Tractable Query Answering in Indefinite Constraint Databases: Basic Results and Applications to Querying Spatiotemporal Information

We consider the scheme of indeenite constraint databases proposed by Koubarakis. This scheme can be used to represent indefinite information arising in temporal, spatial and truly spatiotemporal applications. The main technical problem that we address in this paper is the discovery of tractable classes of databases and queries in this scheme. We start with the assumption that we have a class of constraints C with satissability and variable elimination problems that can be solved in PTIME. Under this assumption, we show that there are several general classes of databases and queries for which query evaluation can be done with PTIME data complexity. We then search for tractable instances of C in the area of temporal and spatial constraints. Classes of constraints with tractable satissability problems can be easily found in the literature. The largest class that we consider is the class of Horn disjunctive linear constraints over the rationals. Because variable elimination for Horn disjunctive linear constraints cannot be done in PTIME, we try to discover subclasses with tractable variable elimination problems. The class of UTVPI 6 = constraints is the largest class that we show to have this property. Finally, we restate the initial general results with C ranging over the newly discovered tractable classes. Tractable query answering problems for indeenite temporal and spatial constraint databases are identiied in this way.