Tight bounds and 2-approximation algorithms for integer programs with two variables per inequality
Mathematical Programming: Series A and B
Approximation algorithms for NP-hard problems
Approximation algorithms for NP-hard problems
Parameterizing above guaranteed values: MaxSat and MaxCut
Journal of Algorithms
An algorithm for counting maximum weighted independent sets and its applications
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
Introduction to Algorithms
On efficient fixed-parameter algorithms for weighted vertex cover
Journal of Algorithms
Digraphs: Theory, Algorithms and Applications
Digraphs: Theory, Algorithms and Applications
Two Edge Modification Problems without Polynomial Kernels
Parameterized and Exact Computation
Preprocessing of min ones problems: a dichotomy
ICALP'10 Proceedings of the 37th international colloquium conference on Automata, languages and programming
Improved parameterized upper bounds for vertex cover
MFCS'06 Proceedings of the 31st international conference on Mathematical Foundations of Computer Science
Kernelization algorithms for d-hitting set problems
WADS'07 Proceedings of the 10th international conference on Algorithms and Data Structures
Parameterized Complexity
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The problem of finding a satisfying assignment for a 2-SAT formula that minimizes the number of variables that are set to 1 (MIN ONES 2-SAT) is NP-complete. It generalizes the well-studied problem of finding the smallest vertex cover of a graph, which can be modeled using a 2-SAT formula with no negative literals. The natural parameterized version of the problem asks for a satisfying assignment of weight at most k. In this paper, we present a polynomial-time reduction from MIN ONES 2-SAT to VERTEX COVER without increasing the parameter and ensuring that the number of vertices in the reduced instance is equal to the number of variables of the input formula. Consequently, we conclude that this problem also has a simple 2-approximation algorithm and a 2k variables kernel subsuming these results known earlier. Further, the problem admits algorithms for the parameterized and optimization versions whose runtimes will always match the runtimes of the best-known algorithms for the corresponding versions of vertex cover.