A point-based representation for intervals

Information about time or space is often expressed in terms of points or intervals, and the relations between points and intervals. The interval based representations fall into two distinct classes based on: (i) closure and (ii) minimal representation of the domain. The advantage of closure based representation is the minimal search time at the expense of time to construct the representation, and the storage requirement. Minimal representation optimises storage required, at the expense of construction and search time. Intervals can be represented in terms of their end points. The information about points can be effectively represented using the closure approach but intervals cannot be represented with their endpoints using a point algebra system.

This paper proposes a point based system of representation for interval relations that does not perform closure. Point information is represented in terms of the known relationships between points. The costs of such a representation lies between the expense of closure and minimisation. The time taken for search and construction is better than for minimisation but not as good as for closure. Respectively, the space used is better than for closure but not as good as for minimisation