(PDF) Peter van Beek and Dennis W. Manchak. The design and experimental analysis of algorithms for temporal reasoning. Journal of Artificial Intelligence Research 4:1-18, 1996.
Many applications---from planning and scheduling to problems in molecular biology---rely heavily on a temporal reasoning component. In this paper, we discuss the design and an empirical analysis of algorithms for a temporal reasoning system based on Allen's influential interval-based framework for representing temporal information. At the core of the system are algorithms for determining whether the temporal information is consistent, and, if so, finding one or more scenarios that are consistent with the temporal information. Two important algorithms for these tasks are a path consistency algorithm and a backtracking algorithm. For the path consistency algorithm, we develop techniques that can result in up to a ten-fold speedup over an already highly optimized implementation. For the backtracking algorithm, we develop variable and value ordering heuristics that are shown empirically to dramatically improve the performance of the algorithm. As well, we show how the backtracking search problem can be reformulated to reduce the time and space requirements of the backtracking search. Taken together, the techniques we develop allow a temporal reasoning component to solve problems that are of practical size.