A polynomial-time algorithm for optimization of quadratic pseudo-boolean functions
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Knowledge AreaMatemática Aplicada
Bibliographic CitationMulero-Martínez, J. I. (2020). A Polynomial-Time Algorithm for Unconstrained Binary Quadratic Optimization. Preprint
We develop a polynomial-time algorithm to minimize pseudo-Boolean functions. The computational complexity is O(n □(15/2)), although very conservative, it is su_cient to prove that this minimization problem is in the class P. A direct application of the algorithm is the 3-SAT problem, which is also guaranteed to be in the class P with a computational complexity of order O(n □(45/2)). The algorithm was implemented in MATLAB and checked by generating one million matrices of arbitrary dimension up to 24 with random entries in the range [-50; 50]. All the experiments were successful.
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