(PDF) Peter van Beek. Approximation algorithms for temporal reasoning. Proceedings of the 11th International Joint Conference on Artificial Intelligence, Detroit, Michigan, 1291-1296, August, 1989.
We consider a representation for temporal relations between intervals introduced by James Allen, and its associated computational or reasoning problem: given possibly indefinite knowledge of the relations between some intervals, how do we compute the strongest possible assertions about the relations between some or all intervals. Determining exact solutions to this problem has been shown to be (almost assuredly) intractable. Allen gives an approximation algorithm based on constraint propagation. We give new approximation algorithms, examine their effectiveness, and determine under what conditions the algorithms are exact.