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| Presentation | 2017-12-21 11:50 Maximum k-path Vertex Cover Problem on Graph Classes Tsuyoshi Yagita, Eiji Miyano, Toshiki Saitoh (Kyutech), Ryuhei Uehara (JAIST), Tom C. van der Zanden (Utrecht U.)  ISEC2017-76 COMP2017-30 |
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| Abstract | (in Japanese) | (See Japanese page) |
| (in English) | This paper introduces the maximum version of the $k$-path vertex cover problem, called the textsc{Maximum $k$-Path Vertex Cover} problem (textsf{Max$P_k$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 $P_k$. Given a graph $G = (V, E)$ and an integer $s$, the goal of textsf{Max$P_k$VC} is to find a vertex subset $Ssubseteq V$ of at most $s$ vertices such that the number of $k$-paths covered by $S$ is maximized. textsf{Max$P_k$VC} is generally NP-hard. In this paper we consider the tractability/intractability of textsf{Max$P_k$VC} on subclasses of graphs: We prove that textsf{Max$P_3$VC} and textsf{Max$P_4$VC} 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 textsf{Max$P_3$VC} can be solved in polynomial time. | |
| Keyword | (in Japanese) | (See Japanese page) |
| (in English) | Maximum k-Path Vertex Cover Problem / NP-hardness / polynomial time algorithm / split graphs / tree graphs / / / | |
| Reference Info. | IEICE Tech. Rep., vol. 117, no. 370, COMP2017-30, pp. 25-31, Dec. 2017. | |
| Paper # | COMP2017-30 | |
| Date of Issue | 2017-12-14 (ISEC, COMP) | |
| ISSN | Print edition: ISSN 0913-5685 Online edition: ISSN 2432-6380 | |
| Copyright and reproduction |
All rights are reserved and no part of this publication may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopy, recording, or any information storage and retrieval system, without permission in writing from the publisher. Notwithstanding, instructors are permitted to photocopy isolated articles for noncommercial classroom use without fee. (License No.: 10GA0019/12GB0052/13GB0056/17GB0034/18GB0034) | |
| Download PDF | ISEC2017-76 COMP2017-30 |
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| Conference Information | |
| Committee | ISEC COMP |
| Conference Date | 2017-12-21 - 2017-12-22 |
| Place (in Japanese) | (See Japanese page) |
| Place (in English) | Eikokuji Campus, Kochi University of Technology |
| Topics (in Japanese) | (See Japanese page) |
| Topics (in English) | |
| Paper Information | |
| Registration To | COMP |
| Conference Code | 2017-12-ISEC-COMP |
| Language | Japanese |
| Title (in Japanese) | (See Japanese page) |
| Sub Title (in Japanese) | (See Japanese page) |
| Title (in English) | Maximum k-path Vertex Cover Problem on Graph Classes |
| Sub Title (in English) | |
| Keyword(1) | Maximum k-Path Vertex Cover Problem |
| Keyword(2) | NP-hardness |
| Keyword(3) | polynomial time algorithm |
| Keyword(4) | split graphs |
| Keyword(5) | tree graphs |
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| 1st Author's Name | Tsuyoshi Yagita |
| 1st Author's Affiliation | Kyushu Institute of Technology (Kyutech) |
| 2nd Author's Name | Eiji Miyano |
| 2nd Author's Affiliation | Kyushu Institute of Technology (Kyutech) |
| 3rd Author's Name | Toshiki Saitoh |
| 3rd Author's Affiliation | Kyushu Institute of Technology (Kyutech) |
| 4th Author's Name | Ryuhei Uehara |
| 4th Author's Affiliation | Japan Advanced Institute of Science and Technology (JAIST) |
| 5th Author's Name | Tom C. van der Zanden |
| 5th Author's Affiliation | Utrecht University (Utrecht U.) |
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| Speaker | Author-1 |
| Date Time | 2017-12-21 11:50:00 |
| Presentation Time | 25 minutes |
| Registration for | COMP |
| Paper # | ISEC2017-76, COMP2017-30 |
| Volume (vol) | vol.117 |
| Number (no) | no.369(ISEC), no.370(COMP) |
| Page | pp.25-31 |
| #Pages | 7 |
| Date of Issue | 2017-12-14 (ISEC, COMP) |
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