The importance of relations among temporal intervals was found in a number of disciplines. In this paper, 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. The contributions of these algorithms can be used to generate the schedule and layout of multimedia presentations, to model the interaction of multimedia applications, to analyze the virtual reality timing constraints, and to compose multimedia documents.