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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Bibliographic Details
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
Online Access:Get full text
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Summary: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.
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ISSN:0304-3975
1879-2294
DOI:10.1016/j.tcs.2011.09.013