Constraint satisfaction problems arise naturally in several different areas of artificial intelligence and computer science. Indeed, constraint satisfaction problems encompass Boolean satisfiability, graph colorability, relational join evaluation, as well as numerous other problems in temporal reasoning, machine vision, belief maintenance, scheduling, and optimization. In their full generality, constraint satisfaction problems are NP-complete and, thus, presumed to be algorithmically intractable. For this reason, significant research efforts have been devoted to the pursuit of "islands of tractability" of constraint satisfaction, that is, special cases of constraint satisfaction problems for which polynomial-time algorithms exist. The aim of this talk is to present an overview of recent advances in the investigation of the computational complexity of constraint satisfaction with emphasis on the connections between islands of tractability of constraint satisfaction, database theory, definability in finite-variable logics, and structures of bounded treewidth.
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