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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 80 (38 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.
PHAST: hardwareaccelerated shortest path trees
 J. PARALLEL DISTRIB. COMPUT
, 2013
"... We present a novel algorithm to solve the nonnegative singlesource shortest path problem on road networks and graphs with low highway dimension. After a quick preprocessing phase, we can compute all distances from a given source in the graph with essentially a linear sweep over all vertices. Becaus ..."
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Cited by 19 (4 self)
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We present a novel algorithm to solve the nonnegative singlesource shortest path problem on road networks and graphs with low highway dimension. After a quick preprocessing phase, we can compute all distances from a given source in the graph with essentially a linear sweep over all vertices. Because this sweep is independent of the source, we are able to reorder vertices in advance to exploit locality. Moreover, our algorithm takes advantage of features of modern CPU architectures, such as SSE and multiple cores. Compared to Dijkstra’s algorithm, our method needs fewer operations, has better locality, and is better able to exploit parallelism at multicore and instruction levels. We gain additional speedup when implementing our algorithm on a GPU, where it is up to three orders of magnitude faster than Dijkstra’s algorithm on a highend CPU. This makes applications based on allpairs shortestpaths practical for continentalsized road networks. Several algorithms, such as computing the graph diameter, arc flags, or exact reaches, can be greatly accelerated by our method.
A Comparison of HighLevel Approaches for Speeding up Pathfinding
 In Proceedings of the 4th Conference on Artificial Intelligence and Interactive Digital Entertainment (AIIDE
"... Most games being shipped today use some form of highlevel abstraction such as a navmesh or waypoint graph for path planning. These structures can generally be represented in a form which is compact enough to meet the tight memory constraints in a game. But, when such a graph grows too large, findi ..."
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Cited by 13 (3 self)
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Most games being shipped today use some form of highlevel abstraction such as a navmesh or waypoint graph for path planning. These structures can generally be represented in a form which is compact enough to meet the tight memory constraints in a game. But, when such a graph grows too large, finding paths can still be a complex task. This challenge was faced in Dragon Age: Origins and solved by adding an additional level of abstraction. In the last few years a variety of novel approaches have been developed for finding optimal paths through graphs with specific design applications for road networks. Currently these techniques cannot be feasibly applied to the lowest detail of movement possible in a game map, but can be applied to the highlevel abstractions which are commonly found in games. In this paper we de
Graph Indexing of Road Networks for Shortest Path Queries with Label Restrictions
"... The current widespread use of locationbased services and GPS technologies has revived interest in very fast and scalable shortest path queries. We introduce a new shortest path query type in which dynamic constraints may be placed on the allowable set of edges that can appear on a valid shortest pa ..."
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Cited by 13 (0 self)
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The current widespread use of locationbased services and GPS technologies has revived interest in very fast and scalable shortest path queries. We introduce a new shortest path query type in which dynamic constraints may be placed on the allowable set of edges that can appear on a valid shortest path (e.g., dynamically restricting the type of roads or modes of travel which may be considered in a multimodal transportation network). We formalize this problem as a specific variant of formal language constrained shortest path problems, which we call the Kleene Language Constrained Shortest Paths problem. To efficiently support this type of dynamically constrained shortest path query for largescale datasets, we extend the hierarchical graph indexing technique known as Contraction Hierarchies. Our experimental evaluation using the North American road network dataset (with over 50 million edges) shows an average query speed and search space improvement of over 3 orders of magnitude compared to the naïve adaptation of the standard Dijkstra’s algorithm to support this query type. We also show an improvement of over 2 orders of magnitude compared to the only previouslyexisting indexing technique which could solve this problem without additional preprocessing. 1.
Distributed TimeDependent Contraction Hierarchies
 In Proceedings of the 9th International Symposium on Experimental Algorithms, volume 6049 of LNCS
, 2010
"... Abstract. Server based route planning in road networks is now powerful enough to find quickest paths in a matter of milliseconds, even if detailed information on timedependent travel times is taken into account. However this requires huge amounts of memory on each query server and hours of preproce ..."
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Abstract. Server based route planning in road networks is now powerful enough to find quickest paths in a matter of milliseconds, even if detailed information on timedependent travel times is taken into account. However this requires huge amounts of memory on each query server and hours of preprocessing even for a medium sized country like Germany. This is a problem since global internet companies would like to work with transcontinental networks, detailed models of intersections, and regular repreprocessing that takes the current traffic situation into account. By giving a distributed memory parallelization of the arguably best current technique – timedependent contraction hierarchies, we remove these bottlenecks. For example, on a medium size network 64 processes accelerate preprocessing by a factor of 28 to 160 seconds, reduce per process memory consumption by a factor of 10.5 and increase query throughput by a factor of 25. Key words: timedependent shortest paths, distributed computation, message passing, algorithm engineering 1
HLDB: Locationbased services in databases
 In Proceedings of the 20th ACM SIGSPATIAL International Symposium on Advances in Geographic Information Systems (GIS’12), 339–348. ACM Press. Best Paper Award
, 2012
"... This paper introduces HLDB, the first practical system that can answer exact spatial queries on continental road networks entirely within a database. HLDB is based on hub labels (HL), the fastest pointtopoint algorithm for road networks, and its queries are implemented (quite naturally) in stan ..."
