Query Evaluation via Tree-Decompositions

A number of efficient methods for evaluating first-order and monadic-second order queries on finite relational structures are based on tree-decompositions of structures or queries. We systematically study these methods. In the first part of the paper we consider arbitrary formulas on tree-like structures. We generalize a theorem of Courcelle [8] by showing that on structures of bounded tree-width a monadic second-order formula (with free first- and second-order variables) can be evaluated in time linear in the structure size plus the size of the output. In the second part we study tree-like formulas on arbitrary structures. We generalize the notions of acyclicity and bounded tree-width from conjunctive queries to arbitrary first-order formulas in a straightforward way and analyze the complexity of evaluating formulas of these fragments. Moreover, we show that the acyclic and bounded tree-width fragments have the same expressive power as the wellknown guarded fragment and the fi...

• Type: Conference
• Year: 2001
• Where: ICDT
• Authors: Jörg Flum, Markus Frick, Martin Grohe
• Keywords: Database, Formulas, ICDT 2001, Tree-width, finite Relational Structures