Approximation of max independent set, min vertex cover and related problems by moderately exponential algorithms

Using ideas and results from polynomial time approximation and exact computation we design approximation algorithms for several NP-hard combinatorial problems achieving ratios that cannot be achieved in polynomial time (unless a very unlikely complexity conjecture is confirmed) with worst-case compl...

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Vydané v:	Discrete Applied Mathematics Ročník 159; číslo 17; s. 1954 - 1970
Hlavní autori:	Bourgeois, Nicolas, Escoffier, Bruno, Paschos, Vangelis Th
Médium:	Journal Article
Jazyk:	English
Vydavateľské údaje:	Kidlington Elsevier B.V 28.10.2011 Elsevier
Predmet:	Algorithmics. Computability. Computer arithmetics Algorithms Applied sciences Approximation Approximation algorithms Approximations and expansions Combinatorial analysis Combinatorics Combinatorics. Ordered structures Complexity Computation Computer science; control theory; systems Exact sciences and technology Exponential time algorithms Mathematical analysis Mathematical models Mathematics Maximum independent set Minimum vertex cover Sciences and techniques of general use Theoretical computing Maximum independent set Minimum vertex cover Approximation algorithms Exponential time algorithms Polynomial Vertex Computer theory Polynomial approximation Approximation algorithm Optimization Polynomial time Computation time NP hard problem Independent set Combinatorics Time complexity
ISSN:	0166-218X, 1872-6771
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Abstract	Using ideas and results from polynomial time approximation and exact computation we design approximation algorithms for several NP-hard combinatorial problems achieving ratios that cannot be achieved in polynomial time (unless a very unlikely complexity conjecture is confirmed) with worst-case complexity much lower (though super-polynomial) than that of an exact computation. We study in particular two paradigmatic problems, max independent set and min vertex cover. ► We propose exponential time approximation algorithms for solving NP-hard problems. ► This approach is considered for Max Independent Set and Min Vertex Cover. ► We achieve interesting tradeoffs between running times and approximation ratios. ► Used techniques are splitting of the instance, parameterized algorithms, randomization.
AbstractList	Using ideas and results from polynomial time approximation and exact computation we design approximation algorithms for several NP-hard combinatorial problems achieving ratios that cannot be achieved in polynomial time (unless a very unlikely complexity conjecture is confirmed) with worst-case complexity much lower (though super-polynomial) than that of an exact computation. We study in particular two paradigmatic problems, max independent set and min vertex cover. Using ideas and results from polynomial time approximation and exact computation we design approximation algorithms for several NP-hard combinatorial problems achieving ratios that cannot be achieved in polynomial time (unless a very unlikely complexity conjecture is confirmed) with worst-case complexity much lower (though super-polynomial) than that of an exact computation. We study in particular two paradigmatic problems, max independent set and min vertex cover. ► We propose exponential time approximation algorithms for solving NP-hard problems. ► This approach is considered for Max Independent Set and Min Vertex Cover. ► We achieve interesting tradeoffs between running times and approximation ratios. ► Used techniques are splitting of the instance, parameterized algorithms, randomization.
Author	Escoffier, Bruno Paschos, Vangelis Th Bourgeois, Nicolas
Author_xml	– sequence: 1 givenname: Nicolas surname: Bourgeois fullname: Bourgeois, Nicolas email: bourgeois@lamsade.dauphine.fr organization: LAMSADE, CNRS and Université Paris-Dauphine, France – sequence: 2 givenname: Bruno surname: Escoffier fullname: Escoffier, Bruno email: escoffier@lamsade.dauphine.fr organization: LAMSADE, CNRS and Université Paris-Dauphine, France – sequence: 3 givenname: Vangelis Th surname: Paschos fullname: Paschos, Vangelis Th email: paschos@lamsade.dauphine.fr organization: LAMSADE, CNRS and Université Paris-Dauphine, France
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Cites_doi	10.1016/j.ipl.2009.05.003 10.1006/jagm.2001.1186 10.1006/jcss.2001.1774 10.1109/CCC.2003.1214437 10.1137/0403025 10.1145/1109557.1109558 10.1109/FOCS.2006.41 10.1007/s00453-010-9460-7 10.1007/BF01580444 10.1016/j.tcs.2009.02.007 10.1145/278298.278306 10.1145/1132516.1132612
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Keywords	Maximum independent set Minimum vertex cover Approximation algorithms Exponential time algorithms Polynomial Vertex Computer theory Polynomial approximation Approximation algorithm Optimization Polynomial time Computation time NP hard problem Independent set Combinatorics Time complexity
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SubjectTerms	Algorithmics. Computability. Computer arithmetics Algorithms Applied sciences Approximation Approximation algorithms Approximations and expansions Combinatorial analysis Combinatorics Combinatorics. Ordered structures Complexity Computation Computer science; control theory; systems Exact sciences and technology Exponential time algorithms Mathematical analysis Mathematical models Mathematics Maximum independent set Minimum vertex cover Sciences and techniques of general use Theoretical computing
Title	Approximation of max independent set, min vertex cover and related problems by moderately exponential algorithms
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