Algorithmica (2012) 62:416–435 DOI 10.1007/s00453-010-9461-6 Shortest Paths in Time-Dependent FIFO Networks Frank Dehne · Masoud T. Omran · Jörg-Rüdiger Sack Received: 5 April 2010 / Accepted: 6 October 2010 / Published online: 28 October 2010 © Springer Science+Business Media, LLC 2010 Abstract In this paper, we study the time-dependent shortest paths problem for two types of time-dependent FIFO networks. First, we consider networks where the availability of links, given by a set of disjoint time intervals for each link, changes over time. Here, each interval is assigned a non-negative real value which represents the travel time on the link during the corresponding interval. The resulting short- est path problem is the time-dependent shortest path problem for availability inter- vals (T DSP int ), which asks to compute all shortest paths to any (or all) destination node(s) d for all possible start times at a given source node s . Second, we study time-dependent networks where the cost of using a link is given by a non-decreasing piece-wise linear function of a real-valued argument. Here, each piece-wise linear function represents the travel time on the link based on the time when the link is used. The resulting shortest paths problem is the time-dependent shortest path prob- lem for piece-wise linear functions (T DSP lin ) which asks to compute, for a given source node s and destination d , the shortest paths from s to d , for all possible starting times. We present an algorithm for the T DSP lin problem that runs in time O((F d + γ )(|E|+|V | log |V |)) where F d is the output size (i.e., number of linear pieces needed to represent the earliest arrival time function to d ) and γ is the input size (i.e., number of linear pieces needed to represent the local earliest arrival time functions for all links in the network). We then solve the T DSP int problem in Research supported by NSERC, SUN Microsystems of Canada and HPCVL. F. Dehne · M.T. Omran · J.-R. Sack ( ) Carleton University, Ottawa, Canada e-mail: sack@scs.carleton.ca F. Dehne e-mail: dehne@scs.carleton.ca M.T. Omran e-mail: mtomran@scs.carleton.ca