An A Algorithm Framework for the point-to-point Time-Dependent Shortest Path Problem

• Published in: Computational Geometry, Graphs and Applications Vol. 7033; pp. 154 - 163
• Main Authors: Ohshima, Tatsuya, Eumthurapojn, Pipaporn, Zhao, Liang, Nagamochi, Hiroshi
• Format: Book Chapter
• Language: English
• Published: Germany Springer Berlin / Heidelberg 2011; Springer Berlin Heidelberg
• Series: Lecture Notes in Computer Science
• Subjects: Algorithm Framework; Algorithms & data structures; Discrete mathematics; Estimator Function; Fast Path; Graphics programming; Road Network; Short Path Problem
• ISBN: 9783642249822; 3642249825
• ISSN: 0302-9743; 1611-3349
• DOI: 10.1007/978-3-642-24983-9_16

Given a directed graph, a nonnegative transit-time function ce(t) for each edge e (where t denotes departure time at the tail of e), a source vertex s, a destination vertex d and a departure time t0, the point-to-point time-dependent shortest path problem (TDSPP) asks to find an s,d-path that leaves s at time t0 and minimizes the arrival time at d. This formulation generalizes the classical shortest path problem in which ce are all constants. This paper presents a novel generalized A* algorithm framework by introducing time-dependent estimator functions. This framework generalizes previous proposals that work with static estimator functions. We provide sufficient conditions on the time-dependent estimator functions for the correctness. As an application, we design a practical algorithm which generalizes the ALT algorithm for the classical problem (Goldberg and Harrelson, SODA05). Finally experimental results on several road networks are shown.