Managing Efficiently Temporal Relations Through Indexed Spanning Trees

We are interested here in the design of a very efficient Time-Map Manager, able to deal with a large knowledge-base of several thou­ sand time-tokens in demanding applications such as reactive planning and execution con­ trol. A system, called IxTeT, aiming at that goal is described. It uses an original represen­ tation of a lattice of time-points that relies for efficiency on a maximum spanning tree of the lattice together with a particular indexing of its nodes. The IxTeT system is sound and complete, it has the same expressive power as the restrict­ ed Interval Algebra that permits complete­ ness in polynomial time. Its average complexi­ ty is shown experimentally to be linear, with a low overhead constant, for both operations: retrieval in and updating of a set of temporal relations.