Dynamic shortest paths minimizing travel times and costs

• Published in: Networks Vol. 41; no. 4; pp. 197 - 205
• Main Authors: Ahuja, Ravindra K., Orlin, James B., Pallottino, Stefano, Scutellà, Maria G.
• Format: Journal Article
• Language: English
• Published: Hoboken Wiley Subscription Services, Inc., A Wiley Company 01-07-2003; John Wiley & Sons
• Subjects: Applied sciences; dynamic shortest path problem; Exact sciences and technology; Flows in networks. Combinatorial problems; Operational research and scientific management; Operational research. Management science; shortest path problem; Telecommunications; Telecommunications and information theory; Teleprocessing networks. Isdn; traffic network; transportation network; Valuation and optimization of characteristics. Simulation; Minimum time; Travel time; FIFO system; traffic network; shortest path problem; Transit time; NP hard problem; Shortest path; Road network; dynamic shortest path problem; transportation network; Polynomial time
• ISSN: 0028-3045; 1097-0037
• DOI: 10.1002/net.10072

In this paper, we study dynamic shortest path problems that determine a shortest path from a specified source node to every other node in the network where arc travel times change dynamically. We consider two problems: the minimum‐time walk problem and the minimum‐cost walk problem. The minimum‐time walk problem is to find a walk with the minimum travel time. The minimum‐cost walk problem is to find a walk with the minimum weighted sum of the travel time and the excess travel time (over the minimum possible travel time). The minimum‐time walk problem is known to be polynomially solvable for a class of networks called FIFO networks. In this paper, (i) we show that the minimum‐cost walk problem is an NP‐hard problem; (ii) we develop a pseudopolynomial‐time algorithm to solve the minimum‐cost walk problem (for integer travel times); and (iii) we develop a polynomial‐time algorithm for the minimum‐time walk problem arising in road networks with traffic lights. © 2003 Wiley Periodicals, Inc.