{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,25]],"date-time":"2025-09-25T18:07:05Z","timestamp":1758823625328,"version":"3.41.0"},"reference-count":25,"publisher":"Association for Computing Machinery (ACM)","issue":"3","license":[{"start":{"date-parts":[[2018,6,27]],"date-time":"2018-06-27T00:00:00Z","timestamp":1530057600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.acm.org\/publications\/policies\/copyright_policy#Background"}],"funder":[{"DOI":"10.13039\/501100005304","name":"Agence Nationale de la Recherche","doi-asserted-by":"publisher","award":["ANR16-CE40-0028"],"award-info":[{"award-number":["ANR16-CE40-0028"]}],"id":[{"id":"10.13039\/501100005304","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":["ACM Trans. Algorithms"],"published-print":{"date-parts":[[2018,7,31]]},"abstract":"<jats:p>\n            A simple digraph is\n            <jats:italic>semicomplete<\/jats:italic>\n            if for any two of its vertices\n            <jats:italic>u<\/jats:italic>\n            and\n            <jats:italic>v<\/jats:italic>\n            , at least one of the arcs (\n            <jats:italic>u<\/jats:italic>\n            ,\n            <jats:italic>v<\/jats:italic>\n            ) and (\n            <jats:italic>v<\/jats:italic>\n            ,\n            <jats:italic>u<\/jats:italic>\n            ) is present. We study the complexity of computing two layout parameters of semicomplete digraphs: cutwidth and optimal linear arrangement (O\n            <jats:sc>la<\/jats:sc>\n            ). We prove the following:\n          <\/jats:p>\n          <jats:p>\u2022 Both parameters are NP-hard to compute and the known exact and parameterized algorithms for them have essentially optimal running times, assuming the Exponential Time Hypothesis.<\/jats:p>\n          <jats:p>\n            \u2022 The cutwidth parameter admits a quadratic Turing kernel, whereas it does not admit any polynomial kernel unless NP \u2286 coNP\/poly. By contrast, O\n            <jats:sc>la<\/jats:sc>\n            admits a linear kernel.\n          <\/jats:p>\n          <jats:p>\n            These results essentially complete the complexity analysis of computing cutwidth and O\n            <jats:sc>la<\/jats:sc>\n            on semicomplete digraphs (with respect to standard parameters). Our techniques also can be used to analyze the sizes of minimal obstructions for having a small cutwidth under the induced subdigraph relation.\n          <\/jats:p>","DOI":"10.1145\/3196276","type":"journal-article","created":{"date-parts":[[2018,6,28]],"date-time":"2018-06-28T16:37:19Z","timestamp":1530203839000},"page":"1-31","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":4,"title":["Exploring the Complexity of Layout Parameters in Tournaments and Semicomplete Digraphs"],"prefix":"10.1145","volume":"14","author":[{"given":"Florian","family":"Barbero","sequence":"first","affiliation":[{"name":"Universit\u00e9 de Montpellier, Montpellier, France"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6519-975X","authenticated-orcid":false,"given":"Christophe","family":"Paul","sequence":"additional","affiliation":[{"name":"Universit\u00e9 de Montpellier, CNRS, Montpellier, 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