On the Complexity of TimeDependent Shortest Paths
 Luca Foschini,
 John Hershberger,
 Subhash Suri
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We investigate the complexity of shortest paths in timedependent graphs where the costs of edges (that is, edge travel times) vary as a function of time, and as a result the shortest path between two nodes s and d can change over time. Our main result is that when the edge cost functions are (polynomialsize) piecewise linear, the shortest path from s to d can change n ^{ Θ(logn)} times, settling a severalyearold conjecture of Dean (Technical Reports, 1999, 2004). However, despite the fact that the arrival time function may have superpolynomial complexity, we show that a minimum delay path for any departure time interval can be computed in polynomial time. We also show that the complexity is polynomial if the slopes of the linear function come from a restricted class and describe an efficient scheme for computing a (1+ϵ)approximation of the travel time function.
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 Title
 On the Complexity of TimeDependent Shortest Paths
 Journal

Algorithmica
Volume 68, Issue 4 , pp 10751097
 Cover Date
 20140401
 DOI
 10.1007/s0045301297147
 Print ISSN
 01784617
 Online ISSN
 14320541
 Publisher
 Springer US
 Additional Links
 Topics
 Keywords

 Timedependent shortest path
 Piecewise linear delay functions
 Parametric shortest path
 Approximation algorithms
 Industry Sectors
 Authors

 Luca Foschini ^{(1)}
 John Hershberger ^{(2)}
 Subhash Suri ^{(1)}
 Author Affiliations

 1. Department of Computer Science, University of California, Santa Barbara, CA, 93106, USA
 2. Mentor Graphics Corp, 8005 SW Boeckman Rd., Wilsonville, OR, 97070, USA