Pairwise-consistency checking of basic cardinal direction constraints

In this paper we study a formal model for qualitative spatial reasoning with cardinal direction relations called direction-relation matrix. We give an O(n²) algorithm to check the pairwise-consistency of basic cardinal direction constraints with the variables ranging over the set of simple regions. To the best of our knowledge, this was an open problem. A previous algorithm of the same model with our paper for this problem works in O(n³).