P versus NP Millennium Prize Problem 2000-2013 Olympics: NP=P for NP-Class by Dedekind-Cut TSP P-Solvability
Lemba D. Nyirenda

Dr. Lemba D. Nyirenda, Electric-Earthing ProtecSystems Ltd(z) [a WorkPlace University ThinkTank], P. O. Box 320384 Woodlands, Lusaka, Zambia
Manuscript received on December 03, 2012. | Revised Manuscript received on December 11, 2012. | Manuscript published on December 15, 2012. | PP: 1-8 | Volume-1, Issue-1, December 2012. | Retrieval Number: A0102111112/2012©BEIESP 
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© The Authors. Published By: Blue Eyes Intelligence Engineering and Sciences Publication (BEIESP). This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/)

Abstract: The paper presents the P-Solvability characteristics of the TSP, an NP-Complete problem, in a 3D Dedekind-Cut-weight Periodic Table domain as defined in the Zambian PACRA Patent No. 2/2008 . Hence by Cooks theorem, the status of all problems in the NP-Complete Class is NP=P, by virtue of the TSP being a member of the NP-Complete Class having the NP=P solvability status. This African Computer Science finding is opposite to Dr Vinay Deolalikar’s 2010 finding of P-NP. This settles the ‘P versus NP’ open millennium prize problem in computer science. The research work was concluded on the 10th Day of August, 2012 before the deadline of 1st January 2013 at 5pm CET USA. The TSP NP=P status is due to the discovery of ND[dn]= {d1 to dn}, the third missing weighted network dimension. This has for the first time made the crossing of the combinatorial intractability barrier practically possible. ND[dn], the Dedekind-Cut weight index set is analogous to: the points of a real number line in one-to-one correspondence with the source-node period weights in accordance with the Cantor-Dedekind axiom.
Keywords: Dedekind-cut periodic table, Cantor-Dedekind axiom, millennium prize problem, p vesus np problem, TSP.