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26
TDrive: Driving directions based on taxi trajectories
 ACM SIGSPATIAL GIS
, 2010
"... GPSequipped taxis can be regarded as mobile sensors probing traffic flows on road surfaces, and taxi drivers are usually experienced in finding the fastest (quickest) route to a destination based on their knowledge. In this paper, we mine smart driving directions from the historical GPS trajectorie ..."
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Cited by 96 (21 self)
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GPSequipped taxis can be regarded as mobile sensors probing traffic flows on road surfaces, and taxi drivers are usually experienced in finding the fastest (quickest) route to a destination based on their knowledge. In this paper, we mine smart driving directions from the historical GPS trajectories of a large number of taxis, and provide a user with the practically fastest route to a given destination at a given departure time. In our approach, we propose a timedependent landmark graph, where a node (landmark) is a road segment frequently traversed by taxis, to model the intelligence of taxi drivers and the properties of dynamic road networks. Then, a VarianceEntropyBased Clustering approach is devised to estimate the distribution of travel time between two landmarks in different time slots. Based on this graph, we design a twostage routing algorithm to compute the practically fastest route. We build our system based on a realworld trajectory dataset generated by over 33,000 taxis in a period of 3 months, and evaluate the system by conducting both synthetic experiments and inthefield evaluations. As a result, 60–70 % of the routes suggested by our method are faster than the competing methods, and 20 % of the routes share the same results. On average, 50 % of our routes are at least 20 % faster than the competing approaches.
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.
TimeDependent Route Planning
 Robust and Online LargeScale Optimization, LNCS
, 2009
"... Abstract. In this paper, we present an overview over existing speedup techniques for timedependent route planning. Apart from only explaining each technique one by one, we follow a more systematic approach. We identify basic ingredients of these recent techniques and show how they need to be augmen ..."
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Cited by 44 (17 self)
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Abstract. In this paper, we present an overview over existing speedup techniques for timedependent route planning. Apart from only explaining each technique one by one, we follow a more systematic approach. We identify basic ingredients of these recent techniques and show how they need to be augmented to guarantee correctness in timedependent networks. With the ingredients adapted, three efficient speedup techniques can be set up: CoreALT, SHARC, and Contraction Hierarchies. Experiments on realworld data deriving from road networks and public transportation confirm that these techniques allow the fast computation of timedependent shortest paths. 1
TimeDependent SHARCRouting
 In Proceedings of the 16th Annual European Symposium on Algorithms (ESA’08
, 2008
"... In recent years, many speedup techniques for Dijkstra’s algorithm have been developed that make the computation of shortest paths in static road networks a matter of microseconds. However, only few of those techniques work in timedependent networks which, unfortunately, appear quite frequently in ..."
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Cited by 17 (9 self)
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In recent years, many speedup techniques for Dijkstra’s algorithm have been developed that make the computation of shortest paths in static road networks a matter of microseconds. However, only few of those techniques work in timedependent networks which, unfortunately, appear quite frequently in reality: Roads are predictably congested by traffic jams, and efficient timetable information systems rely on timedependent networks. Hence, a fast technique for routing in such networks is needed. In this work, we present an efficient timedependent route planning algorithm. It is based on our recently introduced SHARC algorithm, which we adapt by augmenting its basic ingredients such that correctness can still be guaranteed in a timedependent scenario. As a result, we are able to efficiently compute exact shortest paths in timedependent continentalsized transportation networks, both of roads and of railways. It should be noted that timedependent SHARC was the first efficient algorithm for timedependent route planning. 1
Accelerating MultiModal Route Planning by AccessNodes
 PROCEEDINGS OF THE 17TH ANNUAL EUROPEAN SYMPOSIUM ON ALGORITHMS (ESA’09), LECTURE NOTES IN COMPUTER SCIENCE
, 2009
"... Recent research on fast route planning algorithms focused either on road networks or on public transportation. However, on the long run, we are interested in planning routes in a multimodal scenario: we start by car to reach the nearest train station, ride the train to the airport, fly to an airp ..."
