Routing services on the web and on hand-held devices have become ubiquitous in the past couple of years. Websites like Bing or Google Maps allow users to find routes between arbitrary locations comfortably in no time. Likewise onboard navigation units belong to the off-the-shelf equipment of virtually any new car. The amount of volunteered spatial data of… (More)
Contraction hierarchies are a simple hierarchical routing technique that has proved extremely efficient for static road networks. We explain how to generalize them to networks with time-dependent edge weights. This is the first hierarchical speedup technique for time-dependent routing that allows bidirectional query algorithms. For large realistic networks… (More)
We provide an implementation of an exact route planning algorithm on a mobile device that answers distance queries in a road network of a whole continent instantaneously, i.e., with a delay of 20–200 ms, which is virtually not observable for a human user. We exploit spatial and hierarchical locality properties to design a significantly compressed… (More)
Server based route planning in road networks is now powerful enough to find quickest paths in a matter of milliseconds, even if detailed information on time-dependent travel times is taken into account. However this requires huge amounts of memory on each query server and hours of preprocessing even for a medium sized country like Germany. This is a problem… (More)
We present an efficient algorithm for shortest path computation in road networks with turn costs. Each junction is modeled as a node, and each road segment as an edge in a weighted graph. Turn costs are stored in tables that are assigned to nodes. By reusing turn cost tables for identical junctions, we improve the space efficiency. Pre-processing based on… (More)
Time-dependent road networks are represented as weighted graphs, where the weight of an edge depends on the time one passes through that edge. This way, we can model periodic congestions during rush hour and similar effects. In this work we deal with the special case where edge weights are time-dependent travel times. Namely, we consider two problems in… (More)
Time-Dependent Contraction Hierarchies is a routing technique that solves the shortest path problem in graphs with time-dependent edge weights, that have to satisfy the FIFO property. Although it shows great speedups over Dijkstra's Algorithm the preprocessing is slow. We present a parallelized version of the preprocessing taking advantage of the multiple… (More)
We show that two-dimensional continuous time coherent random walks are possible in free space by properly tailoring the associated initial wave functions. Theoretical predictions along with classical experiments demonstrate the feasibility of our scheme.
We report on optical non-paraxial beams that exhibit a self-accelerating behavior in radial direction. Hence, the intensity profile evolves on a spiraling trajectory. The beam parameters have been optimized for high contrast and rotation rate.