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 b H8 was identiied. Interestingly, any constraint in RCC-8 ? b H8 can be consistently reduced to a constraint in b H8, when an appropriate size constraint between the spatial regions is supplied. We propose an O(n 3) 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 b H8. We also provide results on nding a consistent scenario in O(n 3) time both for combined topological and relative size constraints, and for topological constraints alone. This is an O(n 2) improvement over the known methods.