We show that approximate graph colouring is not solved by constantly many levels of the lift-
and-project hierarchy for the combined basic linear programming and affine integer …

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 …

Relaxations for the constraint satisfaction problem (CSP) include bounded width, linear
program (LP), semidefinite program (SDP), affine integer program (AIP), and the combined …

The 1-in-3 and Not-All-Eqal satisfiability problems for Boolean CNF formulas are two well-
known NP-hard problems. In contrast, the promise 1-in-3 vs. Not-All-Eqal problem can be …

We introduce a relaxation for homomorphism problems that combines semidefinite
programming with linear Diophantine equations, and propose a framework for the analysis …

Understanding the computational complexity of fragments of the Constraint Satisfaction
Problem (CSP) has been instrumental in the formulation of Feder-Vardi's Dichotomy …

In this paper we study the interactions between so-called fractional relaxations of the integer
programs (IPs) which encode homomorphism and isomorphism of relational structures. We …

Two particularly active branches of research in constraint satisfaction are the study of
promise constraint satisfaction problems (PCSPs) with finite templates and the study of …

Information-processing tasks modelled by homomorphisms between relational structures
can witness quantum advantage when entanglement is used as a computational resource …

We connect the mixing behaviour of random walks over a graph to the power of the local-
consistency algorithm for the solution of the corresponding constraint satisfaction problem …