A primal–dual approximation algorithm for the vertex cover P 3 problem

We introduce the vertex cover P n ( V C P n ) problem, that is, the problem of finding a minimum weight set F ⊂ V such that the graph G [ V − F ] has no P n , where P n is a path with n vertices. The problem also has its application background. In this paper, we first show that the V C P n problem i...

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Published in:	Theoretical computer science Vol. 412; no. 50; pp. 7044 - 7048
Main Authors:	Tu, Jianhua, Zhou, Wenli
Format:	Journal Article
Language:	English
Published:	Elsevier B.V 25.11.2011
Subjects:	Algorithms Approximation Approximation algorithm Combinatorial optimization Graphs Integers Mathematical analysis Minimum weight The primal–dual method Vertex cover [formula omitted] problem Vertex cover P n problem Combinatorial optimization Approximation algorithm The primal–dual method
ISSN:	0304-3975, 1879-2294
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Abstract	We introduce the vertex cover P n ( V C P n ) problem, that is, the problem of finding a minimum weight set F ⊂ V such that the graph G [ V − F ] has no P n , where P n is a path with n vertices. The problem also has its application background. In this paper, we first show that the V C P n problem is NP-hard for any integer n ≥ 2 . Then we restrict our attention to the V C P 3 problem and give a 2-approximation algorithm using the primal–dual method.
AbstractList	We introduce the vertex cover P n ( V C P n ) problem, that is, the problem of finding a minimum weight set F ⊂ V such that the graph G [ V − F ] has no P n , where P n is a path with n vertices. The problem also has its application background. In this paper, we first show that the V C P n problem is NP-hard for any integer n ≥ 2 . Then we restrict our attention to the V C P 3 problem and give a 2-approximation algorithm using the primal–dual method. We introduce the vertex cover P n ( V C P n ) problem, that is, the problem of finding a minimum weight set F aS, V such that the graph G [ V - F ] has no P n , where P n is a path with n vertices. The problem also has its application background. In this paper, we first show that the V C P n problem is NP-hard for any integer n greater than or equal to 2 . Then we restrict our attention to the V C P 3 problem and give a 2-approximation algorithm using the primal-dual method.
Author	Zhou, Wenli Tu, Jianhua
Author_xml	– sequence: 1 givenname: Jianhua surname: Tu fullname: Tu, Jianhua email: tjhyuyong@yahoo.com.cn organization: School of Science, Beijing University of Chemical Technology, Beijing 100029, China – sequence: 2 givenname: Wenli surname: Zhou fullname: Zhou, Wenli email: wlzhou@cn.ibm.com organization: IBM Research - China, Beijing 100193, China
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References	Vazirani (br000060) 2001 Goemans, Williamson (br000045) 1996 Goemans, Williamson (br000040) 1995; 24 path vertex cover. Submitted on 9 Dec 2010. Chudak, Goemans, Hochbaum, Williamson (br000025) 1998; 22 I. Dinur, S. Safra, The importance of being biased, in: Proc. of the 34th Annu. ACM Symp. on the Theory of Computing, STOC’03, Montral, Qubec, Canada, May 19–21, 2002, pp. 33–42. Even, Naor, Schieber, Zosin (br000035) 2000; 13 Goemans, Williamson (br000050) 1998; 18 B. Brešar, F. Kardoš, J. Katrenič, G. Semanišin, Minimum Williamson, Goemans, Mihail, Vazirami (br000065) 1995; 15 Melkonian (br000055) 2007; 34 Bondy, Murty (br000015) 1976 Bafna, Berman, Fujito (br000005) 1999; 12 Bar-Yehuda, Even (br000010) 1981; 2 Bar-Yehuda (10.1016/j.tcs.2011.09.013_br000010) 1981; 2 Melkonian (10.1016/j.tcs.2011.09.013_br000055) 2007; 34 Bafna (10.1016/j.tcs.2011.09.013_br000005) 1999; 12 Williamson (10.1016/j.tcs.2011.09.013_br000065) 1995; 15 Goemans (10.1016/j.tcs.2011.09.013_br000040) 1995; 24 Goemans (10.1016/j.tcs.2011.09.013_br000045) 1996 Bondy (10.1016/j.tcs.2011.09.013_br000015) 1976 10.1016/j.tcs.2011.09.013_br000030 10.1016/j.tcs.2011.09.013_br000020 Goemans (10.1016/j.tcs.2011.09.013_br000050) 1998; 18 Vazirani (10.1016/j.tcs.2011.09.013_br000060) 2001 Even (10.1016/j.tcs.2011.09.013_br000035) 2000; 13 Chudak (10.1016/j.tcs.2011.09.013_br000025) 1998; 22
