Abstract
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.
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Misra, N., Narayanaswamy, N.S., Raman, V., Shankar, B.S. (2010). Solving minones-2-sat as Fast as vertex cover . In: Hliněný, P., Kučera, A. (eds) Mathematical Foundations of Computer Science 2010. MFCS 2010. Lecture Notes in Computer Science, vol 6281. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-15155-2_48
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DOI: https://doi.org/10.1007/978-3-642-15155-2_48
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