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.
Other approaches do not use graphs at all. (Round-bAsed Public Transit Optimized Router) @cite_16 is a dynamic program. In each round, it computes earliest arrival times for journeys with @math transfers, where @math is the current round number. It does this by scanning along lines and, at each stop, checking for the earliest trip of that line that can be reached. It outperforms Dijkstra-based approaches in practice. The @cite_6 operates on (trip segments of length @math ). It orders them by departure time into a single array. During queries, this array is then scanned once, which is very fast in practice due to the linear memory access pattern.
@cite_16 @cite_6
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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. 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. Exploiting parallelism in route planning algorithms is a challenging algorithmic problem with obvious applications in mobile navigation and timetable information systems. In this work, we present a novel algorithm for the one-to-all profile-search problem in public transportation networks. It answers the question for all fastest connections between a given station S and any other station at any time of the day in a single query. This algorithm allows for a very natural parallelization, yielding excellent speed-ups on standard multicore servers. Our approach exploits the facts that, first, time-dependent travel-time functions in such networks can be represented as a special class of piecewise linear functions and, second, only few connections from S are useful to travel far away. Introducing the connection-setting property, we are able to extend Dijkstra's algorithm in a sound manner. Furthermore, we also accelerate station-to-station queries by preprocessing important connections within the public transportation network. As a result, we are able to compute all relevant connections between two random stations in a complete public transportation network of a big city (New York) on a standard multi-core server in real time.