Abstract
This paper examines the complexity of global verification for MAX-SAT, MAX-k-SAT (for k≥3), Vertex Cover, and Traveling Salesman Problem. These results are obtained by adaptations of the transformations that prove such problems to be NP-complete. The class of problems PGS is defined to be those discrete optimization problems for which there exists a polynomial time algorithm such that given any solution ω, either a solution can be found with a better objective function value or it can be concluded that no such solution exists and ω is a global optimum. This paper demonstrates that if any one of MAX-SAT, MAX-k-SAT (for k≥3), Vertex Cover, or Traveling Salesman Problem are in PGS, then P=NP.
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Armstrong, D.E., Jacobson, S.H. Studying the Complexity of Global Verification for NP-Hard Discrete Optimization Problems. Journal of Global Optimization 27, 83–96 (2003). https://doi.org/10.1023/A:1024680908847
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DOI: https://doi.org/10.1023/A:1024680908847