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Paper Abstract and Keywords
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
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. (No. 10GA0019/12GB0052/13GB0056/17GB0034/18GB0034)
Download PDF ISEC2017-76 COMP2017-30

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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Keyword(8)  
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
Date Time 2017-12-21 11:50:00 
Presentation Time 25 
Registration for COMP 
Paper # IEICE-ISEC2017-76,IEICE-COMP2017-30 
Volume (vol) IEICE-117 
Number (no) no.369(ISEC), no.370(COMP) 
Page pp.25-31 
#Pages IEICE-7 
Date of Issue IEICE-ISEC-2017-12-14,IEICE-COMP-2017-12-14 


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