The complexity and approximability of the constraint satisfaction problem (CSP) has been
actively studied over the past 20 years. A new version of the CSP, the promise CSP (PCSP) …

Polymorphisms, and How to Use Them Page 1 Polymorphisms, and How to Use Them Libor Barto
∗1, Andrei Krokhin2, and Ross Willard †3 1 Department of Algebra, Faculty of Mathematics and …

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 …

We propose a new algorithm for Promise Constraint Satisfaction Problems (PCSPs). It is a
combination of the Constraint Basic LP relaxation and the Affine IP relaxation (CLAP). We …

The approximate graph coloring problem, whose complexity is unresolved in most cases,
concerns finding a-coloring of a graph that is promised to be-colorable, where. This problem …

We provide a unified framework to study hierarchies of relaxations for Constraint Satisfaction
Problems and their Promise variant. The idea is to split the description of a hierarchy into an …

We present new results on approximate colourings of graphs and, more generally,
approximate H-colourings and promise constraint satisfaction problems. First, we show NP …

For a constraint satisfaction problem (CSP), a robust satisfaction algorithm is one that
outputs an assignment satisfying most of the constraints on instances that are near …

Following the success of the so-called algebraic approach to the study of decision constraint
satisfaction problems (CSPs), exact optimization of valued CSPs, and most recently promise …

We give a precise algebraic characterization of the power of Sherali--Adams relaxations for
solvability of valued constraint satisfaction problems (CSPs) to optimality. The condition is …