Looking for Reverse Transformations between NP-Complete Problems-Reference-Cited by-同舟云学术

Looking for Reverse Transformations between NP-Complete Problems

Published:2012 Issue: Volume: Page:181-206
ISSN:
Container-title:Logistics Management and Optimization through Hybrid Artificial Intelligence Systems
language:
Short-container-title:

Author:

R. Rodolfo A.Pazos¹,C. Ernesto Ong²,H. Héctor Fraire³,R. Laura Cruz⁴,F. José A.Martínez⁵

Affiliation:

1. Rodolfo A. Pazos R.Instituto Tecnológico de Cd. Madero, Mexico

2. Ernesto Ong C.Instituto Tecnológico de Cd. Madero, Mexico

3. Héctor Fraire H.Instituto Tecnológico de Cd. Madero, Mexico

4. Laura Cruz R.Instituto Tecnológico de Cd. Madero, Mexico

5. José A. Martínez F.Instituto Tecnológico de Cd. Madero, Mexico

Abstract

The theory of NP-completeness provides a method for telling whether a decision/optimization problem is “easy” (i.e., it belongs to the P class) or “difficult” (i.e., it belongs to the NP-complete class). Many problems related to logistics have been proven to belong to the NP-complete class such as Bin Packing, job scheduling, timetabling, etc. The theory predicts that for any pair of NP-complete problems A and B there must exist a polynomial time transformation from A to B and also a reverse transformation (from B to A). However, for many pairs of NP-complete problems no reverse transformation has been reported in the literature; thus the following question arises: do reverse transformations exist for any pair of NP-complete problems? This chapter presents results on an ongoing investigation for clarifying this issue.

Publisher

IGI Global

Reference22 articles.

1. Barland, I., Kolaitis, P., Vardi, M., & Felleisen, M. (2011). Propositional logic: normal forms. Connexions. Retrieved January 14, 2011, from http://cnx.org/content/ m12075/1.12/

2. Cook, S. A. (1971). The complexity of theorem-proving procedures. In Proceedings of the Third Annual ACM Symposium on Theory of Computing (pp. 151-158). New York, NY: ACM.

3. Efficient lower bounds and heuristics for the variable cost and size bin packing problem

4. Cruz-Reyes, L., Gómez, C. G., Hernández, I. Y., Rangel, N., Álvarez, V. M., & González, J. J. (2008). An architecture for selecting data distribution algorithms. In Proceeding of the 17th International Multi-conference on Advanced Computer Systems (pp. 19-25).