Approximation algorithms for Steiner and directed multicuts
Journal of Algorithms
Finding almost-satisfying assignments
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
Some optimal inapproximability results
Journal of the ACM (JACM)
The importance of being biased
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Improved Rounding Techniques for the MAX 2-SAT and MAX DI-CUT Problems
Proceedings of the 9th International IPCO Conference on Integer Programming and Combinatorial Optimization
Constraint Satisfaction: The Approximability of Minimization Problems
CCC '97 Proceedings of the 12th Annual IEEE Conference on Computational Complexity
O(√log n) approximation algorithms for min UnCut, min 2CNF deletion, and directed cut problems
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
Complexity of approximating bounded variants of optimization problems
Theoretical Computer Science - Foundations of computation theory (FCT 2003)
A better approximation ratio for the vertex cover problem
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
Crown reductions for the Minimum Weighted Vertex Cover problem
Discrete Applied Mathematics
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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 85-15~2.88854, improving the previous bound of 105-21~1.36067 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 32. 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+1))-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 @r-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].