An improved kernel and parameterized algorithm for deletion to induced matching
A graph is called an induced matching if each vertex in the graph is a degree-1 vertex. The Deletion to Induced Matching problem asks whether we can delete at most k vertices from the input graph such that the remaining graph is an induced matching. This paper studies parameterized algorithms for th...
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| Published in: | Theoretical computer science Vol. 1041; p. 115215 |
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| Abstract | A graph is called an induced matching if each vertex in the graph is a degree-1 vertex. The Deletion to Induced Matching problem asks whether we can delete at most k vertices from the input graph such that the remaining graph is an induced matching. This paper studies parameterized algorithms for this problem by taking the size k of the deletion set as the parameter. First, we prove a 6k-vertex kernel for this problem, improving the previous result of 7k. Second, we give an O⁎(1.6477k)-time and polynomial-space algorithm, improving the previous running-time bound of O⁎(1.7485k). |
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| AbstractList | A graph is called an induced matching if each vertex in the graph is a degree-1 vertex. The Deletion to Induced Matching problem asks whether we can delete at most k vertices from the input graph such that the remaining graph is an induced matching. This paper studies parameterized algorithms for this problem by taking the size k of the deletion set as the parameter. First, we prove a 6k-vertex kernel for this problem, improving the previous result of 7k. Second, we give an O⁎(1.6477k)-time and polynomial-space algorithm, improving the previous running-time bound of O⁎(1.7485k). |
| ArticleNumber | 115215 |
| Author | Xiao, Mingyu Liu, Yuxi |
| Author_xml | – sequence: 1 givenname: Yuxi surname: Liu fullname: Liu, Yuxi email: 202211081321@std.uestc.edu.cn – sequence: 2 givenname: Mingyu orcidid: 0000-0002-1012-2373 surname: Xiao fullname: Xiao, Mingyu email: myxiao@uestc.edu.cn |
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| Cites_doi | 10.1007/s00453-003-1035-4 10.1137/09077850X 10.1016/0020-0190(82)90077-1 10.1016/j.jcss.2010.09.001 10.1016/j.disopt.2007.11.010 10.1016/0166-218X(93)90223-B 10.1016/S0166-218X(99)00194-8 10.1016/j.dam.2008.07.011 10.1016/0166-218X(92)90275-F 10.1016/j.jda.2008.09.005 10.1016/j.jda.2004.05.001 10.1016/j.ic.2017.07.006 10.1137/S089548019828371X 10.1016/j.tcs.2020.09.026 10.1016/j.jcss.2011.02.001 |
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| Snippet | A graph is called an induced matching if each vertex in the graph is a degree-1 vertex. The Deletion to Induced Matching problem asks whether we can delete at... |
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| SubjectTerms | Graph algorithms Linear kernel Maximum induced matching Parameterized algorithms |
| Title | An improved kernel and parameterized algorithm for deletion to induced matching |
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