Robustness of spatial relation evaluation in data exchange

Topological relationships between geometric objects are important in several spatial applications, like spatial query evaluation, spatial integrity constraints checking, and spatial reasoning. Although the conceptual aspects of topological relationships between geometric objects embedded in the Euclidean space have been extensively studied, the problems arising when topological relationships are evaluated on real data have been much less explored. In particular, robustness problems arise in the evaluation of topological relationships between geometric objects implemented as vectors in a discrete space. A lack of robustness is characterized by the fact that different systems can produce different evaluations of topological relationships on the same data, and it is caused by the fact that coordinates are represented as finite numbers. The goal of this paper is to formally analyze some rules for increasing the robustness of a topological relationship evaluation and to give some examples w.r.t. a specific topological relationship.