Solving Hard Qualitative Temporal Reasoning Problems Evaluating the E ciency 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 e ciency of algorithms for solving the con sistency problem in this calculus has received only little research atten tion 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 cal culus For this purpose we prove that Ladkin and Reinefeld s algorithm is complete when using the ORD Horn class we identify phase transi tion 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