Current Research in Statistics & Mathematics(CRSM)

Independent scholar, Almaty, Kazakhstan

Publications

• Research Article   
  Partitions, the P Versus NP Problem and Applications
  Author(s): Vassilly Voinov*
  
  A new deterministic polynomial-time algorithm for sets of different positive integers partitioning has been introduced. The most important properties of the algorithm are that its time-complexity is O(nlogn) and that it is invariant w.r.t. the number of elements in a particular part. An implementation of this algorithm and the trivial combinatorial show that the classical Partition and the 4-Partition problem, currently considered to be in the NP-complete and the NP-complete in the strong sense complexity classes, respectively, are both solvable in polynomial time, thus belonging to class P. These results permit to introduce the P-complete class of problems reducible to each other by a polynomial transformation. Since it is a subclass of the NP-complete complexity class, from the well-established theory of NP-completeness, it immediately follows that P = NP. This intriguing research c.. Read More»
  

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