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Engineering Route Planning Algorithms
 ALGORITHMICS OF LARGE AND COMPLEX NETWORKS. LECTURE NOTES IN COMPUTER SCIENCE
, 2009
"... Algorithms for route planning in transportation networks have recently undergone a rapid development, leading to methods that are up to three million times faster than Dijkstra’s algorithm. We give an overview of the techniques enabling this development and point out frontiers of ongoing research on ..."
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Cited by 82 (39 self)
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Algorithms for route planning in transportation networks have recently undergone a rapid development, leading to methods that are up to three million times faster than Dijkstra’s algorithm. We give an overview of the techniques enabling this development and point out frontiers of ongoing research on more challenging variants of the problem that include dynamically changing networks, timedependent routing, and flexible objective functions.
SpeedUp Techniques for ShortestPath Computations
 IN PROCEEDINGS OF THE 24TH INTERNATIONAL SYMPOSIUM ON THEORETICAL ASPECTS OF COMPUTER SCIENCE (STACS’07
, 2007
"... During the last years, several speedup techniques for Dijkstra’s algorithm have been published that maintain the correctness of the algorithm but reduce its running time for typical instances. They are usually based on a preprocessing that annotates the graph with additional information which can ..."
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Cited by 20 (6 self)
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During the last years, several speedup techniques for Dijkstra’s algorithm have been published that maintain the correctness of the algorithm but reduce its running time for typical instances. They are usually based on a preprocessing that annotates the graph with additional information which can be used to prune or guide the search. Timetable information in public transport is a traditional application domain for such techniques. In this paper, we provide a condensed overview of new developments and extensions of classic results. Furthermore, we discuss how combinations of speedup techniques can be realized to take advantage from different strategies.
Experimental Study on SpeedUp Techniques for Timetable Information Systems
 PROCEEDINGS OF THE 7TH WORKSHOP ON ALGORITHMIC APPROACHES FOR TRANSPORTATION MODELING, OPTIMIZATION, AND SYSTEMS (ATMOS 2007
, 2007
"... During the last years, impressive speedup techniques for DIJKSTRA’s algorithm have been developed. Unfortunately, recent research mainly focused on road networks. However, fast algorithms are also needed for other applications like timetable information systems. Even worse, the adaption of recentl ..."
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Cited by 18 (10 self)
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During the last years, impressive speedup techniques for DIJKSTRA’s algorithm have been developed. Unfortunately, recent research mainly focused on road networks. However, fast algorithms are also needed for other applications like timetable information systems. Even worse, the adaption of recently developed techniques to timetable information is more complicated than expected. In this work, we check whether results from road networks are transferable to timetable information. To this end, we present an extensive experimental study of the most prominent speedup techniques on different types of inputs. It turns out that recently developed techniques are much slower on graphs derived from timetable information than on road networks. In addition, we gain amazing insights into the behavior of speedup techniques in general.
Intriguingly Simple and Fast Transit Routing
 In SEA, volume 7933 of LNCS
, 2013
"... Abstract. 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. Des ..."
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Cited by 9 (0 self)
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Abstract. 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 multicriteria 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 272ms on average. 1
The price of robustness in timetable information
, 2011
"... In timetable information in public transport the goal is to search for a good passenger’s path between an origin and a destination. Usually, the travel time and the number of transfers shall be minimized. In this paper, we consider robust timetable information, i.e. we want to identify a path which ..."
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Cited by 7 (1 self)
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In timetable information in public transport the goal is to search for a good passenger’s path between an origin and a destination. Usually, the travel time and the number of transfers shall be minimized. In this paper, we consider robust timetable information, i.e. we want to identify a path which will bring the passenger to the planned destination even in the case of delays. The classic notion of strict robustness leads to the problem of identifying those changing activities which will never break in any of the expected delay scenarios. We show that this is in general a strongly NPhard problem. Therefore, we propose a conservative heuristic which identifies a large subset of these robust changing activities in polynomial time by dynamic programming and so allows us to find strictly robust paths efficiently. We also transfer the notion of light robustness, originally introduced for timetabling, to timetable information. In computational experiments we then study the price of strict and light robustness: How much longer is the travel time of a robust path than of a shortest one according to the published schedule? Based on the schedule of highspeed trains within Germany of 2011, we quantitatively explore the tradeoff between the level of guaranteed robustness and the increase in travel time. Strict robustness turns out to be too conservative, while light robustness is promising: a modest level of guarantees is achievable at a reasonable price for the majority of passengers.
