Dynamic shortest paths minimizing travel times and costs

In this paper, we study dynamic shortest path problems, which is to 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 (which is to find a walk with the minimum travel time) and the minimum cost walk problem (which is to find a walk with the minimum travel cost). The minimum time walk problem is known to be polynomially solvable for a class of networks called FIFO networks. This paper makes the following contributions: (i) we show that the minimum cost walk problem is an NP-complete 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.

[1]  Ronald F. Kirby,et al.  The minimum route problem for networks with turn penalties and prohibitions , 1969 .

[2]  Maria Grazia Scutellà,et al.  Minimum Time and Minimum Cost-Path Problems in Street Networks with Periodic Traffic Lights , 2002, Transp. Sci..

[3]  Athanasios K. Ziliaskopoulos.  Optimum path algorithms on multidimensional networks: Analysis, design, implementation and computational experience. , 1996 .

[4]  Robert L. Smith,et al.  Fastest Paths in Time-dependent Networks for Intelligent Vehicle-Highway Systems Application , 1993, J. Intell. Transp. Syst..

[5]  Ariel Orda,et al.  Minimum weight paths in time-dependent networks , 1991, Networks.

[6]  Robert E. Tarjan,et al.  Fibonacci heaps and their uses in improved network optimization algorithms , 1984, JACM.

[7]  Ismail Chabini,et al.  A New Algorithm for Shortest Paths in Discrete Dynamic Networks , 1997 .

[8]  OrdaAriel,et al.  Shortest-path and minimum-delay algorithms in networks with time-dependent edge-length , 1990 .

[9]  Ariel Orda,et al.  Shortest-path and minimum-delay algorithms in networks with time-dependent edge-length , 1990, JACM.

[10]  Ravindra K. Ahuja,et al.  Network Flows: Theory, Algorithms, and Applications , 1993 .

[11]  Athanasios K. Ziliaskopoulos,et al.  An intermodal optimum path algorithm for multimodal networks with dynamic arc travel times and switching delays , 2000, Eur. J. Oper. Res..

[12]  Hani S. Mahmassani,et al.  A note on least time path computation considering delays and prohibitions for intersection movements , 1996 .

[13]  Ismail Chabini,et al.  Discrete Dynamic Shortest Path Problems in Transportation Applications: Complexity and Algorithms with Optimal Run Time , 1998 .

[14]  Stuart E. Dreyfus,et al.  An Appraisal of Some Shortest-Path Algorithms , 1969, Oper. Res..

[15]  S. Pallottino,et al.  Shortest Path Algorithms in Transportation models: classical and innovative aspects , 1997 .