Related papers: Complexity of Homogeneous Co-Boolean Constraint Sa…
We give a complexity dichotomy theorem for the counting Constraint Satisfaction Problem (#CSP in short) with complex weights. To this end, we give three conditions for its tractability. Let F be any finite set of complex-valued functions,…
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 determine the computational complexity of approximately counting the total weight of variable assignments for every complex-weighted Boolean constraint satisfaction problem (or CSP) with any number of additional unary (i.e., arity 1)…
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…
Schaefer's dichotomy theorem [Schaefer, STOC'78] states that a boolean constraint satisfaction problem (CSP) is polynomial-time solvable if one of six given conditions holds for every type of constraint allowed in its instances. Otherwise,…
The Constraint Satisfaction Problem (CSP) is a problem of computing a homomorphism $\mathbf{R}\to \mathbf{\Gamma}$ between two relational structures, where $\mathbf{R}$ is defined over a domain $V$ and $\mathbf{\Gamma}$ is defined over a…
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…
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…
Constraint satisfaction problem (CSP) is a well-studied combinatorial search problem, in which we are asked to find an assignment of values to given variables so as to satisfy all of given constraints. We study a reconfiguration variant of…
Many natural combinatorial problems can be expressed as constraint satisfaction problems. This class of problems is known to be NP-complete in general, but certain restrictions on the form of the constraints can ensure tractability. The…
Conservative constraint satisfaction problems (CSPs) constitute an important particular case of the general CSP, in which the allowed values of each variable can be restricted in an arbitrary way. Problems of this type are well studied for…
A computational problem exhibits a "gap property" when there is no tractable boundary between two disjoint sets of instances. We establish a Gap Trichotomy Theorem for a family of constraint problem variants, completely classifying the…
A constraint satisfaction problem (CSP) is a computational problem where the input consists of a finite set of variables and a finite set of constraints, and where the task is to decide whether there exists a satisfying assignment of values…
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,…
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…
Constraint satisfaction problems (or CSPs) have been extensively studied in, for instance, artificial intelligence, database theory, graph theory, and statistical physics. From a practical viewpoint, it is beneficial to approximately solve…
A Boolean constraint satisfaction instance is a conjunction of constraint applications, where the allowed constraints are drawn from a fixed set B of Boolean functions. We consider the problem of determining whether two given constraint…
We study the complexity of the Distributed Constraint Satisfaction Problem (DCSP) on a synchronous, anonymous network from a theoretical standpoint. In this setting, variables and constraints are controlled by agents which communicate with…
The constraint satisfaction problem (CSP) can be formulated as a homomorphism problem between relational structures: given a structure $\mathcal{A}$, for any structure $\mathcal{X}$, whether there exists a homomorphism from $\mathcal{X}$ to…
The CSP (constraint satisfaction problems) is a class of problems deciding whether there exists a homomorphism from an instance relational structure to a target one. The CSP dichotomy is a profound result recently proved by Zhuk (2020, J.…