Data Structures and Algorithms

   

Third Edition: Final Results on P vs NP Via Integer Factorization and Optimization

Authors: Yuly Shipilevsky

We reduce integer factorization problem to the equivalent problem of minimizing a quadratic polynomial with integer coefficients over the integer points in a quadratically constrained two-dimensional region. Next, we reduce integer factorization problem to the problem of enumeration of vertices of integer hull of a special two-dimensional rational polyhedron, solvable in time polynomial by Hartmann's algorithm. Finally, as we show that there exists an NP-hard minimization problem, equivalent to the original minimization problem, we conclude that P = NP.

Comments: 18 Pages.

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Submission history

[v1] 2018-05-21 20:28:48

Unique-IP document downloads: 84 times

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