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http://hdl.handle.net/10119/15856
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| Title: | Complexity of the Maximum k-Path Vertex Cover Problem |
| Authors: | Miyano, Eiji
Saitoh, Toshiki
Uehara, Ryuhei
Yagita, Tsuyoshi
Zanden, Tom van der |
| Keywords: | path vertex cover problem
NP-hardness
split graph
treewidth |
| Issue Date: | 2018-01-31 |
| Publisher: | Springer |
| Magazine name: | Lecture Notes in Computer Science |
| Volume: | 10755 |
| Start page: | 240 |
| End page: | 251 |
| DOI: | 10.1007/978-3-319-75172-6_21 |
| Abstract: | This paper introduces the maximum version of the k-path vertex cover problem, called the Maximum k-Path Vertex Cover problem (MaxP_k VC for short): A path consisting of k vertices, i.e., a path of length k－1 is called a k-path. If a k-path P_k includes a vertex v in a vertex set S, then we say that S or v covers Pk . Given a graph G=(V,E) and an integer s, the goal of MaxP_kVC is to find a vertex subset S included in V of at most s vertices such that the number of k-paths covered by S is maximized. MaxPk VC is generally NP-hard. In this paper we consider the tractability/intractability of MaxP_kVC on subclasses of graphs: We prove that MaxP_3 VC and MaxP_4VC remain NP-hard even for split graphs and for chordal graphs, respectively. Furthermore, if the input graph is restricted to graphs with constant bounded treewidth, then MaxP_3 VC can be solved in polynomial time. |
| Rights: | This is the author-created version of Springer, Eiji Miyano, Toshiki Saitoh, Ryuhei Uehara, Tsuyoshi Yagita and Tom van der Zanden, Lecture Notes in Computer Science, 10755, 2018, 240-251. The original publication is available at www.springerlink.com, http://dx.doi.org/10.1007/978-3-319-75172-6_21 |
| URI: | http://hdl.handle.net/10119/15856 |
| Material Type: | author |
| Appears in Collections: | b10-1. 雑誌掲載論文 (Journal Articles)
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