We study the problem of computing all Pareto-optimal journeys in a public transit network regarding the two criteria of arrival time and number of transfers taken. We take a novel approach, focusing on trips and transfers between them, allowing fine-grained modeling. Our experiments on the metropolitan network of London show that the algorithm computes full 24-hour profiles in 70ms after a preprocessing phase of 30s, allowing fast queries in dynamic scenarios.
Speeding up multi-criteria search in real timetable information systems remains a challenge in spite of impressive progress achieved in recent years for related problems in road networks. Our goal is to perform multi-criteria range queries, that is, to find all Pareto-optimal connections with respect to travel time and number of transfers within a given start time interval. This problem can be modeled as a path search problem in a time- and event-dependent graph. In this paper, we investigate two key speed-up techniques for a multi-criteria variant of 's algorithm --- arc flags and contraction --- which seem to be strong candidates for railway networks, too. We describe in detail how these two techniques have to be adapted for a multi-criteria scenario and explain why we can expect only marginal speed-ups (compared to observations in road networks) from a direct implementation. Based on these insights we extend traditional arc-flags to and introduce as a substitute for node contraction. A computational study on real queries demonstrates that these techniques combined with goal-directed search lead to a speed-up of factor 13.08 over the baseline variant for range queries for a full day. We consider two approaches that model timetable information in public transportation systems as shortest-path problems in weighted graphs. In the time-expanded approach, every event at a station, e.g., the departure of a train, is modeled as a node in the graph, while in the time-dependent approach the graph contains only one node per station. Both approaches have been recently considered for (a simplified version of) the earliest arrival problem, but little is known about their relative performance. Thus far, there are only theoretical arguments in favor of the time-dependent approach. In this paper, we provide the first extensive experimental comparison of the two approaches. Using several real-world data sets, we evaluate the performance of the basic models and of several new extensions towards realistic modeling. Furthermore, new insights on solving bicriteria optimization problems in both models are presented. The time-expanded approach turns out to be more robust for modeling more complex scenarios, whereas the time-dependent approach shows a clearly better performance.