#### Conference abstracts

Session B2 - Graph Theory and Combinatorics

July 14, 17:00 ~ 17:50

## Approximation of MIN CSPs

### VĂctor Dalmau

### Universitat Pompeu Fabra, Spain - vdalmau@gmail.com

An instance of the constraint satisfaction problem (CSP) is given by a family of constraints on overlapping sets of variables, and the goal is to assign values from a fixed domain to the variables so that all constraints are satisfied. In the optimization version, the goal is to maximize the number of satisfied constraints (MAX CSP) or, alternatively, to minimize the number of unsatisfied constraints (MIN CSP). This problem is usually parameterized by the set, Gamma, of relations allowed in the constraints, usually called constraint language. It turns out that MAX CSP/MIN CSP is computationally hard for most constraint languages, which motivates the study of approximation algorithms. In this talk we will focus on the approximation of MIN CSPs. We shall start addressing the following question: which constraint languages give rise to a MIN CSPs that is constant-factor approximable? We shall also study some other weaker approximation notions such polynomial loss and robust approximation.