Related papers: Weaker consistency notions for all the CSPs of bou…
Singleton arc consistency is an important type of local consistency which has been recently shown to solve all constraint satisfaction problems (CSPs) over constraint languages of bounded width. We aim to characterise all classes of CSPs…
The Weighted Constraint Satisfaction Problem (WCSP) framework allows representing and solving problems involving both hard constraints and cost functions. It has been applied to various problems, including resource allocation,…
In Constraint Programming, solving discrete minimization problems with hard and soft constraints can be done either using (i) soft global constraints, (ii) a reformulation into a linear program, or (iii) a reformulation into local cost…
One of the central problems in the study of parametrized constraint satisfaction problems is the Dichotomy Conjecture by T. Feder and M. Vardi stating that the constraint satisfaction problem (CSP) over a fixed, finite constraint language…
The Constraint Satisfaction Problem (CSP) has been intensively studied in many areas of computer science and mathematics. The approach to the CSP based on tools from universal algebra turned out to be the most successful one to study the…
The notion of arc consistency plays a central role in constraint satisfaction. It is known that the notion of local consistency can be extended to constraint optimisation problems defined by soft constraint frameworks based on an idempotent…
In this paper, we propose a comprehensive study of second-order consistencies (i.e., consistencies identifying inconsistent pairs of values) for constraint satisfaction. We build a full picture of the relationships existing between four…
One of the key research interests in the area of Constraint Satisfaction Problem (CSP) is to identify tractable classes of constraints and develop efficient solutions for them. In this paper, we introduce generalized staircase (GS)…
A natural and established way to restrict the constraint satisfaction problem is to fix the relations that can be used to pose constraints; such a family of relations is called a constraint language. In this article, we study arc…
Characterising tractable fragments of the constraint satisfaction problem (CSP) is an important challenge in theoretical computer science and artificial intelligence. Forbidding patterns (generic sub-instances) provides a means of defining…
This paper studies peek arc consistency, a reasoning technique that extends the well-known arc consistency technique for constraint satisfaction. In contrast to other more costly extensions of arc consistency that have been studied in the…
Feder-Vardi conjecture, which proposed that every finite-domain Constraint Satisfaction Problem (CSP) is either in P or it is NP-complete, has been solved independently by Bulatov and Zhuk almost ten years ago. Bodirsky-Pinsker conjecture…
Enforcing local consistencies is one of the main features of constraint reasoning. Which level of local consistency should be used when searching for solutions in a constraint network is a basic question. Arc consistency and partial forms…
We study the use of local consistency methods as reductions between constraint satisfaction problems (CSPs), and promise version thereof, with the aim to classify these reductions in a similar way as the algebraic approach classifies gadget…
The study of the complexity of the constraint satisfaction problem (CSP), centred around the Feder-Vardi Dichotomy Conjecture, has been very prominent in the last two decades. After a long concerted effort and many partial results, the…
In Constraint Programming (CP), achieving arc-consistency (AC) of a global constraint with costs consists in removing from the domains of the variables all the values that do not belong to any solution whose cost is below a fixed bound. We…
We study the power of the bounded-width consistency algorithm in the context of the fixed-template Promise Constraint Satisfaction Problem (PCSP). Our main technical finding is that the template of every PCSP that is solvable in bounded…
The path to the solution of Feder-Vardi dichotomy conjecture by Bulatov and Zhuk led through showing that more and more general algebraic conditions imply polynomial-time algorithms for the finite-domain Constraint Satisfaction Problems…
Many combinatorial problems deal with preferences and violations, the goal of which is to find solutions with the minimum cost. Weighted constraint satisfaction is a framework for modeling such problems, which consists of a set of cost…
This paper presents an algorithm that achieves hyper-arc consistency for the soft alldifferent constraint. To this end, we prove and exploit the equivalence with a minimum-cost flow problem. Consistency of the constraint can be checked in…