A New Tractable Subclass of the Rectangle Algebra

This paper presents the 169 permitted relations between two rectangles whose sides are parallel to the axes of some orthogonal basis in a 2-dimensional Euclidean space. Elaborating rectangle algebra just like interval algebra, it defines the concept of convexity as well as the ones of weak preconvexity and strong precon­ vexity. It introduces afterwards the fundamen­ tal operations of intersection, composition and inversion and demonstrates that the concept of weak preconvexity is preserved by the operation of composition whereas the concept of strong preconvexity is preserved by the operation of intersection. Finally, fitting the propagation techniques conceived to solve interval networks, it shows that the polynomial path-consistency algorithm is a decision method for the problem of proving the consistency of strongly preconvex rectangle networks.