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This paper introduces HLDB, the first practical system that can answer exact spatial queries on continental road networks entirely within a database. HLDB is based on hub labels (HL), the fastest pointtopoint algorithm for road networks, and its queries are implemented (quite naturally) in standard SQL. Within the database, HLDB answers exact distance queries and retrieves full shortestpath descriptions in real time, even on networks with tens of millions of vertices. The basic algorithm can be extended in a natural way (still in SQL) to answer much more sophisticated queries, such as finding the ten closest fastfood restaurants. We also introduce efficient new HLbased algorithms for even harder problems, such as best via point, ride sharing, and point of interest prediction. The HLDB framework makes it easy to implement these algorithms in SQL, enabling interactive applications on continental road networks.
Efficient data management in support of shortestpath computation
 In Proceedings of the 4th ACM SIGSPATIAL International Workshop on Computational Transportation Science, CTS ’11
, 2011
"... While many efficient proposals exist for solving the singlepair shortestpath problem, a solution that sees the algorithmic solution in combination with efficient data management has received considerably little attention. This work proposes a data management approach for efficient shortest path co ..."
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Cited by 5 (4 self)
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While many efficient proposals exist for solving the singlepair shortestpath problem, a solution that sees the algorithmic solution in combination with efficient data management has received considerably little attention. This work proposes a data management approach for efficient shortest path computation that exploits road network hierarchies. Hierarchies allow us to minimize the portion of the network that is kept in main memory. This approach is insensitive to changes to the network as it does not rely on any precomputation, but only on given road network properties. In that we specifically target large road networks that exhibit a high degree of change (e.g., OpenStreetMap). Extensive experimental evaluation shows that the presented solution is both efficient and scalable and provides competitive shortestpath computation performance without requiring a preprocessing stage for the road network graph.
On computational models for flash memory devices
 in Experimental Algorithms, 2009
"... Abstract. Flash memorybased solidstate disks are fast becoming the dominant form of enduser storage devices, partly even replacing the traditional harddisks. Existing twolevel memory hierarchy models fail to realize the full potential of flashbased storage devices. We propose two new computati ..."
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Abstract. Flash memorybased solidstate disks are fast becoming the dominant form of enduser storage devices, partly even replacing the traditional harddisks. Existing twolevel memory hierarchy models fail to realize the full potential of flashbased storage devices. We propose two new computation models, the general flash model and the unitcost model, for memory hierarchies involving these devices. Our models are simple enough for meaningful algorithm design and analysis. In particular, we show that a broad range of existing externalmemory algorithms and data structures based on the merging paradigm can be adapted efficiently into the unitcost model. Our experiments show that the theoretical analysis of algorithms on our models corresponds to the empirical behavior of algorithms when using solidstate disks as external memory. 1
Design and Implementation of a Practical I/Oefficient Shortest Paths Algorithm
"... We report on initial experimental results for a practical I/Oefficient SingleSource ShortestPaths (SSSP) algorithm on general undirected sparse graphs where the ratio between the largest and the smallest edge weight is reasonably bounded (for example integer weights in {1,...,2 32}) and the reali ..."
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We report on initial experimental results for a practical I/Oefficient SingleSource ShortestPaths (SSSP) algorithm on general undirected sparse graphs where the ratio between the largest and the smallest edge weight is reasonably bounded (for example integer weights in {1,...,2 32}) and the realistic assumption holds that main memory is big enough to keep one bit per vertex. While our implementation only guarantees averagecase efficiency, i.e., assuming randomly chosen edgeweights, it turns out that its performance on realworld instances with nonrandom edge weights is actually even better than on the respective inputs with random weights. Furthermore, compared to the currently best implementation for externalmemory BFS [6], which in a sense constitutes a lower bound for SSSP, the running time of our approach always stayed within a factor of five, for the most difficult graph classes the difference was even less than a factor of two. We are not aware of any previous I/Oefficient implementation for the classic general SSSP in a (semi) external setting: in two recent projects [10, 23], Kumar/Schwabelike SSSP approaches on graphs of at most 6 million vertices have been tested, forcing the authors to artificially restrict the main memory size, M, to rather unrealistic 4 to 16 MBytes in order not to leave the semiexternal setting or produce huge running times for larger graphs: for random graphs of 2 20 vertices, the best previous approach needed over six hours. In contrast, for a similar ratio of input size vs. M, but on a 128 times larger and even sparser random graph, our approach was less than seven times slower, a relative gain of nearly 20. On a realworld 24 million node street graph, our implementation was over 40 times faster. Even larger gains of over 500 can be estimated for ran
Optimizing landmarkbased routing and preprocessing
 In Proceedings of the 6th ACM SIGSPATIAL International Workshop on Computational Transportation Science, IWCTS ’13
, 2013
"... Many acceleration techniques exist for the singlepair shortest path problem on road networks. Most of them have been significantly improved over the years to achieve faster preprocessing times and superior performance. In this spirit, our current work significantly improves the classic ALT (A ∗ + L ..."
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Cited by 3 (3 self)
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Many acceleration techniques exist for the singlepair shortest path problem on road networks. Most of them have been significantly improved over the years to achieve faster preprocessing times and superior performance. In this spirit, our current work significantly improves the classic ALT (A ∗ + Landmarks + Triangle equality) algorithm. By carefully optimizing both preprocessing and query phases, we managed to effectively minimize preprocessing time to a few seconds, making the ALT algorithm also suitable for dynamic scenarios, i.e., road networks with changing edge weights due to traffic updates. We also accelerated the query phase for both unidirectional and bidirectional versions of the ALT algorithm, providing fast enough query times (including fullpath unpacking) suitable for realtime services and continental road networks. Categories and Subject Descriptors