Dynamic shortest paths minimizing travel times and costs
Abstract
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.
Document Details
- Document Type
- Pub Defense Publication
- Publication Date
- May 07, 2003
- Source ID
- 10.1002/net.10072
Entities
People
- James B. Orlin
- Maria G. Scutellà
- Ravindra K. Ahuja
- Stefano Pallottino
Organizations
- Gruppo Nazionale per l'Analisi Matematica, la Probabilità e le loro Applicazioni
- National Science Foundation
- Office of Naval Research