Journal of Applied Intelligence 3, 47-70 (1993) © 1993 Kluwer Academic Publishers, Boston. Manufactured in The Netherlands. Reasoning about Networks of Temporal Relations and Its Applications to Problem Solving S. KERETHO Dept. ~'Computer Engineering, Kasetsart University, Bangkok 10900, ~ailand R. LOGANANTHARAJ Center ~r Advanced Computer Studies, University ~ Southwestern Louisiana, L@lyette, LA 70504 Abstract. An interval algebra (IA) has been proposed as a model for representing and reasoning about qualitative temporal relations between time intervals. Unfortunately, reasoning tasks with IA that in- volve deciding the satisfiability of the temporal constraints, or providing all the satisfying instances of the temporal constraints, are NP-complete. That is, solving these problems are computationally expo- nential in the "worst case." However, several directions in improving their computational performance are still possible. This paper presents a new backtracking algorithm for finding a solution called consis- tent scenario. This algorithm has an O(n 3) best-case complexity, compared to O(n 4) of previous known backtrack algorithms, where n denotes the number of intervals. By computational experiments, we tested the performance of different backtrack algorithms on a set of randomly generated networks with the results favoring our proposal. In this paper, we also present a new path consistency algorithm, which has been used for finding approximate solutions towards the minimal labeling networks. The worst-case complexity of the proposed algorithm is still O(n3); however, we are able to improve its performance by eliminating the unnecessary duplicate computation as presented in Allen's original algorithm, and by employing a most-constrained first principle, which ensures a faster convergence. The performance of the proposed scheme is evaluated through a large set of experimental data. Key words: Temporal reasoning, constraint satisfactive problems, backtrack algorithms, temporal con- straint propagation 1. Introduction In solving many real-world problems, one often finds the need to incorporate time for describing changes of objects' properties. A tool for repre- senting and reasoning about events taken place in a domain is required. Much of the temporal relationships between events, if not all, are qual- #alive information in which there is no direct ref- erence to absolute time. For example, in the statement "The meeting is scheduled before the lunch break," the meeting event is qualitatively "before" the lunch event. In many situations temporal knowledge about the relationship be- tween events may not be definite; instead it is indefinite or incomplete. In such situations, dis- junctive sentences can be used to express such indefinite information (e.g., "The meeting is scheduled before or after the lunch break."). In this paper, we confine ourselves to the qualita- tive and disjunctive temporal knowledge, since a large part of temporal relationships used in everyday life involves these kinds of informa- tion. Allen [1] has proposed an interval-based temporal algebra that has become a very popular approach for representing and reasoning about such temporal knowledge. This interval algebra has been cited for its expressive power and ease