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Efficient Algorithms for the max k -vertex cover Problem

Della Croce, Federico; Paschos, Vangelis (2012), Efficient Algorithms for the max k -vertex cover Problem, in Beaten, Jos C.M.; Ball, Tom; De Boer, Frank S., Theoretical Computer Science 7th IFIP TC1/WG 2.2 International Conference, TCS 2012, Amsterdam, The Netherlands, September 26-28, 2012, Proceedings, Springer : Berlin, p. 295-309. 10.1007/978-3-642-33475-7_21

Type
Communication / Conférence
Date
2012
Conference title
7th IFIP TC1/WG 2.2 International Conference on Theoretical Computer Science, TCS 2012
Conference date
2012-09
Conference city
Amsterdam
Conference country
Netherlands
Book title
Theoretical Computer Science 7th IFIP TC1/WG 2.2 International Conference, TCS 2012, Amsterdam, The Netherlands, September 26-28, 2012, Proceedings
Book author
Beaten, Jos C.M.; Ball, Tom; De Boer, Frank S.
Publisher
Springer
Series title
Lecture Notes in Computer Science
Series number
7604
Published in
Berlin
ISBN
978-3-642-33474-0
Number of pages
393
Pages
295-309
Publication identifier
10.1007/978-3-642-33475-7_21
Metadata
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Author(s)
Della Croce, Federico

Paschos, Vangelis
Laboratoire d'analyse et modélisation de systèmes pour l'aide à la décision [LAMSADE]
Abstract (EN)
We first devise moderately exponential exact algorithms for max k -vertex cover, with time-complexity exponential in n but with polynomial space-complexity by developing a branch and reduce method based upon the measure-and-conquer technique. We then prove that, there exists an exact algorithm for max k -vertex cover with complexity bounded above by the maximum among c k and γ τ , for some γ < 2, where τ is the cardinality of a minimum vertex cover of G (note that \textsc{maxk-vertex cover}{} \notin \textbf{FPT} with respect to parameter k unless FPT=W[1] ), using polynomial space. We finally study approximation of max k -vertex cover by moderately exponential algorithms. The general goal of the issue of moderately exponential approximation is to catch-up on polynomial inapproximability, by providing algorithms achieving, with worst-case running times importantly smaller than those needed for exact computation, approximation ratios unachievable in polynomial time.
Subjects / Keywords
max k -vertex cover

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