Exact space–time prism of an activity program: bidirectional searches in multi-state supernetwork

Space–time prism (STP) modeling for activity programs with various realizations of activity chains has been a challenging research topic. This study claims that a bidirectional search scheme in a multi-state supernetwork is capable of pinpointing the exact STP of an activity program. The correctness and search space are first analyzed for the existing two-stage bidirectional search methods originally suggested for constructing trip-based STPs. Two simultaneous bidirectional search methods are further suggested. Travel time lower bounds based on A*, landmarks, and triangular inequalities are applied in goal-directed searches to reduce the search space. The small twists in formalism over the existing methods ensure accuracy and computational efficiency. The performances of the different search methods are compared for conducting activity programs in large networks.