A unified theory of structural tractability for constraint satisfaction problems

A unified theory of structural tractability for constraint satisfaction problems

In this paper we derive a generic form of structural decomposition for the constraint satisfaction problem, which we call a guarded decomposition. We show that many existing decomposition methods can be characterised in terms of finding guarded decompositions satisfying certain specified additional conditions. Using the guarded decomposition framework we are also able to define a new form of de...

A Unified Theory of Structural Tractability for Constraint Satisfaction and Spread Cut Decomposition

In this paper we introduce a generic form of structural decomposition for the constraint satisfaction problem, which we call a guarded decomposition. We show that many existing decomposition methods can be characterized in terms of finding guarded decompositions satisfying certain specified additional conditions. Using the guarded decomposition framework we are also able to define a new form of...

Harnessing Tractability in Constraint Satisfaction Problems

The Constraint Satisfaction Problem (CSP) is a fundamental problem in computer science that takes as input a finite set of variables, a finite set of values and a set of constraints, which are arbitrary relations imposed on certain subsets of variables. The goal is to find an assignment of values to variables that satisfies every constraint. The generality of CSP and its connections to logic, u...

Hybrid tractability of constraint satisfaction problems with global constraints

A wide range of problems can be modelled as constraint satisfaction problems (CSPs), that is, a set of constraints that must be satisfied simultaneously. Constraints can either be represented extensionally, by explicitly listing allowed combinations of values, or intensionally, whether by an equation, propositional logic formula, or other means. Intensionally represented constraints, known as g...

Tractability of Constraint Satisfaction Problems and Projective Clone Homomorphisms