On an algorithm for solving NP-complete problem, if there is no or odd number of solutions

В.А. Любецкий, А.В. Селиверстов

Abstract


If there is no or odd number of solutions, we propose a solution to the weighted set partition problem in terms of both the complex number field theory and non-determined polynomial algorithm. The problem is reduced to a recursive finding of singular points on an explicitly determined lower rank cubic hypersurface.


Full Text:

PDF (Russian)

References


S. B. Gashkov, E. T. Shavgulidze, “O predstavlenii proizvedenij v vide summy stepenej linejnyh form,” Vestnik Moskovskogo universiteta. Serija 1: Matematika. Mehanika., # 2, str. 9–14, 2014. Perevod: S. B. Gashkov, E. T. Shavgulidze, Representation of monomials as a sum of powers of linear forms, Moscow Univ. Math. Bull., vol. 69, no 2, 51–55, 2014.

A. V. Seliverstov, “Kubicheskie formy bez monomov ot dvuh peremennyh,” Vestnik Udmurtskogo universiteta. Matematika. Mehanika. Komp'juternye nauki, tom 25, # 1, str. 71–77, 2015.

A. Ju. Morozov, Sh. R. Shakirov, “Novye i starye rezul'taty v teorii rezul'tantov,” Teoreticheskaja i matematicheskaja fizika, tom 163, # 2, str. 222–257, 2010. Perevod: A. Yu. Morozov, Sh. R. Shakirov, “New and old results in resultant theory,” Theoret. and Math. Phys., vol. 163, no 2, pp. 587–617, 2010.

L. I. Rubanov, “O rasparallelivanii neodnorodnyh ciklov na superkomp'juterah s raspredeljonnoj pamjat'ju,” Informacionnye processy, tom 13, # 4, str. 295–305, 2013. Perevod: L. I. Rubanov, “Parallelization of Nonuniform Loops in Supercomputers with Distributed Memory,” Journal of Communications Technology and Electronics, vol. 59, no. 6, pp. 639–646, 2014.


Refbacks

  • There are currently no refbacks.


Abava  Absolutech IT-EDU 2019

ISSN: 2307-8162