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Algorithms"],"published-print":{"date-parts":[[2018,7,31]]},"abstract":"<jats:p>\n            In the I\n            <jats:sc>nterval<\/jats:sc>\n            C\n            <jats:sc>ompletion<\/jats:sc>\n            problem we are given an\n            <jats:italic>n<\/jats:italic>\n            -vertex graph\n            <jats:italic>G<\/jats:italic>\n            and an integer\n            <jats:italic>k<\/jats:italic>\n            , and the task is to transform\n            <jats:italic>G<\/jats:italic>\n            by making use of at most\n            <jats:italic>k<\/jats:italic>\n            edge additions into an interval graph. This is a fundamental graph modification problem with applications in sparse matrix multiplication and molecular biology. The question about fixed-parameter tractability of I\n            <jats:sc>nterval<\/jats:sc>\n            C\n            <jats:sc>ompletion<\/jats:sc>\n            was asked by Kaplan et al.\u00a0[FOCS 1994; SIAM J. Comput. 1999] and was answered affirmatively more than a decade later by Villanger et al.\u00a0[STOC 2007; SIAM J. Comput. 2009], who presented an algorithm with running time\n            <jats:italic>O<\/jats:italic>\n            (\n            <jats:italic>k<\/jats:italic>\n            <jats:sup>\n              2\n              <jats:italic>k<\/jats:italic>\n            <\/jats:sup>\n            <jats:italic>n<\/jats:italic>\n            <jats:sup>3<\/jats:sup>\n            <jats:italic>m<\/jats:italic>\n            ). We give the first subexponential parameterized algorithm solving I\n            <jats:sc>nterval<\/jats:sc>\n            C\n            <jats:sc>ompletion<\/jats:sc>\n            in time\n            <jats:italic>k<\/jats:italic>\n            <jats:sup>\n              <jats:italic>O<\/jats:italic>\n              (\u221a\n              <jats:italic>k<\/jats:italic>\n              )\n            <\/jats:sup>\n            <jats:italic>n<\/jats:italic>\n            <jats:sup>\n              <jats:italic>O<\/jats:italic>\n              (1)\n            <\/jats:sup>\n            . This adds I\n            <jats:sc>nterval<\/jats:sc>\n            C\n            <jats:sc>ompletion<\/jats:sc>\n            to a very small list of parameterized graph modification problems solvable in subexponential time.\n          <\/jats:p>","DOI":"10.1145\/3186896","type":"journal-article","created":{"date-parts":[[2018,6,28]],"date-time":"2018-06-28T16:37:19Z","timestamp":1530203839000},"page":"1-62","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":6,"title":["Subexponential Parameterized Algorithm for I\n            <scp>nterval<\/scp>\n            C\n            <scp>ompletion<\/scp>"],"prefix":"10.1145","volume":"14","author":[{"given":"Ivan","family":"Bliznets","sequence":"first","affiliation":[{"name":"St. Petersburg Academic University of the Russian Academy of Sciences, Russia, Fontanka, St.Petersburg, Russia"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Fedor V.","family":"Fomin","sequence":"additional","affiliation":[{"name":"Department of Informatics, University of Bergen, Bergen, Norway"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Marcin","family":"Pilipczuk","sequence":"additional","affiliation":[{"name":"Institute of Informatics, University of Warsaw, Warsaw, Poland"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Micha\u0141","family":"Pilipczuk","sequence":"additional","affiliation":[{"name":"Institute of Informatics, University of Warsaw, Warsaw, Poland"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"320","published-online":{"date-parts":[[2018,6,27]]},"reference":[{"key":"e_1_2_1_1_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-02927-1_6"},{"key":"e_1_2_1_2_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.ic.2013.08.006"},{"key":"e_1_2_1_3_1","volume-title":"SODA","author":"Bliznets Ivan","year":"2016","unstructured":"Ivan Bliznets , Marek Cygan , Pawe\u0142 Komosa , Luk\u00e1s Mach , and Micha\u0142 Pilipczuk . 2016. Lower bounds for the parameterized complexity of minimum fill-in and other completion problems . In SODA 2016 . SIAM , 1132--1151. Ivan Bliznets, Marek Cygan, Pawe\u0142 Komosa, Luk\u00e1s Mach, and Micha\u0142 Pilipczuk. 2016. Lower bounds for the parameterized complexity of minimum fill-in and other completion problems. In SODA 2016. SIAM, 1132--1151."},{"key":"e_1_2_1_4_1","doi-asserted-by":"publisher","DOI":"10.1137\/140988565"},{"key":"e_1_2_1_5_1","doi-asserted-by":"publisher","DOI":"10.1016\/S0304-3975(97)00228-4"},{"key":"e_1_2_1_6_1","volume-title":"Van Bang Le, and Jeremy P. Spinrad","author":"Brandst\u00e4dt Andreas","year":"1999","unstructured":"Andreas Brandst\u00e4dt , Van Bang Le, and Jeremy P. Spinrad . 1999 . Graph Classes. A Survey. SIAM. Andreas Brandst\u00e4dt, Van Bang Le, and Jeremy P. Spinrad. 1999. Graph Classes. A Survey. SIAM."},{"key":"e_1_2_1_7_1","volume-title":"An efficient branching algorithm for interval completion. 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