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21
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 24 (11 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.
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 23 (14 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 SpeedUp Techniques for ShortestPath Computations
 In Proc. 3rd Workshop on Experimental and Efficient Algorithms. LNCS
, 2004
"... Computing a shortest path from one node to another in a directed graph is a very common task in practice. This problem is classically solved by Dijkstra's algorithm. Many techniques are known to speed up this algorithm heuristically, while optimality of the solution can still be guaranteed. In m ..."
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Cited by 20 (6 self)
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Computing a shortest path from one node to another in a directed graph is a very common task in practice. This problem is classically solved by Dijkstra's algorithm. Many techniques are known to speed up this algorithm heuristically, while optimality of the solution can still be guaranteed. In most studies, such techniques are considered individually.
private communication
"... We study a graphaugmentation problem arising from a technique applied in recent approaches for route planning. Many such methods enhance the graph by inserting shortcuts, i.e., additional edges (u,v) such that the length of (u,v) is the distance from u to v. Given a weighted, directed graph G and a ..."
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Cited by 19 (2 self)
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We study a graphaugmentation problem arising from a technique applied in recent approaches for route planning. Many such methods enhance the graph by inserting shortcuts, i.e., additional edges (u,v) such that the length of (u,v) is the distance from u to v. Given a weighted, directed graph G and a number c ∈ Z>0, the shortcut problem asks how to insert c shortcuts into G such that the expected number of edges that are contained in an edgeminimal shortest path from a random node s to a random node t is minimal. In this work, we study the algorithmic complexity of the problem and give approximation algorithms for a special graph class. Further, we state ILPbased exact approaches and show how to stochastically evaluate a given shortcut assignment on graphs that are too large to do so exactly. Submitted:
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 15 (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.
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 13 (7 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 11 (7 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.
Engineering the LabelConstrained Shortest Path Algorithm NDSSL
, 2007
"... We consider a generalization of the pointtopoint (and singlesource) shortest path problem to instances where the shortest path must satisfy a formal language constraint. Given an alphabet Σ, a (directed) network G whose edges are weighted and Σlabeled, and a regular grammar L ⊆ Σ ∗ , the Regular ..."
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Cited by 9 (1 self)
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We consider a generalization of the pointtopoint (and singlesource) shortest path problem to instances where the shortest path must satisfy a formal language constraint. Given an alphabet Σ, a (directed) network G whose edges are weighted and Σlabeled, and a regular grammar L ⊆ Σ ∗ , the Regular Language Constrained Shortest Path problem consists of finding a shortest path p in G complying with the additional constraint that l(p) ∈ L. Here l(p) denotes the unique word given by concatenating the Σlabels of the edges along the path p. In this chapter, we summarize our recent results and present new theoretical and experimental results for the Regular Language Constrained Shortest problem. We also present extensions of several speedup techniques developed earlier for the standard pointtopoint shortest path problem. These speedup techniques are integrated within the basic algorithmic framework to yield new algorithms for the problem. In order to evaluate the performance of the basic algorithm and its extensions, we have performed preliminary experimental analysis. Through our experiments, we study the scalability of the algorithm with respect to the network size as well as with respect to the constraining language complexity. Further, we study the effectiveness of speedup techniques such as goaldirected and bidirectional search when applied to the Regular Language Constrained Shortest problem. 1
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 4 (3 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.
The Shortcut Problem  Complexity and Approximation
, 2009
"... During the last years, speedup techniques for DIJKSTRA’s algorithm have been developed that make the computation of shortest paths a matter of microseconds even on huge road networks. The most sophisticated methods enhance the graph by inserting shortcuts, i.e. additional edges, that represent sh ..."
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Cited by 3 (2 self)
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During the last years, speedup techniques for DIJKSTRA’s algorithm have been developed that make the computation of shortest paths a matter of microseconds even on huge road networks. The most sophisticated methods enhance the graph by inserting shortcuts, i.e. additional edges, that represent shortest paths in the graph. Until now, all existing shortcutinsertion strategies are heuristics and no theoretical results on the topic are known. In this work, we formalize the problem of adding shortcuts as a graph augmentation problem, study the algorithmic complexity of the problem, give approximation algorithms and show how to stochastically evaluate a given shortcut assignment on graphs that are too big to evaluate it exactly.