Advanced Route Planning in Transportation Networks

Many interesting route planning problems can be solved by computing shortest paths in a suitably modeled, weighted graph representing a transportation network. Such networks are naturally road networks or timetable networks of public transportation. For large networks, the classical Dijkstra algorithm to compute shortest paths is too slow. And therefore have faster algorithms been developed in recent years. These new algorithms have in common that they use precomputation and store auxiliary data to speedup subsequent shortest-path queries. However, these algorithms often consider only the simplest problem of computing a shortest path between source and target node in a graph with non-negative real edge weights. But real-life problems are often not that simple, and therefore, we need to extend the problem definition. For example, we need to consider time-dependent edge weights, road restrictions, or multiple source and target nodes. While some of the previous algorithms can be used to solve such extended problems, they are usually inefficient. It is therefore important to develop new algorithmic ingredients, or even completely new algorithmic ideas. We contribute solutions to three practically relevant classes of such extended problems: public transit networks, flexible queries, and batched shortest paths computation. These classes are introduced in the following paragraphs. Public transit networks, for example train and bus networks, are inherently eventbased, so that a time-dependent model of the network is mandatory. Furthermore, as they are much less hierarchically structured than road networks, algorithms for road networks perform much worse or even fail, depending on the scenario. We contribute to both cases, first an algorithm that has its initial ideas taken from a technique for road networks, but with significant algorithmic changes. It is based on the concept of node contraction, but now applied to stations. A key point to the success was the usage of a station graph model, having a single node per station. In contrast, the established time-expanded or time-dependent models require multiple nodes per station in general. And second, we contribute to a new algorithm specifically designed for transit networks supporting a fully realistic scenario. It is based on the concept of transfer patterns: a connection is described as the sequence of station where a transfer happens. Although there are potentially hundreds of optimal connections between a pair of stations during a week, the set of transfer patterns is usually much smaller. The main problem is the computation of the transfer patterns. A naïve way would be a Dijkstra-like one-to-all query from each station. But this is too time-consuming so that we develop heuristics to achieve a feasible precomputation time. The term flexible queries refers to the problem of computing shortest paths with further query parameters, such as the edge weight (e. g. travel time or distance), or restrictions (e. g. no toll roads). While Dijkstra’s algorithm only requires small changes to support such query parameters efficiently, existing algorithms based on precomputation become much more complicated. A naïve adaption of these algorithms would perform a separate precomputation for each possible value of the query parameters, but this is