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We present a Transformer-based framework for Constraint Satisfaction Problems (CSPs). CSPs find use in many applications and thus accelerating their solution with machine learning is of wide interest. Most existing approaches rely on…
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,…
Algorithms for learning decision trees often include heuristic local-search operations such as (1) adjusting the threshold of a cut or (2) also exchanging the feature of that cut. We study minimizing the number of classification errors by…
Valued constraint satisfaction problems (VCSPs) are a large class of combinatorial optimisation problems. The computational complexity of VCSPs depends on the set of allowed cost functions in the input. Recently, the computational…
Structural decomposition methods have been developed for identifying tractable classes of instances of fundamental problems in databases, such as conjunctive queries and query containment, of the constraint satisfaction problem in…
We investigate the impact of modifying the constraining relations of a Constraint Satisfaction Problem (CSP) instance, with a fixed template, on the set of solutions of the instance. More precisely we investigate sensitive instances: an…
Constraint Satisfaction Problems (CSPs) typically have many solutions that satisfy all constraints. Often though, some solutions are preferred over others, that is, some solutions dominate other solutions. We present solution dominance as a…
An instance of the Valued Constraint Satisfaction Problem (VCSP) is given by a finite set of variables, a finite domain of labels, and a sum of functions, each function depending on a subset of the variables. Each function can take finite…
We show that several important resource allocation problems in wireless networks fit within the common framework of Constraint Satisfaction Problems (CSPs). Inspired by the requirements of these applications, where variables are located at…
Answer Set Programming (ASP) is an increasingly popular framework for declarative programming that admits the description of problems by means of rules and constraints that form a disjunctive logic program. In particular, many AI problems…
We investigate the `local consistency implies global consistency' principle of strict width among structures within the scope of the Bodirsky-Pinsker dichotomy conjecture for infinite-domain Constraint Satisfaction Problems (CSPs). Our main…
We study a model of constraint satisfaction problems geared towards instances with few variables but with domain of unbounded size (udCSP). Our model is inspired by recent work on FPT algorithms for MinCSP where frequently both upper and…
We initiate the study of constraint satisfaction problems (CSPs) in the presence of counting quantifiers, which may be seen as variants of CSPs in the mould of quantified CSPs (QCSPs). We show that a single counting quantifier strictly…
Temporal graphs are graphs whose edges are labelled with times at which they are active. Their time-sensitivity provides a useful model of real networks, but renders many problems studied on temporal graphs more computationally complex than…
We study the complexity of the parameterised counting constraint satisfaction problem: given a set of constraints over a set of variables and a positive integer $k$, how many ways are there to assign $k$ variables to 1 (and the others to 0)…
Quantified constraints and Quantified Boolean Formulae are typically much more difficult to reason with than classical constraints, because quantifier alternation makes the usual notion of solution inappropriate. As a consequence, basic…
We study the complexity of constraint satisfaction problems for templates $\Gamma$ that are first-order definable in $(\Bbb Z; succ)$, the integers with the successor relation. Assuming a widely believed conjecture from finite domain…
The constraint satisfaction problem (CSP) on a finite relational structure B is to decide, given a set of constraints on variables where the relations come from B, whether or not there is a assignment to the variables satisfying all of the…
After substantial progress over the last 15 years, the "algebraic CSP-dichotomy conjecture" reduces to the following: every local constraint satisfaction problem (CSP) associated with a finite idempotent algebra is tractable if and only if…
We investigate the Constraint Satisfaction Problem (CSP) over templates with a group structure, and algorithms solving CSP that are equivariant, i.e. invariant under a natural group action induced by a template. Our main result is a method…