The algebra of spatio-temporal intervals

The relations among temporal intervals can be used to model all time dependent objects. We propose a fast mechanism for temporal relation compositions. A temporal transitive closure table is derived, and an interval-based temporal relation algebraic system is constructed. Thus, we propagate the time constraints of arbitrary two objects across long distances n by linear time. We also give a complete discussion of different possible domains of interval relations. A set of algorithms is proposed to detect time conflicts and to derive reasonable interval relations. The algorithms are extended for time-based media in an arbitrary n-dimensional space.