On Redundant Topological Constraints

The Region Connection Calculus (RCC) is a well-known calculus for representing part-whole and topological relations. It plays an important role in qualitative spatial reasoning, geographical information science, and ontology. The computational complexity of reasoning with RCC5 and RCC8 (two fragments of RCC) as well as other qualitative spatial/temporal calculi has been investigated in depth in the literature. Most of these works focus on the consistency of qualitative constraint networks. In this paper, we consider the important problem of redundant qualitative constraints. For a set Gamma of qualitative constraints, we say a constraint (x R y) in Gamma is redundant if it is entailed by the rest of Gamma. A prime subnetwork of Gamma is a subset of Gamma which contains no redundant constraints and has the same solution set as Gamma. It is natural to ask how to compute such a prime subnetwork, and when it is unique. In this paper, we show that this problem is in general intractable, but becomes tractable if Gamma is over a tractable subalgebra S of a qualitative calculus. Furthermore, if S is a subalgebra of RCC5 or RCC8 in which weak composition distributes over nonempty intersections, then Gamma has a unique prime subnetwork, which can be obtained in cubic time by removing all redundant constraints simultaneously from Gamma. As a byproduct, we show that any path-consistent network over such a distributive subalgebra is weakly globally consistent and minimal. A thorough empirical analysis of the prime subnetwork upon real geographical data sets demonstrates the approach is able to identify significantly more redundant constraints than previously proposed algorithms, especially in constraint networks with larger proportions of partial overlap relations.