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18
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.
Combining Hierarchical and GoalDirected SpeedUp Techniques for Dijkstra’s Algorithm
 PROCEEDINGS OF THE 7TH WORKSHOP ON EXPERIMENTAL ALGORITHMS (WEA’08), VOLUME 5038 OF LECTURE NOTES IN COMPUTER SCIENCE
, 2008
"... In recent years, highly effective hierarchical and goaldirected speedup techniques for routing in large road networks have been developed. This paper makes a systematic study of combinations of such techniques. These combinations turn out to give the best results in many scenarios, including graphs ..."
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Cited by 60 (24 self)
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In recent years, highly effective hierarchical and goaldirected speedup techniques for routing in large road networks have been developed. This paper makes a systematic study of combinations of such techniques. These combinations turn out to give the best results in many scenarios, including graphs for unit disk graphs, grid networks, and timeexpanded timetables. Besides these quantitative results, we obtain general insights for successful combinations.
SHARC: Fast and robust unidirectional routing
 IN: WORKSHOP ON ALGORITHM ENGINEERING AND EXPERIMENTS (ALENEX
, 2008
"... During the last years, impressive speedup techniques for Dijkstra’s algorithm have been developed. Unfortunately, the most advanced techniques use bidirectional search which makes it hard to use them in scenarios where a backward search is prohibited. Even worse, such scenarios are widely spread, e ..."
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Cited by 52 (20 self)
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During the last years, impressive speedup techniques for Dijkstra’s algorithm have been developed. Unfortunately, the most advanced techniques use bidirectional search which makes it hard to use them in scenarios where a backward search is prohibited. Even worse, such scenarios are widely spread, e.g., timetableinformation systems or timedependent networks. In this work, we present a unidirectional speedup technique which competes with bidirectional approaches. Moreover, we show how to exploit the advantage of unidirectional routing for fast exact queries in timetable information systems and for fast approximative queries in timedependent scenarios. By running experiments on several inputs other than road networks, we show that our approach is very robust to the input.
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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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
RoundBased Public Transit Routing
 In ALENEX
, 2012
"... We study the problem of computing all Paretooptimal journeys in a dynamic public transit network for two criteria: arrival time and number of transfers. Existing algorithms consider this as a graph problem, and solve it using variants of Dijkstra’s algorithm. Unfortunately, this leads to either h ..."
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Cited by 8 (3 self)
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We study the problem of computing all Paretooptimal journeys in a dynamic public transit network for two criteria: arrival time and number of transfers. Existing algorithms consider this as a graph problem, and solve it using variants of Dijkstra’s algorithm. Unfortunately, this leads to either high query times or suboptimal solutions. We take a different approach. We introduce RAPTOR, our novel roundbased public transit router. Unlike previous algorithms, it is not Dijkstrabased, 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. Moreover, it can be easily extended to handle flexible departure times or arbitrary additional criteria, such as fare zones. When run on London’s complex public transportation network, RAPTOR computes all Paretooptimal journeys between two random locations an order of magnitude faster than previous approaches, which easily enables interactive applications. 1
Engineering TimeExpanded Graphs for Faster Timetable Information
, 2009
"... We present an extension of the wellknown timeexpanded approach for timetable information. By remodeling unimportant stations, we are able to obtain faster query times with less space consumption than the original model. Moreover, we show that our extensions harmonize well with speedup techniques ..."
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Cited by 7 (4 self)
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We present an extension of the wellknown timeexpanded approach for timetable information. By remodeling unimportant stations, we are able to obtain faster query times with less space consumption than the original model. Moreover, we show that our extensions harmonize well with speedup techniques whose adaption to timetable networks is more challenging than one might expect.
MultiHop Ride Sharing
"... We study the problem of ride sharing in road networks. Current approaches to this problem focus on simple bulletin board like services or on algorithms that do not allow to transfer. In this work, we present a solution with an arbitrary number of transfers that respects personal preferences of the ..."
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Cited by 4 (0 self)
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We study the problem of ride sharing in road networks. Current approaches to this problem focus on simple bulletin board like services or on algorithms that do not allow to transfer. In this work, we present a solution with an arbitrary number of transfers that respects personal preferences of the users. We engineer the ride sharing problem by searching a graph that represents a timetable network similar to those used for train networks. Our experimental analysis shows that our solution provides good performance and that it is significantly faster than a naive search. The algorithm achieves about an order of magnitude higher speedups over Dijkstra’s algorithm than what could be expected from previous work.
Batch Dynamic SingleSource ShortestPath Algorithms: An Experimental Study
, 2009
"... A dynamic shortestpath algorithm is called a batch algorithm if it is able to handle graph changes that consist of multiple edge updates at a time. In this paper we focus on fullydynamic batch algorithms for singlesource shortest paths in directed graphs with positive edge weights. We give an exte ..."
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Cited by 3 (0 self)
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A dynamic shortestpath algorithm is called a batch algorithm if it is able to handle graph changes that consist of multiple edge updates at a time. In this paper we focus on fullydynamic batch algorithms for singlesource shortest paths in directed graphs with positive edge weights. We give an extensive experimental study of the existing algorithms for the singleedge and the batch case, including a broad set of test instances. We further present tuned variants of the already existing SWSFFPalgorithm being up to 15 times faster than SWSFFP. A surprising outcome of the paper is the astonishing level of data dependency of the algorithms.
A Generalization of Dijkstra’s Shortest Path Algorithm with Applications to VLSI Routing
"... We generalize Dijkstra’s algorithm for finding shortest paths in digraphs with nonnegative integral edge lengths. Instead of labeling individual vertices we label subgraphs which partition the given graph. We can achieve much better running times if the number of involved subgraphs is small compare ..."
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Cited by 3 (2 self)
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We generalize Dijkstra’s algorithm for finding shortest paths in digraphs with nonnegative integral edge lengths. Instead of labeling individual vertices we label subgraphs which partition the given graph. We can achieve much better running times if the number of involved subgraphs is small compared to the order of the original graph and the shortest path problems restricted to these subgraphs is computationally easy. As an application we consider the VLSI routing problem, where we need to find millions of shortest paths in partial grid graphs with billions of vertices. Here, our algorithm can be applied twice, once in a coarse abstraction (where the labeled subgraphs are rectangles), and once in a detailed model (where the labeled subgraphs are intervals). Using the result of the first algorithm to speed up the second one via goaloriented techniques leads to considerably reduced running time. We illustrate this with a stateoftheart routing tool on leadingedge industrial chips.
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 *