On point-duration networks for temporal reasoning

We present here a point-duration network formalism which extends the point algebra model to include additional variables that represent durations between points of time. Thereafter the new qualitative model is enlarged for allowing unary metric constraints on points and durations, subsuming in this way several point-based approaches to temporal reasoning. We deal with some reasoning tasks within the new models and we show that the main problem, deciding consistency, is NP-complete. However, tractable special cases are identified and we show efficient algorithms for checking consistency, finding a solution and obtaining the minimal network.     

Solving hard qualitative temporal reasoning problems: Evaluating the efficiency of using the ORD-Horn class

While the worst-case computational properties of Allen's calculus for qualitative temporal reasoning have been analyzed quite extensively, the determination of the empirical efficiency of algorithms for solving the consistency problem in this calculus has received only little research attention. In this paper, we will demonstrate that using the ORD-Horn class in Ladkin and Reinefeld's backtracking algorithm leads to performance improvements when deciding consistency of hard instances in Allen's calculus. For this purpose, we prove that Ladkin and Reinefeld's algorithm is complete when using the ORD-Horn class, we identify phase transition regions of the reasoning problem, and compare the improvements of ORD-Horn with other heuristic methods when applied to instances in the phase transition region. Finally, we give evidence that combining search methods orthogonally can dramatically improve the performance of the backtracking algorithm.