional","affiliation":[{"name":"University of Warsaw, Poland"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Micha\u0142","family":"Pilipczuk","sequence":"additional","affiliation":[{"name":"University of Warsaw, Poland"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jakub Onufry","family":"Wojtaszczyk","sequence":"additional","affiliation":[{"name":"Google Inc., Warsaw, Poland"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"320","published-online":{"date-parts":[[2013,5,29]]},"reference":[{"key":"e_1_2_1_1_1","doi-asserted-by":"publisher","DOI":"10.1145\/1993636.1993698"},{"key":"e_1_2_1_2_1","doi-asserted-by":"publisher","DOI":"10.1007\/s00453-007-9130-6"},{"key":"e_1_2_1_3_1","doi-asserted-by":"publisher","DOI":"10.1145\/1374376.1374404"},{"key":"e_1_2_1_4_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-28050-4_1"},{"key":"e_1_2_1_5_1","doi-asserted-by":"publisher","DOI":"10.1137\/S0097539792225297"},{"key":"e_1_2_1_6_1","volume-title":"Fellows","author":"Downey Rodney G.","year":"1999"},{"key":"e_1_2_1_7_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.tcs.2008.09.065"},{"key":"e_1_2_1_8_1","volume-title":"Parameterized Complexity Theory","author":"Flum J\u00f6rg","edition":"1"},{"key":"e_1_2_1_9_1","doi-asserted-by":"publisher","DOI":"10.1016\/S0196-6774(03)00111-1"},{"key":"e_1_2_1_10_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.disopt.2010.05.003"},{"key":"e_1_2_1_11_1","doi-asserted-by":"publisher","DOI":"10.1007\/s00224-010-9262-y"},{"key":"e_1_2_1_12_1","doi-asserted-by":"publisher","DOI":"10.5555\/1888935.1888973"},{"key":"e_1_2_1_13_1","doi-asserted-by":"publisher","DOI":"10.1006\/jagm.1998.0996"},{"key":"e_1_2_1_14_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.tcs.2005.10.007"},{"key":"e_1_2_1_15_1","doi-asserted-by":"publisher","DOI":"10.1145\/1993636.1993699"},{"key":"e_1_2_1_16_1","volume-title":"Proceedings of the 29th International Symposium on Theoretical Aspects of Computer Science (STACS'12)","author":"Narayanaswamy N. S.","year":"2012"},{"key":"e_1_2_1_17_1","volume-title":"Invitation to Fixed Parameter Algorithms","author":"Niedermeier Rolf","year":"1985"},{"key":"e_1_2_1_18_1","doi-asserted-by":"publisher","DOI":"10.5555\/2040572.2040615"},{"key":"e_1_2_1_19_1","volume-title":"Computing multiway cut within the given excess over the largest minimum isolating cut. CoRR abs\/1011.6267","author":"Razgon Igor","year":"2010"},{"key":"e_1_2_1_20_1","volume-title":"Large isolating cuts shrink the multiway cut. 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