Central Asia Business Journal



An Experimental Supported by Some Strong Theoretical Arguments Proof of the Fundamental Equality P=NP

Published 11.05.2023
Categories: 1

A refined version of the algorithm for constructing all 0-1 integer solutions for linear Diophantine equations is introduced. The correctness and its polynomial time complexity is confirmed by a Monte Carlo experiment that uses the trivial simple combinatorics. An implementation of this algorithm proves the polynomial time solvability of many business decision and optimization problems that are currently considered as being intractable: bin packing and cutting stock, open-shop and job-shop scheduling, production planning, dynamic storage allocation and many others. It is shown that all these problems admit polynomial time algorithms for their solution. An experimental proof of the important for the theory fact that every planar symmetric graph possesses at least one Hamiltonian circuit is given. A much faster exact polynomial time algorithm for solving symmetric traveling salesman problems is suggested. The algorithm shows that such problems may have several optimal solutions. Numeric randomly generated instances with such solutions that can be used as test examples for newly developed algorithms are presented. Results of this research present a reliable experimental proof of the fundamental equality P=NP. AMS subject classifications (2010): 05A18, 05C45, 90C10, 90C27, 11D04, 68Q15, 68Q17

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