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Cited by 12 (5 self)
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Recent research on fast route planning algorithms focused either on road networks or on public transportation. However, on the long run, we are interested in planning routes in a multimodal scenario: we start by car to reach the nearest train station, ride the train to the airport, fly to an airport near our destination and finally take a taxi. In other words, we need to incorporate public transportation into road networks. However, we do not want to switch the type of transportation too often. We end up in a label constrained variant of the shortest path problem. In this work, we present a first efficient solution to a restricted variant of this problem including experimental results for transportation networks with up to 125 Mio. edges.
Shortest paths in fifo timedependent networks: theory and algorithms
, 2004
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Parallel Computation of Best Connections in Public Transportation Networks. Journal version. Submitted for publication. Online available at i11www.iti.unikarlsruhe
, 2011
"... Abstract—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 socalled onetoall profilesearch problem in public transportation ..."
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Cited by 4 (3 self)
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Abstract—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 socalled onetoall profilesearch 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 speedups on standard multicore servers. Our approach exploits the facts that first, timedependent traveltime functions in such networks can be represented as a special class of piecewise linear functions, and that second, only few connections from S are useful to travel far away. Introducing the connectionsetting property, we are able to extend DIJKSTRA’s algorithm in a sound manner. Furthermore, we also accelerate stationtostation 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 (Los Angeles) on a standard multicore server in less than 55 ms on average. I.
Shortest Paths in TimeDependent FIFO Networks Using Edge Load Forecasts
, 2009
"... We study the problem of finding shortest paths in timedependent networks with edge load forecasts where the behavior of each edge is modeled as a timedependent arrival function with FIFO property. Here, we present a new algorithm that computes for a given start node s and destination node d, the sh ..."
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Cited by 4 (0 self)
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We study the problem of finding shortest paths in timedependent networks with edge load forecasts where the behavior of each edge is modeled as a timedependent arrival function with FIFO property. Here, we present a new algorithm that computes for a given start node s and destination node d, the shortest paths and earliest arrival times for all possible starting times. Our algorithm runs in time O((Fd + λ)(E  + V log V )) where Fd is the output size (number of linear pieces needed to represent the earliest arrival time function) and λ is the input size (number of linear pieces needed to represent the local earliest arrival time functions for all edges in the network). Our method improves significantly on the best previously known algorithm which requires time O(FmaxV E) where Fmax ≥ Fd is the maximum number of linear pieces needed to represent the earliest arrival time function between the start node s to any node in the network. It has been conjectured that there are cases where Fmax is of superpolynomial size; however, even in such cases, Fd might still be of linear size. In such cases, our algorithm would take polynomial time to find the solution, while other methods require superpolynomial time. Both of the above methods are not useful in practice for graphs where Fd is of superpolynomial size. For such graphs, we present the first approximation method to compute for all possible starting times at s, the earliest arrival times at d within error at most ǫ. Our algorithm runs in time O ( ∆ (E  + V log V )) where ∆ is the difference beǫ tween the earliest arrival times at d for the latest and earliest starting times at s.
On the Complexity of TimeDependent Shortest Paths
"... We investigate the complexity of shortest paths in timedependent graphs, in which the costs of edges vary as a function of time, and as a result the shortest path between two nodes s and d can change over time. Our main result is that when the edge cost functions are (polynomialsize) piecewise line ..."
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Cited by 4 (0 self)
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We investigate the complexity of shortest paths in timedependent graphs, in which the costs of edges vary as a function of time, and as a result the shortest path between two nodes s and d can change over time. Our main result is that when the edge cost functions are (polynomialsize) piecewise linear, the shortest path from s to d can change Θ(log n) n times, settling a severalyearold conjecture of Dean [Technical Reports, 1999, 2004]. We also show that the complexity is polynomial if the slopes of the linear function come from a restricted class, present an outputsensitive algorithm for the general case, and describe a scheme for a (1 + ɛ)approximation of the travel time function in nearquadratic space. Finally, despite the fact that the arrival time function may have superpolynomial complexity, we show that a minimum delay path for any departure time interval can be computed in polynomial time. 1