Improved Parameterized Algorithms for Cluster Vertex Deletion
In the Cluster Vertex Deletion problem, we are given a graph G and an integer k , and the goal is to determine whether we can delete at most k vertices from G to make the remaining graph a cluster graph, i.e., a graph in which every connected component is a complete graph. In this paper, we show tha...
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| Veröffentlicht in: | Theory of computing systems Jg. 69; H. 4; S. 37 |
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01.12.2025
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| Abstract | In the
Cluster Vertex Deletion
problem, we are given a graph
G
and an integer
k
, and the goal is to determine whether we can delete at most
k
vertices from
G
to make the remaining graph a cluster graph, i.e., a graph in which every connected component is a complete graph. In this paper, we show that
Cluster Vertex Deletion
can be solved in
time, improving the previous result of
. To obtain this result, one crucial step is to show that
Cluster Vertex Deletion
on graphs of maximum degree at most 4 can be solved in
time. For a general graph, after a series of reductions, if the maximum degree of the reduced graph is at most 4, we introduce a new technique, called core branching processing, to solve the problem; if the reduced graph has a vertex of degree at least 5, we adopt the previous method of automated generation of search trees to obtain the improved running time. |
|---|---|
| AbstractList | In the
Cluster Vertex Deletion
problem, we are given a graph
G
and an integer
k
, and the goal is to determine whether we can delete at most
k
vertices from
G
to make the remaining graph a cluster graph, i.e., a graph in which every connected component is a complete graph. In this paper, we show that
Cluster Vertex Deletion
can be solved in
time, improving the previous result of
. To obtain this result, one crucial step is to show that
Cluster Vertex Deletion
on graphs of maximum degree at most 4 can be solved in
time. For a general graph, after a series of reductions, if the maximum degree of the reduced graph is at most 4, we introduce a new technique, called core branching processing, to solve the problem; if the reduced graph has a vertex of degree at least 5, we adopt the previous method of automated generation of search trees to obtain the improved running time. In the Cluster Vertex Deletion problem, we are given a graph G and an integer k, and the goal is to determine whether we can delete at most k vertices from G to make the remaining graph a cluster graph, i.e., a graph in which every connected component is a complete graph. In this paper, we show that Cluster Vertex Deletion can be solved in time, improving the previous result of . To obtain this result, one crucial step is to show that Cluster Vertex Deletion on graphs of maximum degree at most 4 can be solved in time. For a general graph, after a series of reductions, if the maximum degree of the reduced graph is at most 4, we introduce a new technique, called core branching processing, to solve the problem; if the reduced graph has a vertex of degree at least 5, we adopt the previous method of automated generation of search trees to obtain the improved running time. |
| ArticleNumber | 37 |
| Author | Tian, Kangyi Xiao, Mingyu Yang, Boting |
| Author_xml | – sequence: 1 givenname: Kangyi surname: Tian fullname: Tian, Kangyi organization: School of Computer Science and Engineering, University of Electronic Science and Technology of China – sequence: 2 givenname: Mingyu orcidid: 0000-0002-1012-2373 surname: Xiao fullname: Xiao, Mingyu email: myxiao@uestc.edu.cn organization: School of Computer Science and Engineering, University of Electronic Science and Technology of China – sequence: 3 givenname: Boting surname: Yang fullname: Yang, Boting organization: Department of Computer Science, University of Regina |
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| Cites_doi | 10.1007/s00224-015-9631-7 10.1007/s00224-020-10005-w 10.1007/s00453-004-1090-5 10.1007/s00224-004-1178-y 10.1016/j.jda.2012.04.005 10.1007/s00224-008-9150-x 10.1016/j.ipl.2021.106171 10.1016/j.tcs.2019.03.013 10.1023/B:MACH.0000033116.57574.95 10.1089/106652799318274 10.1016/0020-0190(96)00050-6 10.1007/978-3-642-11269-0_8 10.1145/2897518.2897551 10.1016/j.tcs.2009.05.006 10.1007/978-3-031-49190-0_13 |
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| Snippet | In the
Cluster Vertex Deletion
problem, we are given a graph
G
and an integer
k
, and the goal is to determine whether we can delete at most
k
vertices from
G... In the Cluster Vertex Deletion problem, we are given a graph G and an integer k, and the goal is to determine whether we can delete at most k vertices from G... |
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| StartPage | 37 |
| SubjectTerms | Algorithms Apexes Cluster analysis Clusters Computer Science Deletion Graph theory Graphs Run time (computers) Theory of Computation Trees (mathematics) |
| Title | Improved Parameterized Algorithms for Cluster Vertex Deletion |
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