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We study the complexity of constraint satisfaction problems involving global constraints, i.e., special-purpose constraints provided by a solver and represented implicitly by a parametrised algorithm. Such constraints are widely used;…
The problem of deciding whether CSP instances admit solutions has been deeply studied in the literature, and several structural tractability results have been derived so far. However, constraint satisfaction comes in practice as a…
We study the Constraint Satisfaction Problem CSP(A), where A is first-order definable in (Z;+,1) and contains +. We prove such problems are either in P or NP-complete.
We show that the uniform Constraint Satisfaction Problem (CSP) parameterized by the size of the solution is in W[1] (the problem is W[1]-hard and it is easy to place it in W[3]). Given a single "free" element of the domain, denoted by $0$,…
Constraint satisfaction problems (CSPs) are a natural class of decision problems where one must decide whether there is an assignment to variables that satisfies a given formula. Schaefer's dichotomy theorem, and its extension to all…
A classic result due to Schaefer (1978) classifies all constraint satisfaction problems (CSPs) over the Boolean domain as being either in $\mathsf{P}$ or $\mathsf{NP}$-hard. This paper considers a promise-problem variant of CSPs called…
We introduce a problem class we call Polynomial Constraint Satisfaction Problems, or PCSP. Where the usual CSPs from computer science and optimization have real-valued score functions, and partition functions from physics have monomials,…
We present a Rice-like complexity lower bound for any MSO-definable problem on binary structures succinctly encoded by circuits. This work extends the framework recently developed as a counterpoint to Courcelle's theorem for graphs encoded…
We show that every NP problem is polynomially equivalent to a simple combinatorial problem: the membership problem for a special class of digraphs. These classes are defined by means of shadows (projections) and by finitely many forbidden…
The quantified constraint satisfaction problem $\mathrm{QCSP}(\mathcal{A})$ is the problem to decide whether a positive Horn sentence, involving nothing more than the two quantifiers and conjunction, is true on some fixed structure…
The role of polymorphisms in determining the complexity of constraint satisfaction problems is well established. In this context we study the stability of CSP complexity and polymorphism properties under some basic graph theoretic…
Valued constraint satisfaction problems (VCSPs) are discrete optimisation problems with a $(\mathbb{Q}\cup\{\infty\})$-valued objective function given as a sum of fixed-arity functions. In Boolean surjective VCSPs, variables take on labels…
The dominating set problem (DSP) is one of the most famous problems in combinatorial optimization. It is defined as follows. For a given simple graph $G=(V,E)$, a dominating set of $G$ is a subset $S\subseteq V$ such that every vertex in $…
The field of constraint satisfaction problems (CSPs) studies homomorphism problems between relational structures where the target structure is fixed. Classifying the complexity of these problems has been a central quest of the field,…
This paper establishes some of the fundamental barriers in the theory of computations and finally settles the long-standing computational spectral problem. That is to determine the existence of algorithms that can compute spectra…
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 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 the field of constraint satisfaction problems (CSP), promise CSPs are an exciting new direction of study. In a promise CSP, each constraint comes in two forms: "strict" and "weak," and in the associated decision problem one must…
A finite constraint language $\mathscr{R}$ is a finite set of relations over some finite domain $A$. We show that intractability of the constraint satisfaction problem $\operatorname{CSP}(\mathscr{R})$ can, in all known cases, be replaced…
A subset of Q^n is called semilinear (or piecewise linear) if it is Boolean combination of linear half-spaces. We study the computational complexity of the constraint satisfaction problem (CSP) over the rationals when all the constraints…