Improving Vertex Cover as a Graph Parameter
Parameterized algorithms are often used to efficiently solve NP-hard problems on graphs. In this context, vertex cover is used as a powerful parameter for dealing with graph problems which are hard to solve even when parameterized by tree-width; however, the drawback of vertex cover is that bounding...
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| Format: | Article |
| Language: | English |
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Discrete Mathematics & Theoretical Computer Science
2015-09-01
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| Series: | Discrete Mathematics & Theoretical Computer Science |
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| Online Access: | https://dmtcs.episciences.org/2136/pdf |
| _version_ | 1797270091624087552 |
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| author | Robert Ganian |
| author_facet | Robert Ganian |
| author_sort | Robert Ganian |
| collection | DOAJ |
| description | Parameterized algorithms are often used to efficiently solve NP-hard problems on graphs. In this context, vertex cover is used as a powerful parameter for dealing with graph problems which are hard to solve even when parameterized by tree-width; however, the drawback of vertex cover is that bounding it severely restricts admissible graph classes. We introduce a generalization of vertex cover called twin-cover and show that FPT algorithms exist for a wide range of difficult problems when parameterized by twin-cover. The advantage of twin-cover over vertex cover is that it imposes a lesser restriction on the graph structure and attains low values even on dense graphs. Apart from introducing the parameter itself, this article provides a number of new FPT algorithms parameterized by twin-cover with a special emphasis on solving problems which are not in FPT even when parameterized by tree-width. It also shows that MS1 model checking can be done in elementary FPT time parameterized by twin-cover and discusses the field of kernelization. |
| first_indexed | 2024-04-25T01:58:46Z |
| format | Article |
| id | doaj.art-a10c581544ab46cab89d58ab241deb7d |
| institution | Directory Open Access Journal |
| issn | 1365-8050 |
| language | English |
| last_indexed | 2024-04-25T01:58:46Z |
| publishDate | 2015-09-01 |
| publisher | Discrete Mathematics & Theoretical Computer Science |
| record_format | Article |
| series | Discrete Mathematics & Theoretical Computer Science |
| spelling | doaj.art-a10c581544ab46cab89d58ab241deb7d2024-03-07T15:28:21ZengDiscrete Mathematics & Theoretical Computer ScienceDiscrete Mathematics & Theoretical Computer Science1365-80502015-09-01Vol. 17 no.2Discrete Algorithms10.46298/dmtcs.21362136Improving Vertex Cover as a Graph ParameterRobert Ganian0https://orcid.org/0000-0002-7762-8045Vienna University of TechnologyParameterized algorithms are often used to efficiently solve NP-hard problems on graphs. In this context, vertex cover is used as a powerful parameter for dealing with graph problems which are hard to solve even when parameterized by tree-width; however, the drawback of vertex cover is that bounding it severely restricts admissible graph classes. We introduce a generalization of vertex cover called twin-cover and show that FPT algorithms exist for a wide range of difficult problems when parameterized by twin-cover. The advantage of twin-cover over vertex cover is that it imposes a lesser restriction on the graph structure and attains low values even on dense graphs. Apart from introducing the parameter itself, this article provides a number of new FPT algorithms parameterized by twin-cover with a special emphasis on solving problems which are not in FPT even when parameterized by tree-width. It also shows that MS1 model checking can be done in elementary FPT time parameterized by twin-cover and discusses the field of kernelization.https://dmtcs.episciences.org/2136/pdfparameterized complexitytwin-coververtex cover[info.info-dm] computer science [cs]/discrete mathematics [cs.dm] |
| spellingShingle | Robert Ganian Improving Vertex Cover as a Graph Parameter Discrete Mathematics & Theoretical Computer Science parameterized complexity twin-cover vertex cover [info.info-dm] computer science [cs]/discrete mathematics [cs.dm] |
| title | Improving Vertex Cover as a Graph Parameter |
| title_full | Improving Vertex Cover as a Graph Parameter |
| title_fullStr | Improving Vertex Cover as a Graph Parameter |
| title_full_unstemmed | Improving Vertex Cover as a Graph Parameter |
| title_short | Improving Vertex Cover as a Graph Parameter |
| title_sort | improving vertex cover as a graph parameter |
| topic | parameterized complexity twin-cover vertex cover [info.info-dm] computer science [cs]/discrete mathematics [cs.dm] |
| url | https://dmtcs.episciences.org/2136/pdf |
| work_keys_str_mv | AT robertganian improvingvertexcoverasagraphparameter |