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20
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.
Landmarkbased routing in dynamic graphs
 IN: 6TH WORKSHOP ON EXPERIMENTAL ALGORITHMS
, 2007
"... Many speedup techniques for route planning in static graphs exist, only few of them are proven to work in a dynamic scenario. Most of them use preprocessed information, which has to be updated whenever the graph is changed. However, goal directed search based on landmarks (ALT) still performs cor ..."
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Cited by 29 (8 self)
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Many speedup techniques for route planning in static graphs exist, only few of them are proven to work in a dynamic scenario. Most of them use preprocessed information, which has to be updated whenever the graph is changed. However, goal directed search based on landmarks (ALT) still performs correct queries as long as an edge weight does not drop below its initial value. In this work, we evaluate the robustness of ALT with respect to traffic jams. It turns out that—by increasing the efficiency of ALT—we are able to perform fast (down to 20 ms on the Western European network) random queries in a dynamic scenario without updating the preprocessing as long as the changes in the network are moderate. Furthermore, we present how to update the preprocessed data without any additional space consumption and how to adapt the ALT algorithm to a timedependent scenario. A timedependent scenario models predictable changes in the network, e.g. traffic jams due to rush hour.
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.
Bidirectional A ∗ Search for TimeDependent Fast Paths
"... Abstract. The computation of pointtopoint shortest paths on timedependent road networks has many practical applications, but there have been very few works that propose efficient algorithms for large graphs. One of the difficulties of route planning on timedependent graphs is that we do not know ..."
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Cited by 16 (10 self)
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Abstract. The computation of pointtopoint shortest paths on timedependent road networks has many practical applications, but there have been very few works that propose efficient algorithms for large graphs. One of the difficulties of route planning on timedependent graphs is that we do not know the exact arrival time at the destination, hence applying bidirectional search is not straightforward; we propose a novel approach based on A ∗ with landmarks (ALT) that starts a search from both the source and the destination node, where the backward search is used to bound the set of nodes that have to be explored by the forward search. Extensive computational results show that this approach is very effective in practice if we are willing to accept a small approximation factor, resulting in a speedup of several times with respect to Dijkstra’s algorithm while finding only slightly suboptimal solutions. 1
Highperformance multilevel graphs
 IN: 9TH DIMACS IMPLEMENTATION CHALLENGE
, 2006
"... Shortestpath computation is a frequent task in practice. Owing to evergrowing realworld graphs, there is a constant need for faster algorithms. In the course of time, a large number of techniques to heuristically speed up Dijkstra’s shortestpath algorithm have been devised. This work reviews the ..."
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Cited by 13 (4 self)
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Shortestpath computation is a frequent task in practice. Owing to evergrowing realworld graphs, there is a constant need for faster algorithms. In the course of time, a large number of techniques to heuristically speed up Dijkstra’s shortestpath algorithm have been devised. This work reviews the multilevel technique to answer shortestpath queries exactly [SWZ02, HSW06], which makes use of a hierarchical decomposition of the input graph and precomputation of supplementary information. We develop this preprocessing to the maximum and introduce several ideas to enhance this approach considerably, by reorganizing the precomputed data in partial graphs and optimizing them individually. To answer a given query, certain partial graphs are combined to a search graph, which can be explored by a simple and fast procedure. Experiments confirm query times of less than 200 µs for a road graph with over 15 million vertices.
On kskip Shortest Paths
"... Given two vertices s, t in a graph, let P be the shortest path (SP) from s to t, and P ⋆ a subset of the vertices in P. P ⋆ is a kskip shortest path from s to t, if it includes at least a vertex out of every k consecutive vertices in P. In general, P ⋆ succinctly describes P by sampling the vertice ..."
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Cited by 11 (0 self)
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Given two vertices s, t in a graph, let P be the shortest path (SP) from s to t, and P ⋆ a subset of the vertices in P. P ⋆ is a kskip shortest path from s to t, if it includes at least a vertex out of every k consecutive vertices in P. In general, P ⋆ succinctly describes P by sampling the vertices in P with a rate of at least 1/k. This makes P ⋆ a natural substitute in scenarios where reporting every single vertex of P is unnecessary or even undesired. This paper studies kskip SP computation in the context of spatial network databases (SNDB). Our technique has two properties crucial for realtime query processing in SNDB. First, our solution is able to answer kskip queries significantly faster than finding the original SPs in their entirety. Second, the previous objective is achieved with a structure that occupies less space than storing the underlying road network. The proposed algorithms are the outcome of a careful theoretical analysis that reveals valuable insight into the characteristics of the kskip SP problem. Their efficiency has been confirmed by extensive experiments with real data.
Timetable Information: Models and Algorithms
, 2006
"... We give an overview of models and efficient algorithms for optimally solving timetable information problems like “given a departure and an arrival station as well as a departure time, which is the connection that arrives as early as possible at the arrival station?” Two main approaches that transfor ..."
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Cited by 10 (7 self)
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We give an overview of models and efficient algorithms for optimally solving timetable information problems like “given a departure and an arrival station as well as a departure time, which is the connection that arrives as early as possible at the arrival station?” Two main approaches that transform the problems into shortest path problems are reviewed, including issues like the modeling of realistic details (e.g., train transfers) and further optimization criteria (e.g., the number of transfers). An important topic is also multicriteria optimization, where in general all attractive connections with respect to several criteria shall be determined. Finally, we discuss the performance of the described algorithms, which is crucial for their application in a real system.
HighPerformance MultiLevel Routing
 DIMACS SERIES IN DISCRETE MATHEMATICS AND THEORETICAL COMPUTER SCIENCE
, 2008
"... Shortestpath computation is a frequent task in practice. Owing to evergrowing realworld graphs, there is a constant need for faster algorithms. In the course of time, a large number of techniques to heuristically speed up Dijkstra’s shortestpath algorithm have been devised. This work reviews the ..."
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Cited by 9 (7 self)
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Shortestpath computation is a frequent task in practice. Owing to evergrowing realworld graphs, there is a constant need for faster algorithms. In the course of time, a large number of techniques to heuristically speed up Dijkstra’s shortestpath algorithm have been devised. This work reviews the multilevel technique to answer shortestpath queries exactly [24, 9], which makes use of a hierarchical decomposition of the input graph and precomputation of supplementary information. We develop this preprocessing to the maximum and introduce several ideas to enhance this approach considerably, by reorganizing the precomputed data in partial graphs and optimizing them individually. To answer a given query, certain partial graphs are combined to a search graph, which can be explored by a simple and fast procedure. The concept behind the construction of the search graph is such that query times depend mainly on the number of partial graphs included. This is confirmed by experiments with different road graphs, each containing several million vertices, and time, distance, and unit metrics. Our query algorithm computes the distance between any pair of vertices in no more than 40 µs, however, a lengthy preprocessing is required to achieve this query performance.