TY - GEN
T1 - On the minimal constraint satisfaction problem
T2 - 9th International Conference on Combinatorial Optimization and Applications, COCOA 2015
AU - Escamocher, Guillaume
AU - O’Sullivan, Barry
N1 - Publisher Copyright:
© Springer International Publishing Switzerland 2015.
PY - 2015
Y1 - 2015
N2 - The Minimal Constraint Satisfaction Problem, or Minimal CSP for short, arises in a number of real-world applications, most notably in constraint-based product configuration. Despite its very permissive structure, it is NP-hard, even when bounding the size of the domains by d≥9. Yet very little is known about the Minimal CSP beyond that. Our contribution through this paper is twofold. Firstly, we generalize the complexity result to any value of d. We prove that the Minimal CSP remains NP-hard for d≥3, as well as for d=2 if the arity k of the instances is strictly greater than 2. Our complexity result can be seen as providing a dichotomy theorem for the Minimal CSP. Secondly, we build a generator that can create Minimal CSP instances of any size, using the constrainedness as a parameter. Our generator can be used to study behaviors that are typical of NP-hard problems, such as the presence of a phase transition, in the case of the Minimal CSP.
AB - The Minimal Constraint Satisfaction Problem, or Minimal CSP for short, arises in a number of real-world applications, most notably in constraint-based product configuration. Despite its very permissive structure, it is NP-hard, even when bounding the size of the domains by d≥9. Yet very little is known about the Minimal CSP beyond that. Our contribution through this paper is twofold. Firstly, we generalize the complexity result to any value of d. We prove that the Minimal CSP remains NP-hard for d≥3, as well as for d=2 if the arity k of the instances is strictly greater than 2. Our complexity result can be seen as providing a dichotomy theorem for the Minimal CSP. Secondly, we build a generator that can create Minimal CSP instances of any size, using the constrainedness as a parameter. Our generator can be used to study behaviors that are typical of NP-hard problems, such as the presence of a phase transition, in the case of the Minimal CSP.
UR - https://www.scopus.com/pages/publications/84951968258
U2 - 10.1007/978-3-319-26626-8_54
DO - 10.1007/978-3-319-26626-8_54
M3 - Conference proceeding
AN - SCOPUS:84951968258
SN - 9783319266251
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 731
EP - 745
BT - Combinatorial Optimization and Applications - 9th International Conference, COCOA 2015, Proceedings
A2 - Kim, Donghyun
A2 - Wu, Weili
A2 - Du, Ding-Zhu
A2 - Lu, Zaixin
A2 - Li, Wei
PB - Springer Verlag
Y2 - 18 December 2015 through 20 December 2015
ER -