Combining topological and qualitative size constraints for spatial reasoning

Information about the relative size of spatial regions is often easily accessible and, when combined with other types of spatial information, it can be practically very useful. In this paper we combine a simple framework for reasoning about qualitative size relations with the Region Connection Calculus RCC-8, a widely studied approach for qualitative spatial reasoning with topological relations. Reasoning about RCC-8 relations is NP-hard, but a large maximal tractable subclass of RCC-8 called Ĥ₈ was identified. Interestingly, any constraint in RCC-8 - Ĥ₈ can be consistently reduced to a constraint in Ĥ₈, when an appropriate size constraint between the spatial regions is supplied. We propose an O(n³) time path-consistency algorithm based on a novel technique for combining RCC-8 constraints and relative size constraints, where n is the number of spatial regions. We prove its correctness and completeness for deciding consistency when the input contains topological constraints in Ĥ₈. We also provide results on finding a consistent scenario in O(n³) time both for combined topological and relative size constraints, and for topological constraints alone. This is an O(n²) improvement over the known methods.