Related papers: Symmetry Breaking with Polynomial Delay
A semilinear relation is a finite union of finite intersections of open and closed half-spaces over, for instance, the reals, the rationals, or the integers. Semilinear relations have been studied in connection with algebraic geometry,…
The constraint satisfaction problem asks to decide if a set of constraints over a relational structure $\mathcal{A}$ is satisfiable (CSP$(\mathcal{A})$). We consider CSP$(\mathcal{A} \cup \mathcal{B})$ where $\mathcal{A}$ is a structure and…
The Promise Constraint Satisfaction Problem (PCSP for short) is a generalization of the well-studied Constraint Satisfaction Problem (CSP). The PCSP has its roots in such classic problems as the Approximate Graph Coloring and the…
A class of valued constraint satisfaction problems (VCSPs) is characterised by a valued constraint language, a fixed set of cost functions on a finite domain. An instance of the problem is specified by a sum of cost functions from the…
In this paper, we define the reoptimization variant of the closest substring problem (CSP) under sequence addition. We show that, even with the additional information we have about the problem instance, the problem of finding a closest…
A semilinear relation S is max-closed if it is preserved by taking the componentwise maximum. The constraint satisfaction problem for max-closed semilinear constraints is at least as hard as determining the winner in Mean Payoff Games, a…
We prove a complexity dichotomy theorem for all non-negative weighted counting Constraint Satisfaction Problems (CSP). This caps a long series of important results on counting problems including unweighted and weighted graph homomorphisms…
Constraint satisfaction problems (CSPs) are about finding values of variables that satisfy the given constraints. We show that Transformer extended with recurrence is a viable approach to learning to solve CSPs in an end-to-end manner,…
The Constraint-satisfaction problem (CSP) is fundamental in mathematics, physics, and theoretical computer science. Continuous local search (CLS) solvers, as recent advancements, can achieve highly competitive results on certain classes of…
Answering Conjunctive Queries (CQs) and solving Constraint Satisfaction Problems (CSPs) are arguably among the most fundamental tasks in Computer Science. They are classical NP-complete problems. Consequently, the search for tractable…
The degree of a CSP instance is the maximum number of times that any variable appears in the scopes of constraints. We consider the approximate counting problem for Boolean CSP with bounded-degree instances, for constraint languages…
We show that any submodular minimization (SM) problem defined on a linear constraint set with constraints having up to two variables per inequality, are 2-approximable in polynomial time. If the constraints are monotone (the two variables…
We generalize the polynomial-time solvability of $k$-\textsc{Diverse Minimum s-t Cuts} (De Berg et al., ISAAC'23) to a wider class of combinatorial problems whose solution sets have a distributive lattice structure. We identify three…
Symmetry is an important feature of many constraint programs. We show that any problem symmetry acting on a set of symmetry breaking constraints can be used to break symmetry. Different symmetries pick out different solutions in each…
The degree of a CSP instance is the maximum number of times that a variable may appear in the scope of constraints. We consider the approximate counting problem for Boolean CSPs with bounded-degree instances, for constraint languages…
We analyse how the standard reductions between constraint satisfaction problems affect their proof complexity. We show that, for the most studied propositional, algebraic, and semi-algebraic proof systems, the classical constructions of…
Efficient omission of symmetric solution candidates is essential for combinatorial problem-solving. Most of the existing approaches are instance-specific and focus on the automatic computation of Symmetry Breaking Constraints (SBCs) for…
To any fixed, finite relational structure, $\mathbb{D}$, there is an associated decision problem, CSP$(\mathbb{D})$, which is a restricted version of the constraint satisfaction problem. In [8], the so called "algebraic approach" to the…
A central task in knowledge compilation is to compile a CNF-SAT instance into a succinct representation format that allows efficient operations such as testing satisfiability, counting, or enumerating all solutions. Useful representation…
The binary Constraint Satisfaction Problem (CSP) is to decide whether there exists an assignment to a set of variables which satisfies specified constraints between pairs of variables. A binary CSP instance can be presented as a labelled…