Result: Minimum 2SAT-DELETION : Inapproximability results and relations to Minimum Vertex Cover

Title:
Minimum 2SAT-DELETION : Inapproximability results and relations to Minimum Vertex Cover
Authors:
CHLEBIK, Miroslav, CHLEBIKOVA, Janka
Source:
29th symposium on mathematical foundations of computer science MFCS 2004Discrete applied mathematics. 155(2):172-179
Publisher Information:
Amsterdam; Lausanne; New York, NY: Elsevier, 2007.
Publication Year:
2007
Physical Description:
print, 18 ref
Original Material:
INIST-CNRS
Subject Terms:
Control theory, operational research, Automatique, recherche opérationnelle, Computer science, Informatique, Mathematics, Mathématiques, Sciences exactes et technologie, Exact sciences and technology, Sciences et techniques communes, Sciences and techniques of general use, Mathematiques, Mathematics, Combinatoire. Structures ordonnées, Combinatorics. Ordered structures, Combinatoire, Combinatorics, Théorie des graphes, Graph theory, Sciences appliquees, Applied sciences, Informatique; automatique theorique; systemes, Computer science; control theory; systems, Informatique théorique, Theoretical computing, Algorithmique. Calculabilité. Arithmétique ordinateur, Algorithmics. Computability. Computer arithmetics, Recherche information. Graphe, Information retrieval. Graph, Algorithme approximation, Approximation algorithm, Algoritmo aproximación, Borne inférieure, Lower bound, Cota inferior, Calcul automatique, Computing, Cálculo automático, Combinatoire, Combinatorics, Combinatoria, Complexité calcul, Computational complexity, Complejidad computación, Couplage graphe, Graph matching, Acoplamiento grafo, Informatique théorique, Computer theory, Informática teórica, Minimisation, Minimization, Minimización, Optimisation, Optimization, Optimización, Satisfaction contrainte, Constraint satisfaction, Satisfaccion restricción, Sommet graphe, Vertex(graph), Vértice grafo, Approximabilité, Conception algorithme, Difficulté approximation, Approximation hardness, Délétion 2SAT, 2SAT-Deletion, Graphe parfait, Recouvrement sommet, Vertex cover
Document Type:
Conference Conference Paper
File Description:
text
Language:
English
Author Affiliations:
Max Planck Institute for Mathematics in the Sciences, Inselstraße 22-26, 04103 Leipzig, Germany
Faculty of Mathematics, Physics and Informatics, Comenius University, Mlynská dolina, 842 48 Bratislava, Slovakia
ISSN:
0166-218X
Access URL:
http://pascal-francis.inist.fr/vibad/index.php?action=search&terms=18454952
Rights:
Copyright 2007 INIST-CNRS
CC BY 4.0
Sauf mention contraire ci-dessus, le contenu de cette notice bibliographique peut être utilisé dans le cadre d’une licence CC BY 4.0 Inist-CNRS / Unless otherwise stated above, the content of this bibliographic record may be used under a CC BY 4.0 licence by Inist-CNRS / A menos que se haya señalado antes, el contenido de este registro bibliográfico puede ser utilizado al amparo de una licencia CC BY 4.0 Inist-CNRS
Notes:
Computer science; theoretical automation; systems

Mathematics
Accession Number:
edscal.18454952
Database:
PASCAL Archive

Further Information

The MINIMUM 2SAT-DELETION problem is to delete the minimum number of clauses in a 2SAT instance to make it satisfiable. It is one of the prototypes in the approximability hierarchy of minimization problems Khanna et al. [Constraint satisfaction: the approximability of minimization problems, Proceedings of the 12th Annual IEEE Conference on Computational Complexity, Ulm, Germany, 24-27 June, 1997, pp. 282-296], and its approximability is largely open. We prove a lower approximation bound of 8√5 - 15 ≈ 2.88854, improving the previous bound of 10√5 - 21 ≈ 1.36067 by Dinur and Safra [The importance of being biased, Proceedings of the 34th Annual ACM Symposium on Theory of Computing (STOC), May 2002, pp. 33-42, also ECCC Report TR01-104, 2001]. For highly restricted instances with exactly four occurrences of every variable we provide a lower bound of 3/2. Both inapproximability results apply to instances with no mixed clauses (the literals in every clause are both either negated, or unnegated). We further prove that any k-approximation algorithm for the MINIMUM 2SAT-DELETION problem polynomially reduces to a (2 - 2/(k + I ))-approximation algorithm for the MINIMUM VERTEX COVER problem. One ingredient of these improvements is our proof that the MINIMUM VERTEX COVER problem is hardest to approximate on graphs with perfect matching. More precisely, the problem to design a p-approximation algorithm for the MINIMUM VERTEX COVER on general graphs polynomially reduces to the same problem on graphs with perfect matching. This improves also on the results by Chen and Kanj [On approximating minimum vertex cover for graphs with perfect matching, Proceedings of the 11st ISAAC, Taipei, Taiwan, Lecture Notes in Computer Science, vol. 1969, Springer, Berlin, 2000, pp. 132-143].