Tractable Combinations of Global Constraints

We study the complexity of constraint satisfaction problems involving global constraints, i.e., special-purpose constraints provided by a solver and represented implicitly by a parametrised algorithm. Such constraints are widely used; indeed, they are one of the key reasons for the success of constraint programming in solving real-world problems. Previous work has focused on the development of efficient propagators for individual constraints. In this paper, we identify a new tractable class of constraint problems involving global constraints of unbounded arity. To do so, we combine structural restrictions with the observation that some important types of global constraint do not distinguish between large classes of equivalent solutions.Comment: To appear in proceedings of CP'13, LNCS 8124. arXiv admin note: text overlap with arXiv:1307.179

Combining Symmetry Breaking and Global Constraints

Abstract. We propose a new family of constraints which combine together lexicographical ordering constraints for symmetry breaking with other common global constraints. We give a general purpose propagator for this family of constraints, and show how to improve its complexity by exploiting properties of the included global constraints.

A Parallel, Backjumping Subgraph Isomorphism Algorithm Using Supplemental Graphs

This registry entry contains a reference to the code, data and experimental scripts needed to reproduce the subgraph isomorphism paper: Ciaran McCreesh and Patrick Prosser, "A Parallel, Backjumping Subgraph Isomorphism Algorithm using Supplemental Graphs". To appear at the 21st International Conference on Principles and Practice of Constraint Programming (CP 2015)

Constraint Solving on Bounded String Variables

Abstract Constraints on strings of unknown length occur in a wide variety of real-world problems, such as test case generation, program analysis, model checking, and web security. We describe a set of con-straints sufficient to model many standard benchmark problems from these fields. For strings of an unknown length bounded by an integer, we describe propagators for these constraints. Finally, we provide an experi-mental comparison between a state-of-the-art dedicated string solver, CP approaches utilising fixed-length string solving, and our implementation extending an off-the-shelf CP solver.

The polytope of context-free grammar constraints

Context-free grammar constraints enforce that a sequence of variables forms a word in a language defined by a context-free grammar. The constraint has received a lot of attention in the last few years as it represents an effective and highly expressive modeling entity. Its application has been studied in the field of Constraint Programming, Mixed Integer Programming, and SAT to solve complex decision problems such as shift scheduling. In this theoretical study we demonstrate how the constraint can be linearized efficiently. In particular, we pro-pose a lifted polytope which has only integer extreme points. Based on this result, for shift scheduling problems we prove the equivalence of Dantzig’s original set covering model and a lately introduced grammar-based model

Definability and computability over finite structures

Our research deals with several aspects of Definability and Computability on Finite Structures. Among them: Model theoretic characterization of various complexity classes; Expressive power of various logical systems over finite structures, both ordered and unordered; Probabilistic approaches to finite model theory and its relationship to complexity theory; Logical criteria for approximability of combinatorial optimization problems; Application of the above to extensions of the relational database model. According to the work plan, this research project was divided into nine research tasks. On all of them, substantial progress has been made. In addition, we have gone beyond the original proposal by investigating one further research topic, namely. Bound-variable logic: decidability, complexity, model-theoretic properties. (orig.)Available from TIB Hannover: DtF QN1(78,3) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekSIGLEGerman-Israeli Foundation for Scientific Research and Development (GIF), Oberschleissheim (Germany)DEGerman

The Parameterized Complexity of Global Constraints

We argue that parameterized complexity is a useful tool with which to study global constraints. In particular, we show that many global constraints which are intractable to propagate completely have natural parameters which make them fixedparameter tractable and which are easy to compute. This tractability tends either to be the result of a simple dynamic program or of a decomposition which has a strong backdoor of bounded size. This strong backdoor is often a cycle cutset. We also show that parameterized complexity can be used to study other aspects of constraint programming like symmetry breaking. For instance, we prove that value symmetry is fixed-parameter tractable to break in the number of symmetries. Finally, we argue that parameterized complexity can be used to derive results about the approximability of constraint propagation