The computation of point-to-point shortest paths on time-dependent road networks has many practical applications which are interesting from an industrial point of view. Typically, users are interested in the path leading to their destination which has the smallest travel time among all possible paths; it is natural to model the shortest paths problem on a time-dependent graph, where the arc weights are travel times that depend on the time of day at which the arc is traversed. We study both fully combinatorial methods and mathematical formulation based methods. From a combinatorial point of view, if we impose some restrictions on the arc weights, the problem can be solved in polynomial time with the well known Dijkstra’s algorithm. However, applying Dijkstra’s algorithm on a graph with several millions of vertices and arcs, such as a continental road network, may require several seconds of CPU time. This is not acceptable for real-time industrial applications; therefore, the need for speedup techniques arises. Bidirectional search is a standard technique to

hal-00843628, version 1-Carpooling is an appropriate solution to address traffic congestion and to reduce the ecological footprint of the car use. In this paper, we address an essential problem for providing dynamic carpooling: how to compute the shortest driver’s and passenger’s paths. Indeed, those two paths are synchronized in the sens that they have a common subpath between two points: the location where the passenger is picked up and the one where he is dropped off the car. The passenger path may include time-dependent public transportation parts before or after the common subpath. This defines the 2 Synchronization Points Shortest Path Problem (2SPSPP) and focus explicitely on the computation of optimal itineraries for the 2SPSPP, i.e. determining the (optimal) pickup and drop-off points and the two synchronized paths that minimize the total traveling time. We also define restrictions areas for reasonable pick-up and drop-off points and use them to guide the algorithms using heuristics based on landmarks. Experiments are conducted on real transportation network showing the efficiency of the proposed algorithms and accelerations.

Abstract. We present the first approximate distance oracle for sparse directed networks with time-dependent arc-travel-times determined by continuous, piecewise linear, positive functions possessing the FIFO prop-erty. Our approach precomputes (1 + ε)−approximate distance sum-maries from selected landmark vertices to all other vertices in the network, and provides two sublinear-time query algorithms that deliver constant and (1+σ)−approximate shortest-travel-times, respectively, for arbitrary origin-destination pairs in the network. Our oracle is based only on the sparsity of the network, along with two quite natural assumptions about travel-time functions which allow the smooth transition towards asymmetric and time-dependent distance metrics. 1

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to wh d rot u an it hoc networks. The link failures and node failures in ad hoc networks form a major problem due to the depleted the network lifetime. A link failure in one path should not affect other routes. The multiple paths utilized in Natarajan and Rajendran EURASIP Journal on Wireless Communications and Networking 2014, 2014:90