Backdoor Sets for CSP.

Abstract

A backdoor set of a CSP instance is a set of variables whose instantiation moves the instance into a fixed class of tractable instances (an island of tractability). An interesting algorithmic task is to find a small backdoor set efficiently: once it is found we can solve the instance by solving a number of tractable instances. Parameterized complexity provides an adequate framework for studying and solving this algorithmic task, where the size of the backdoor set provides a natural parameter. In this survey we present some recent parameterized complexity results on CSP backdoor sets, focusing on backdoor sets into islands of tractability that are defined in terms of constraint languages.