Solving minones-2-sat as Fast as vertex cover

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 corres...

• Type: Journal
• Year: 2010
• Where: MFCS
• Authors: Neeldhara Misra, N. S. Narayanaswamy, Venkatesh Raman, Bal Sri Shankar
• Keywords: 2-SAT Formula, MFCS 2010, Satisfying Assignment, Theoretical Computer Science, Vertex Cover