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...ing timetable information as shortest path problem, the time-expanded and the time-dependent approach. For an overview of models and algorithms for optimally solving timetable information we refer to =-=[28]-=-. In any case the particular graphs considered are huge, especially if the model used for timetable information expands time by modelling each event by a single vertex in the graph. Moreover, the numb...

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...r contract no. FP6-021235-2 (project ARRIVAL).In this work, we evaluate the most prominent speed-up techniques on different types of input classes. At a glance, using the techniques on time-expanded =-=[7]-=- graphs for timetable information seems promising. Since road networks seem to have similar properties as railway networks—both incorporate some kind of natural hierarchy and both are sparse—one might...

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...n very successful on road networks [8, 16], but their adaption to public transit networks [2, 10] is harder than expected [1, 3, 4]. The problem of computing “best” journeys comes in several variants =-=[14]-=-: The simplest, called earliest arrival, takes a departure time as input, and determines a journey that arrives at the destination as early as possible. If further criteria, such as the number of tran...

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...o main approaches to model a public transport networks, known as Time-Dependent and Time-Expanded models. For an exhaustive description of the models and existing techniques we address the readers to =-=[7, 9]-=-. Typically the Time-Expanded model has three types of nodes: arrival node, departure node and transfer node. In our new model we eliminate transfer nodes and all the links from transfer nodes to depa...

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... and arrive before the time tA. Finally, we suggest an alternative simple measure for reliability of a given journey, expressed simply as the fraction of recorded timetables where the journey was successful and allowed to arrive at the destination on time. We provide efficient algorithms for computation of this measure. 2 Related Work The problem of finding a fastest journey (according to the planned timetable) using public transportation has been extensively studied in the literature. Common approaches model the transportation network as a graph and compute a shortest path in this graph (see [12] for a survey). Various improvements have been developed, and experimental studies suggest that these can also be used in practice (see, e.g., [2, 5, 14]). Recent approaches avoid the construction of a graph and process the timetable directly [6, 7]. For example, Delling et al. [6] describe an approach which is centered around transportation lines (such as train or bus lines) and which can be used to find all pareto-optimal journeys when the arrival time and the number of stops are considered as criteria. Bast et al. [1] observe that for two given stops, we can find and encode each sequence of...

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...works with appropriate link vertices, i. e., vertices (or stops) in different networks are identified with one another to allow for changes in modes of transportation. Note that, unlike previous work =-=[18]-=-, we do not necessarily require explicit footpaths in the public transportation networks (to walk between nearby stops). A query takes as input a source location s, a target location t, and a departur...