We present the first fast route planning algorithm that answers shortest paths queries for a customizable linear combination of two different metrics, e. g. travel time and energy cost, on large scale road networks. The precomputation receives as input a directed graph, two edge weight functions t(e) and c(e), and a discrete interval [L, U ]. The resulting flexible query algorithm finds for a parameter p ∈ [L, U ] an exact shortest path for the edge weight t(e)+p·c(e). This allows for different tradeoffs between the two edge weight functions at query time. We apply precomputation based on node contraction, which adds all necessary shortcuts for any parameter choice efficiently. To improve the node ordering, we developed the new concept of gradual parameter interval splitting. Additionally, we improve performance by combining node contraction and a goaldirected technique in our flexible scenario.

Abstract. We present a practical parallel algorithm for finding shortest paths in the presence of two objective functions. The algorithm builds on a recent theoretical result that on the first glance looks impractical. We address the problem of significant constant factor overheads due to numerous prefix sum computations by carefully re-engineering the algorithm for moderate parallelism. In addition, we develop a parallel weight-balanced B-tree data structure that cache efficiently supports bulk updates. This result might be of independent interest and closes the gap between the full-blown search tree data structure required by the theoretical result over the simple priority queue for the sequential algorithm. Comparing our implementation against a highly tuned sequential bi-objective search, we achieve speedups of 8 on 16 cores.

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Computing driving directions interactively on continental road networks requires preprocessing. This step can be costly, limiting our ability to incorporate new optimization functions, including traffic information or personal preferences. We show how the performance of the state-of-the-art customizable route planning (CRP) framework is boosted by GPUs, even though it has highly irregular structure. Our experimental study reveals that our method is an order of magnitude faster than a highly-optimized parallel CPU implementation, enabling interactive personalized driving directions on continental scale.

We study the problem of route planning on mobile devices. There are two current approaches to this problem. One option is to have all the routing data on the device, which can then compute routes by itself. This makes it hard to incorporate traffic updates, leading to suboptimal routes. An alternative approach outsources the route computation to a server, which then sends only the route to the device. The downside is that a user is lost when deviating from the proposed route in an area with limited connectivity. In this work, we present an approach that combines the best of both worlds. The server performs the route computation but, instead of sending only the route to the user, it sends a corridor that is robust against deviations. We define these corridors properly and show that their size can be theoretically bounded in road networks. We evaluate their quality experimentally in terms of size and robustness on a continental road network. Finally, we introduce several algorithms to compute corridors efficiently. Our experimental analysis shows that our corridors are small but very robust against deviations, and can be computed quickly on a standard server.