Interval Algebra for Spatio-Temporal Relation Reasoning

Abstract

Constraint satisfaction techniques play an important role in current computer science. Many difficult problems involving search from areas such as machine vision, scheduling, graph algorithms, machine design, and manufacturing can be considered to be the cases of the constraint satisfaction problem. In this paper, we construct a Infinite Temporal Interval Group for temporal constraint propagation. This interval algebra is also extended for spatial constraint reasoning. A temporal transitive closure table is derived, and we propagate the time constraints of arbitrary two objects across long distances n by linear time. A set of algorithms is proposedto manage spatio-temporal knowledge. The algorithms are extended for time-based media in an n-dimensional space. Possible conflicts in the user specification are detected and eliminated. We derive and prove many properties of spatio-temporal relations.