The weighted region problem: finding shortest paths through a weighted planar subdivision
Journal of the ACM (JACM)
An analysis of stochastic shortest path problems
Mathematics of Operations Research
Shortest-path and minimum-delay algorithms in networks with time-dependent edge-length
Journal of the ACM (JACM)
A new algorithm for computing shortest paths in weighted planar subdivisions (extended abstract)
SCG '97 Proceedings of the thirteenth annual symposium on Computational geometry
Kinetic data structures: a state of the art report
WAFR '98 Proceedings of the third workshop on the algorithmic foundations of robotics on Robotics : the algorithmic perspective: the algorithmic perspective
Data structures for mobile data
Journal of Algorithms
Introduction to Algorithms
A Lower Bound for the Shortest Path Problem
COCO '00 Proceedings of the 15th Annual IEEE Conference on Computational Complexity
Fully Dynamic Algorithms for Maintaining All-Pairs Shortest Paths and Transitive Closure in Digraphs
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
Sensitivity analysis for combinatorial optimization
Sensitivity analysis for combinatorial optimization
Worst-case update times for fully-dynamic all-pairs shortest paths
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
Finding Fastest Paths on A Road Network with Speed Patterns
ICDE '06 Proceedings of the 22nd International Conference on Data Engineering
Stochastic shortest paths via Quasi-convex maximization
ESA'06 Proceedings of the 14th conference on Annual European Symposium - Volume 14
Finding time-dependent shortest paths over large graphs
EDBT '08 Proceedings of the 11th international conference on Extending database technology: Advances in database technology
Shortest paths in time-dependent FIFO networks using edge load forecasts
Proceedings of the Second International Workshop on Computational Transportation Science
Robust and Online Large-Scale Optimization
Bidirectional A* search for time-dependent fast paths
WEA'08 Proceedings of the 7th international conference on Experimental algorithms
Maximum flows and parametric shortest paths in planar graphs
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
A critical-time-point approach to all-start-time lagrangian shortest paths: a summary of results
SSTD'11 Proceedings of the 12th international conference on Advances in spatial and temporal databases
Online computation of fastest path in time-dependent spatial networks
SSTD'11 Proceedings of the 12th international conference on Advances in spatial and temporal databases
Time-dependent route planning with generalized objective functions
ESA'12 Proceedings of the 20th Annual European conference on Algorithms
Polynomial-Time approximation schemes for shortest path with alternatives
ESA'12 Proceedings of the 20th Annual European conference on Algorithms
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We investigate the complexity of shortest paths in time-dependent graphs, in which the costs of edges 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 (polynomial-size) piecewise linear, the shortest path from s to d can change nθ(log n) times, settling a several-year-old conjecture of Dean [Technical Reports, 1999, 2004]. We also show that the complexity is polynomial if the slopes of the linear function come from a restricted class, present an output-sensitive algorithm for the general case, and describe a scheme for a (1 + ε)-approximation of the travel time function in near-quadratic space. Finally, 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.