Towards a theory of spatial database queries (extended abstract)
PODS '94 Proceedings of the thirteenth ACM SIGACT-SIGMOD-SIGART symposium on Principles of database systems
Complete geometrical query languages (extended abstract)
PODS '97 Proceedings of the sixteenth ACM SIGACT-SIGMOD-SIGART symposium on Principles of database systems
Finitely representable databases
Journal of Computer and System Sciences - Special issue on principles of database systems
Relational expressive power of constraint query languages
Journal of the ACM (JACM)
Constraint query languages (preliminary report)
PODS '90 Proceedings of the ninth ACM SIGACT-SIGMOD-SIGART symposium on Principles of database systems
Foundations of Databases: The Logical Level
Foundations of Databases: The Logical Level
Constraint Databases
Hauptvortrag: Quantifier elimination for real closed fields by cylindrical algebraic decomposition
Proceedings of the 2nd GI Conference on Automata Theory and Formal Languages
On Expressing Topological Connectivity in Spatial Datalog
CDB '97 Second International Workshop on Constraint Database Systems, Constraint Databases and Their Applications
Termination Properties of Spatial Datalog Programs
LID '96 Proceedings of the International Workshop on Logic in Databases
DBPL '01 Revised Papers from the 8th International Workshop on Database Programming Languages
| Hi-index | 0.00 |
We consider two-dimensional spatial databases defined in terms of polynomial inequalities and focus on the potential of programming languages for such databases to express queries related to topological connectivity. It is known that the topological connectivity test is not first-order expressible. One approach to obtain a language in which connectivity queries can be expressed would be to extend FO+Poly with a generalized (or Lindström) quantifier expressing that two points belong to the same connected component of a given database. For the expression of topological connectivity, extensions of first-order languages with recursion have been studied (in analogy with the classical relational model). Two such languages are spatial Datalog and FO+Poly+WHILE. Although both languages allow the expression of non-terminating programs, their (proven for FO+Poly+WHILE and conjectured for spatial Datalog) computational completeness makes them interesting objects of study. Previously, spatial Datalog programs have been studied for more restrictive forms of connectivity (e.g., piece-wise linear connectivity) and these programs were proved to correctly test connectivity on restricted classes of spatial databases (e.g., linear databases) only. In this paper, we present a spatial Datalog program that correctly tests topological connectivity of arbitrary compact (i.e., closed and bounded) spatial databases. In particular, it is guaranteed to terminate on this class of databases. This program is based on a first-order description of a known topological property of spatial databases, namely that locally they are conical. We also give a very natural implementation of topological connectivity in FO+Poly+WHILE, that is based on a first-order implementation of the curve selection lemma, and that works correctly on arbitrary spatial databases inputs. Finally, we raise the question whether topological connectivity of arbitrary spatial databases can also be expressed in spatial Datalog.