Bounded Width Dichotomies in Constraint Satisfaction Problems

Abstract

In this thesis we examine the connection between structures with bounded width, polymorphisms and pebble games. There has been extensive work on trying to prove the dichotomy conjecture for finite structures, namely, the Constraint Satisfaction Problem (CSP) of a finite structure is either in P or NP-complete. We are interested in finding classes in which a stronger dichotomy exists; namely, where every structure has either bounded width or a hard CSP. We call this kind of dichotomy a bounded width dichotomy. We will investigate properties of polymorphisms of structures with bounded width, and use this to look at classes of directed graphs with a bounded width dichotomy.