{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,9,10]],"date-time":"2024-09-10T13:15:30Z","timestamp":1725974130623},"reference-count":0,"publisher":"Centre pour la Communication Scientifique Directe (CCSD)","issue":"Discrete Algorithms","license":[{"start":{"date-parts":[[2021,4,30]],"date-time":"2021-04-30T00:00:00Z","timestamp":1619740800000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/arxiv.org\/licenses\/nonexclusive-distrib\/1.0"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"abstract":"A mixed dominating set is a collection of vertices and edges that dominates\nall vertices and edges of a graph. We study the complexity of exact and\nparameterized algorithms for \\textsc{Mixed Dominating Set}, resolving some open\nquestions. In particular, we settle the problem's complexity parameterized by\ntreewidth and pathwidth by giving an algorithm running in time $O^*(5^{tw})$\n(improving the current best $O^*(6^{tw})$), as well as a lower bound showing\nthat our algorithm cannot be improved under the Strong Exponential Time\nHypothesis (SETH), even if parameterized by pathwidth (improving a lower bound\nof $O^*((2 - \\varepsilon)^{pw})$). Furthermore, by using a simple but so far\noverlooked observation on the structure of minimal solutions, we obtain\nbranching algorithms which improve both the best known FPT algorithm for this\nproblem, from $O^*(4.172^k)$ to $O^*(3.510^k)$, and the best known\nexponential-time exact algorithm, from $O^*(2^n)$ and exponential space, to\n$O^*(1.912^n)$ and polynomial space.<\/jats:p>","DOI":"10.46298\/dmtcs.6824","type":"journal-article","created":{"date-parts":[[2021,8,23]],"date-time":"2021-08-23T22:38:20Z","timestamp":1629758300000},"source":"Crossref","is-referenced-by-count":1,"title":["New Algorithms for Mixed Dominating Set"],"prefix":"10.46298","volume":"vol. 23 no. 1","author":[{"given":"Louis","family":"Dublois","sequence":"first","affiliation":[]},{"given":"Michael","family":"Lampis","sequence":"additional","affiliation":[]},{"given":"Vangelis Th.","family":"Paschos","sequence":"additional","affiliation":[]}],"member":"25203","published-online":{"date-parts":[[2021,4,30]]},"container-title":["Discrete Mathematics & Theoretical Computer Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dmtcs.episciences.org\/7407\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/dmtcs.episciences.org\/7407\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,6,20]],"date-time":"2023-06-20T20:31:23Z","timestamp":1687293083000},"score":1,"resource":{"primary":{"URL":"https:\/\/dmtcs.episciences.org\/6824"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,4,30]]},"references-count":0,"journal-issue":{"issue":"Discrete Algorithms","published-online":{"date-parts":[[2021,4,30]]}},"URL":"http:\/\/dx.doi.org\/10.46298\/dmtcs.6824","relation":{"has-preprint":[{"id-type":"arxiv","id":"1911.08964v4","asserted-by":"subject"},{"id-type":"arxiv","id":"1911.08964v3","asserted-by":"subject"},{"id-type":"arxiv","id":"1911.08964v2","asserted-by":"subject"}],"is-same-as":[{"id-type":"arxiv","id":"1911.08964","asserted-by":"subject"},{"id-type":"doi","id":"10.48550\/arXiv.1911.08964","asserted-by":"subject"}]},"ISSN":["1365-8050"],"issn-type":[{"value":"1365-8050","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,4,30]]}}}
