A General Strategy for Decomposing Topological Invariants of Spatial Databases and an Application

Topological invariants of spatial databases (i.e., finite structures that capture the topological properties of the database) are receiving increasing attention since they can act as a basic structure to tackle relevant problems in the field (e.g., assessment of the topological equivalence). In this paper, the novel notion of boundary decomposition of a topological invariant is introduced and a polynomial time algorithm to compute such a decomposition is given. The decomposition consists of a recursive subdivision of the to- pological invariant into a finite set of simpler structures, each being a topological invariant in itself. The decomposition is proved to be lossless, a nice property which makes the boundary decomposition useful in real applications. As a relevant application, we use the boundary decomposition as the basis for devising a polynomial time algorithm for testing the topological equivalence of two two-dimensional spatial data- bases.