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The approximability behavior of some combinatorial problems with respect to the approximability of a class of maximum independent set problems

Demange, Marc; Paschos, Vangelis (1997), The approximability behavior of some combinatorial problems with respect to the approximability of a class of maximum independent set problems, Computational Optimization and Applications, 7, 3, p. 307-324. http://dx.doi.org/10.1023/A:1008660812834

Type
Article accepté pour publication ou publié
External document link
http://www.lamsade.dauphine.fr/FILES/publi168.pdf
Date
1997
Journal name
Computational Optimization and Applications
Volume
7
Number
3
Publisher
Springer
Pages
307-324
Publication identifier
http://dx.doi.org/10.1023/A:1008660812834
Metadata
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Author(s)
Demange, Marc
Paschos, Vangelis
Abstract (EN)
We prove that the existence of a polynomial timergr-approximation algorithm (wherergr < 1 is a fixed constant)for a class of independent set problems, leads to a polynomial timeapproximation algorithm with approximation ratio strictly smallerthan 2 for vertex covering, while the non-existence of such analgorithm induces a lower bound on the ratio of every polynomialtime approximation algorithm for vertex covering. We also prove asimilar result for a (maximization) convex programming problemincluding quadratic programming as subproblem.
Subjects / Keywords
NP-complete problem; quadratic programming; independent set; vertex covering; polynomial time approximation algorithm

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