A weighted constraint satisfaction problem (WCSP) is a constraint satisfaction problem in which preferences among solutions can be expressed. Bucket elimination is a complete technique commonly used to solve this kind of constraint satisfaction problem. When the memory required to apply bucket elimination is too high, a heuristic method based on it (denominated mini-buckets) can be used to calc...

The modelling bottleneck in Constraint Modelling prevents the widespread use of Constraint Programming techniques. Automated Constraint Modelling addresses this problem. To enhance automatically generated models, we eliminate common subexpressions during the modelling process, as compilers do when compiling source code. Common subexpression elimination can lead to a dramatic reduction in the si...

The paper provides a unifying perspective of tree-decomposition algorithms appearing in various automated reasoning areas, such as join-tree clustering for constraint-satisfaction and the clique-tree algorithm for probabilistic reasoning. Subsequently, the paper extends the variable-elimination scheme called bucket-elimination (BE) into a two-phase message passing along a bucket-tree (BTE), mak...

A variable elimination rule allows the polynomialtime identification of certain variables whose elimination does not affect the satisfiability of an instance. Variable elimination in the constraint satisfaction problem (CSP) can be used in preprocessing or during search to reduce search space size. We show that there are essentially just four variable elimination rules defined by forbidding gen...

Arc-consistency algorithms prune the search-space of Constraint Satisfaction Problems (CSPs). They use support-checks to find out about the properties of CSPs. Their arc-heuristics select the constraint and their domain-heuristics select the values for the next support-check. We shall combine AC-3 and DEE and equip the resulting hybrid with a double-support domain-heuristic. The resulting hybri...

In constraint logic programming, proof procedures for Horn clauses are enhanced with an interface to efficient constraint solvers. In this paper we show how to incorporate constraint processing into a general, non-Horn theorem proving calculus. A framework for a new calculus is introduced which combines model elimination with constraint solving, following the lines of Bürckert (1991). A prototy...

Broken triangles constitute an important concept not only for solving constraint satisfaction problems in polynomial time, but also for variable elimination or domain reduction by merging domain values. Specifically, for a given variable in a binary arc-consistent CSP, if no broken triangle occurs on any pair of values, then this variable can be eliminated while preserving satisfiability. More ...

Abstract. The formulation of a Propositional Satisfiability (SAT) problem instance is vital to efficient solving. This has motivated research on preprocessing, and inprocessing techniques where reformulation of a SAT instance is interleaved with solving. Preprocessing and inprocessing are highly effective in extending the reach of SAT solvers, however they necessarily operate on the lowest leve...