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Dynamic shortest paths minimizing travel times and costs
Author(s) -
Ahuja Ravindra K.,
Orlin James B.,
Pallottino Stefano,
Scutellà Maria G.
Publication year - 2003
Publication title -
networks
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.977
H-Index - 64
eISSN - 1097-0037
pISSN - 0028-3045
DOI - 10.1002/net.10072
Subject(s) - shortest path problem , random walk , node (physics) , path (computing) , computer science , time complexity , mathematical optimization , fifo (computing and electronics) , travel time , mathematics , algorithm , combinatorics , graph , statistics , structural engineering , transport engineering , computer hardware , engineering , programming language
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.