A general strategy for decomposing topological invariants of spatial databases and an application

Topological invariants of spatial databases (i.e., finite structures that capture thetopological properties of the database) are receiving increasing attention since theycan act as a basic structure to tackle relevant problems in the field (e.g., assessmentof the topological equivalence). In this paper, the novel notion of boundary decom-position of a topological invariant is introduced and a polynomial time algorithm tocompute such a decomposition is given. The decomposition consists of a recursivesubdivision of the topological invariant into a finite set of simpler structures, eachbeing a topological invariant in itself. The decomposition is proved to be lossless, anice property which makes the boundary decomposition useful in real applications.As a relevant application, we use the boundary decomposition as the basis for de-vising a polynomial time algorithm for testing the topological equivalence of two2-dimensional spatial databases.