Survey of polynomial transformations between NP-complete problems

  • Authors:

  • Jorge A. Ruiz-Vanoye;Joaquín Pérez-Ortega;Rodolfo A. Pazos R.;Ocotlán Díaz-Parra;Juan Frausto-Solís;Hector J. Fraire Huacuja;Laura Cruz-Reyes;José A. Martínez F.

  • Affiliations:

  • Universidad Popular Autónoma del Estado de Puebla, 21 sur 1103 Barrio de Santiago, Puebla, Puebla, Mexico;Centro Nacional de Investigación y Desarrollo Tecnológico, Interior internado Palmira s/n, Col. Palmira, Cuernavaca, Morelos, Mexico;Instituto Tecnológico de Ciudad Madero, Av. 1o. de Mayo, Col. Los Mangos, Ciudad Madero, Tamaulipas, Mexico;Universidad Autónoma del Estado de Morelos, Av. Universidad 1001, Col. Chamilpa, Cuernavaca, Morelos, Mexico;Tecnológico de Monterrey Campus Cuernavaca, Autopista del Sol km 104, Colonia Real del Puente, Xochitepec, Morelos, Mexico;Instituto Tecnológico de Ciudad Madero, Av. 1o. de Mayo, Col. Los Mangos, Ciudad Madero, Tamaulipas, Mexico;Instituto Tecnológico de Ciudad Madero, Av. 1o. de Mayo, Col. Los Mangos, Ciudad Madero, Tamaulipas, Mexico;Instituto Tecnológico de Ciudad Madero, Av. 1o. de Mayo, Col. Los Mangos, Ciudad Madero, Tamaulipas, Mexico

  • Venue:
  • Journal of Computational and Applied Mathematics
  • Year:
  • 2011

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Abstract

This paper aims at being a guide to understand polynomial transformations and polynomial reductions between NP-complete problems by presenting the methodologies for polynomial reductions/transformations and the differences between reductions and transformations. To this end the article shows examples of polynomial reductions/transformations and the restrictions to reduce/transform between NP-complete problems. Finally, this paper includes a digraph with the historical reductions/transformations between instances of NP-complete problems and introduces the term family of polynomial transformations.