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A go at the Clay Millennium problem NP=PEditor Note : This submitted article is for now anonymized. Its author choosed to use the Creative commons license. As long as the article is not published, the copyright is owned by Publications Online editor. Publications Online publish this article as an Attribution-Noncommercial-No Derivative Works 3.0AbstractThe problem posed is whether Non Computational time (Non deterministic Polynomialtime-NP) Algorithm produce Polynomial time (deterministic polynomial time-P) algorithm results, that is whether they are equal. That is NP=P. A six City traverse of the of a traveling Sales man is considered . There exists a starting city and an ending city. The problem is to converge into a minimal cost tour from the starting city to the destination city without traversing a city twice. An algorithm is developed which employs Bubble Sort (BS) as component which is proved NP complete. The same Algorithm when Quick Sort (QS) is employed instead of BS turns out to be P type. They produce the same minimal cost, proving NP=P. The Halting problem remain resolved. To read and review this article, first register for free access here |
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