References_xml	– volume: 12 start-page: 289 year: 1999 end-page: 297 ident: br000005 article-title: A 2-approximation algorithm for the undirected feedback vertex set problem publication-title: SIAM J. Discrete Math. – volume: 22 start-page: 111 year: 1998 end-page: 118 ident: br000025 article-title: A primal–dual interpretation of two 2-approximation algorithms for the feedback vertex set problem in undirected graphs publication-title: Oper. Res. Lett. – volume: 18 start-page: 37 year: 1998 end-page: 59 ident: br000050 article-title: Primal–dual approximation algorithms for feedback problems in planar graph publication-title: Combinatorica – volume: 15 start-page: 435 year: 1995 end-page: 454 ident: br000065 article-title: A primal–dual approximation algorithm for generalized Steiner network problems publication-title: Combinatorica – year: 1976 ident: br000015 article-title: Graph Theory with Applications – volume: 2 start-page: 198 year: 1981 end-page: 203 ident: br000010 article-title: A linear-time approximation algorithm for the weighted vertex cover problem publication-title: J. Algorithms – volume: 34 start-page: 2147 year: 2007 end-page: 2167 ident: br000055 article-title: New primal–dual algorithms for Steiner tree problems publication-title: Comput. Oper. Res. – year: 1996 ident: br000045 article-title: The Primal–dual method for approximation algorithms and its applicaion to network design problems publication-title: Approximation Algorithms for NP-hard Problems – year: 2001 ident: br000060 article-title: Approximation Algorithms – reference: -path vertex cover. – reference: , Submitted on 9 Dec 2010. – reference: B. Brešar, F. Kardoš, J. Katrenič, G. Semanišin, Minimum – volume: 24 start-page: 296 year: 1995 end-page: 317 ident: br000040 article-title: A general approximation technique for constrained forest problems publication-title: SIAM J. Comput. – volume: 13 start-page: 255 year: 2000 end-page: 267 ident: br000035 article-title: Approximating minimum subset feedback sets in undirected graphs with applications publication-title: SIAM J. Discrete Math. – reference: I. Dinur, S. Safra, The importance of being biased, in: Proc. of the 34th Annu. ACM Symp. on the Theory of Computing, STOC’03, Montral, Qubec, Canada, May 19–21, 2002, pp. 33–42. – volume: 12 start-page: 289 issue: 3 year: 1999 ident: 10.1016/j.tcs.2011.09.013_br000005 article-title: A 2-approximation algorithm for the undirected feedback vertex set problem publication-title: SIAM J. Discrete Math. doi: 10.1137/S0895480196305124 – volume: 15 start-page: 435 issue: 3 year: 1995 ident: 10.1016/j.tcs.2011.09.013_br000065 article-title: A primal–dual approximation algorithm for generalized Steiner network problems publication-title: Combinatorica doi: 10.1007/BF01299747 – year: 1996 ident: 10.1016/j.tcs.2011.09.013_br000045 article-title: The Primal–dual method for approximation algorithms and its applicaion to network design problems – volume: 18 start-page: 37 issue: 1 year: 1998 ident: 10.1016/j.tcs.2011.09.013_br000050 article-title: Primal–dual approximation algorithms for feedback problems in planar graph publication-title: Combinatorica doi: 10.1007/PL00009810 – year: 2001 ident: 10.1016/j.tcs.2011.09.013_br000060 – volume: 24 start-page: 296 issue: 2 year: 1995 ident: 10.1016/j.tcs.2011.09.013_br000040 article-title: A general approximation technique for constrained forest problems publication-title: SIAM J. Comput. doi: 10.1137/S0097539793242618 – year: 1976 ident: 10.1016/j.tcs.2011.09.013_br000015 – ident: 10.1016/j.tcs.2011.09.013_br000020 – volume: 13 start-page: 255 issue: 2 year: 2000 ident: 10.1016/j.tcs.2011.09.013_br000035 article-title: Approximating minimum subset feedback sets in undirected graphs with applications publication-title: SIAM J. Discrete Math. doi: 10.1137/S0895480195291874 – volume: 2 start-page: 198 issue: 2 year: 1981 ident: 10.1016/j.tcs.2011.09.013_br000010 article-title: A linear-time approximation algorithm for the weighted vertex cover problem publication-title: J. Algorithms doi: 10.1016/0196-6774(81)90020-1 – volume: 34 start-page: 2147 issue: 7 year: 2007 ident: 10.1016/j.tcs.2011.09.013_br000055 article-title: New primal–dual algorithms for Steiner tree problems publication-title: Comput. Oper. Res. doi: 10.1016/j.cor.2005.08.009 – volume: 22 start-page: 111 issue: 4–5 year: 1998 ident: 10.1016/j.tcs.2011.09.013_br000025 article-title: A primal–dual interpretation of two 2-approximation algorithms for the feedback vertex set problem in undirected graphs publication-title: Oper. Res. Lett. doi: 10.1016/S0167-6377(98)00021-2 – ident: 10.1016/j.tcs.2011.09.013_br000030 doi: 10.1145/509907.509915
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SubjectTerms	Algorithms Approximation Approximation algorithm Combinatorial optimization Graphs Integers Mathematical analysis Minimum weight The primal–dual method Vertex cover [formula omitted] problem
Title	A primal–dual approximation algorithm for the vertex cover P 3 problem
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