Subexponential Time Complexity of CSP with Global Constraints

Not all NP-complete problems share the same practical hardness with respect to exact computation. Whereas some NP-complete problems are amenable to efficient computational methods, others are yet to show any such sign. It becomes a major challenge to develop a theoretical framework that is more fine-grained than the theory of NP-completeness, and that can explain the distinction between the exact complexities of various NP-complete problems. This distinction is highly relevant for constraint satisfaction problems under natural restrictions, where various shades of hardness can be observed in practice. Acknowledging the NP-hardness of such problems, one has to look beyond polynomial time computation. The theory of subexponential time complexity provides such a framework, and has been enjoying increasing popularity in complexity theory. Recently, a first analysis of the subexponential time complexity of classical CSPs (where all constraints are given extensionally as tables) was given. In this paper, we extend this analysis to CSPs in which constraints are given intensionally in the form of global constraints. In particular, we consider CSPs that use the fundamental global constraints AllDifferent, AtLeastNValue, AtMostNValue, and constraints that are specified by compressed tuples (cTable). We provide tight characterizations of the subexponential time complexity of the aforementioned problems with respect to several natural structural parameters. 1 Institute of Information Systems, Vienna University of Technology, Vienna, Austria 2 School of Computing, DePaul University, Chicago, IL ∗ Supported by the European Research Council (ERC), project 239962 (COMPLEX REASON), and the Austrian Science Fund (FWF), project P26200 (Parameterized Compilation). Publication Information: This is the authors’ self-archived copy of a paper that appeared in the Proceedings of the 20th International Conference on Principles and Practice of Constraint Programming (CP 2014), dx.doi.org/10.1007/978-3-319-10428-7 21. The final publication is available at www.springer.com. 2 INFSYS RR 1843-14-06