Finding Multicriteria Optimal Paths in Multimodal Public Transportation Networks using the Transit Algorithm
"... We present an algorithm to find optimal routes in a multimodal public transportation network. Our model takes into account many realistic features such as walking between multimodal stations, transfer times, traffic days, multiple objectives and finding connections between geographical locations r ..."
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We present an algorithm to find optimal routes in a multimodal public transportation network. Our model takes into account many realistic features such as walking between multimodal stations, transfer times, traffic days, multiple objectives and finding connections between geographical locations rather than just source and destination stations. In order to provide useful routing directions, we consider the robustness of the provided solutions. In addition we present numerous speed up techniques that reduce both the preprocessing time and storage. Our preliminary experiments on the Sydney transit network are promising.
Robust routing in urban public transportation: How to find reliable journeys based on past observations.
 In ATMOS,
, 2013
"... Abstract We study the problem of robust routing in urban public transportation networks. In order to propose solutions that are robust for typical delays, we assume that we have past observations of real traffic situations available. In particular, we assume that we have "daily records" c ..."
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Abstract We study the problem of robust routing in urban public transportation networks. In order to propose solutions that are robust for typical delays, we assume that we have past observations of real traffic situations available. In particular, we assume that we have "daily records" containing the observed travel times in the whole network for a few past days. We introduce a new concept to express a solution that is feasible in any record of a given public transportation network. We adapt the method of Buhmann et al. ACM Subject Classification F.2.2 Nonnumerical Algorithms and Problems, G.2.2 Graph Theory (Graph algorithms, Network problems), I.2.6 Learning Keywords and phrases Introduction We study the problem of routing in urban public transportation networks, such as tram and bus networks in large cities, focusing on the omnipresent uncertain situations when (typical) delays occur. In particular, we search for robust routes that allow reliable yet quick passenger transportation. We think of a "dense" tram network in a large city containing many tram lines, where each tram line is a sequence of stops that is served repeatedly during the day, and where there are several options to get from one location to another. Such a network usually does not contain clear hierarchical structure (as opposed to train networks), and each line is served with high frequency. Given two tram stops a and b together with a latest arrival time t A , our goal is to provide a simple yet robust description of how to travel in the *
Computing Multimodal Journeys in Practice?
"... Abstract. We study the problem of finding multimodal journeys in transportation networks, including unrestricted walking, driving, cycling, and schedulebased public transportation. A natural solution to this problem is to use multicriteria search, but it tends to be slow and to produce too many jou ..."
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Abstract. We study the problem of finding multimodal journeys in transportation networks, including unrestricted walking, driving, cycling, and schedulebased public transportation. A natural solution to this problem is to use multicriteria search, but it tends to be slow and to produce too many journeys, several of which are of little value. We propose algorithms to compute a full Pareto set and then score the solutions in a postprocessing step using techniques from fuzzy logic, quickly identifying the most significant journeys. We also propose several (still multicriteria) heuristics to find similar journeys much faster, making the approach practical even for large metropolitan areas. 1
Recoverable Robust Timetable Information ∗
, 2013
"... Timetable information is the process of determining a suitable travel route for a passenger. Due to delays in the original timetable, in practice it often happens that the travel route cannot be used as originally planned. For a passenger being already en route, it would hence be useful to know abou ..."
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Timetable information is the process of determining a suitable travel route for a passenger. Due to delays in the original timetable, in practice it often happens that the travel route cannot be used as originally planned. For a passenger being already en route, it would hence be useful to know about alternatives that ensure that his/her destination can be reached. In this work we propose a recoverable robust approach to timetable information; i.e., we aim at finding travel routes that can easily be updated when delays occur during the journey. We present polynomialtime algorithms for this problem and evaluate the performance of the routes obtained this way on schedule data of the German train network of 2013 and simulated delay scenarios.
Shortest Paths in Networks
"... Finding the shortest path between two points in a network is a fundamental problem in computer science with many applications. By exploiting properties of the underlying networks we improve and extend one of the stateoftheart al ..."
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Finding the shortest path between two points in a network is a fundamental problem in computer science with many applications. By exploiting properties of the underlying networks we improve and extend one of the stateoftheart al