We study the problem of planning Pareto-optimal journeys in public transit networks. Most existing algorithms and speed-up techniques work by computing subjourneys to intermediary stops until the destination is reached. In contrast, the trip-based model focuses on trips and transfers between them, constructing journeys as a sequence of trips. In this paper, we develop a speed-up technique for this model inspired by principles behind existing state-of-the-art speed-up techniques, Transfer Pattern and Hub Labelling. The resulting algorithm allows us to compute Pareto-optimal (with respect to arrival time and number of transfers) 24-hour profiles on very large real-world networks in less than half a millisecond. Compared to the current state of the art for bicriteria queries on public transit networks, this is up to two orders of magnitude faster, while increasing preprocessing overhead by at most one order of magnitude.
RAPTOR @cite_19 foregoes modelling the data as a graph and instead operates directly on the timetable data. In addition to travel time and number of transfers, they also consider price as a criteria. The Connection Scan Algorithm (CSA) @cite_12 also eschews graphs and instead works on an ordered array of connections to find Pareto-optimal journeys with respect to travel time and number of transfers. Accelerated CSA @cite_7 is a speed-up technique for CSA that works via partitioning of the network. Unlike the original CSA, it was only evaluated as a single-criterion algorithm, using the number of transfers as a tiebreaker between journeys with identical arrival time.
@cite_19 @cite_7 @cite_12
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This paper studies the problem of computing optimal journeys in dynamic public transit networks. We introduce a novel algorithmic framework, called Connection Scan Algorithm (CSA), to compute journeys. It organizes data as a single array of connections, which it scans once per query. Despite its simplicity, our algorithm is very versatile. We use it to solve earliest arrival and multi-criteria profile queries. Moreover, we extend it to handle the minimum expected arrival time (MEAT) problem, which incorporates stochastic delays on the vehicles and asks for a set of (alternative) journeys that in its entirety minimizes the user’s expected arrival time at the destination. Our experiments on the dense metropolitan network of London show that CSA computes MEAT queries, our most complex scenario, in 272 ms on average. We study the problem of computing all Pareto-optimal journeys in a dynamic public transit network for multiple criteria, such as arrival time and number of transfers. Existing algorithms consider this as a graph problem and solve it using various graph search algorithms. Unfortunately, this leads to either high query times or suboptimal solutions. We take a different approach. We introduce RAPTOR, our novel round-based public transit router. Unlike previous algorithms, it is not Dijkstra-based, looks at each route such as a bus line in the network at most once per round, and can be made even faster with simple pruning rules and parallelization using multiple cores. Because it does not rely on preprocessing, RAPTOR works in fully dynamic scenarios. Starting from arrival time and number of transfers as criteria, it can be easily extended to handle flexible departure times or arbitrary additional criteria. As practical examples we consider fare zones and reliability of transfers. When run on complex public transportation networks such as London, RAPTOR computes all Pareto-optimal journeys between two random locations an order of magnitude faster than previous approaches, which easily enables interactive applications. We consider the application of route planning in large public-transportation networks (buses, trains, subways, etc). Many connections in such networks are operated at periodic time intervals. When a set of connections has sufficient periodicity, it becomes more efficient to store the time range and frequency (e.g., every 15 minutes from 8:00am-6:00pm) instead of storing each of the time events separately. Identifying an optimal frequency-compression is NP-hard, so we present a time- and space-efficient heuristic. We show how we can use this compression to not only save space but also query time. We particularly consider profile queries, which ask for all optimal routes with departure times in a given interval (e.g., a whole day). In particular, we design a new version of Dijkstra's algorithm that works with frequency-based labels and is suitable for profile queries. We evaluate the savings of our approach on two metropolitan and three country-wide public-transportation networks. On our largest network, we simultaneously achieve a better space consumption than all previous methods as well as profile query times that are about 5 times faster than the best previous method. We also improve Transfer Patterns, a state-of-the-art technique for fully realistic route planning in large public-transportation networks. In particular, we accelerate the expensive preprocessing by a factor of 60 compared to the original publication. 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.