Refined notions of parameterized enumeration kernels with applications to matching cut enumeration
An enumeration kernel as defined by Creignou et al. (2017) [11] for a parameterized enumeration problem consists of an algorithm that transforms each instance into one whose size is bounded by the parameter plus a solution-lifting algorithm that efficiently enumerates all solutions from the set of t...
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| Vydáno v: | Journal of computer and system sciences Ročník 123; s. 76 - 102 |
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01.02.2022
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| Abstract | An enumeration kernel as defined by Creignou et al. (2017) [11] for a parameterized enumeration problem consists of an algorithm that transforms each instance into one whose size is bounded by the parameter plus a solution-lifting algorithm that efficiently enumerates all solutions from the set of the solutions of the kernel. We propose to consider two new versions of enumeration kernels by asking that the solutions of the original instance can be enumerated in polynomial time or with polynomial delay from the kernel solutions. Using the NP-hard Matching Cut problem parameterized by structural parameters such as the vertex cover number or the cyclomatic number of the input graph, we show that the new enumeration kernels present a useful notion of data reduction for enumeration problems which allows to compactly represent the set of feasible solutions. |
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| AbstractList | An enumeration kernel as defined by Creignou et al. (2017) [11] for a parameterized enumeration problem consists of an algorithm that transforms each instance into one whose size is bounded by the parameter plus a solution-lifting algorithm that efficiently enumerates all solutions from the set of the solutions of the kernel. We propose to consider two new versions of enumeration kernels by asking that the solutions of the original instance can be enumerated in polynomial time or with polynomial delay from the kernel solutions. Using the NP-hard Matching Cut problem parameterized by structural parameters such as the vertex cover number or the cyclomatic number of the input graph, we show that the new enumeration kernels present a useful notion of data reduction for enumeration problems which allows to compactly represent the set of feasible solutions. |
| Author | Komusiewicz, Christian Golovach, Petr A. Kratsch, Dieter Le, Van Bang |
| Author_xml | – sequence: 1 givenname: Petr A. orcidid: 0000-0002-2619-2990 surname: Golovach fullname: Golovach, Petr A. email: petr.golovach@uib.no organization: Department of Informatics, University of Bergen, N-5020 Bergen, Norway – sequence: 2 givenname: Christian surname: Komusiewicz fullname: Komusiewicz, Christian organization: Fachbereich Mathematik und Informatik, Philipps-Universität Marburg, Marburg, Germany – sequence: 3 givenname: Dieter surname: Kratsch fullname: Kratsch, Dieter organization: Université de Lorraine, LITA, Metz, France – sequence: 4 givenname: Van Bang surname: Le fullname: Le, Van Bang organization: Institut für Informatik, Universität Rostock, Rostock, Germany |
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| Cites_doi | 10.1137/S0097539793251219 10.1016/j.dam.2019.12.010 10.1007/s00224-016-9702-4 10.1111/j.1749-6632.1970.tb56468.x 10.1016/j.jctb.2005.10.006 10.1137/120862612 10.1007/s00453-012-9663-1 10.1002/jgt.3190080106 10.3390/a12090189 10.1016/j.cosrev.2020.100344 10.1007/s00453-011-9554-x 10.1016/j.jcss.2019.02.004 10.1016/j.dam.2008.08.021 10.1137/120880240 10.1016/j.jcss.2009.04.001 10.1016/j.tcs.2005.10.004 10.1007/s00453-018-0404-y 10.1007/s00224-008-9130-1 10.1016/j.tcs.2015.10.016 10.1137/0222038 10.1007/978-3-642-16533-7 10.1145/1435375.1435385 10.1145/1597036.1597045 10.1137/12089051X |
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| Keywords | Enumeration problems Output-sensitive algorithms Polynomial delay Structural parameterizations Kernelization Matching cuts |
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| SubjectTerms | Enumeration problems Kernelization Matching cuts Output-sensitive algorithms Polynomial delay Structural parameterizations |
| Title | Refined notions of parameterized enumeration kernels with applications to matching cut enumeration |
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