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19
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, time-dependent routing, and flexible objective functions.
PHAST: hardware-accelerated shortest path trees
- J. PARALLEL DISTRIB. COMPUT
, 2013
"... We present a novel algorithm to solve the nonnegative single-source 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 20 (4 self)
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We present a novel algorithm to solve the nonnegative single-source 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 multi-core 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 high-end CPU. This makes applications based on all-pairs shortest-paths practical for continental-sized 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 High-Level 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 high-level 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 con-straints in a game. But, when such a graph grows too large, findi ..."
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Cited by 15 (3 self)
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Most games being shipped today use some form of high-level 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 con-straints 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 ad-ditional level of abstraction. In the last few years a variety of novel approaches have been developed for finding opti-mal paths through graphs with specific design applications for road networks. Currently these techniques cannot be fea-sibly applied to the lowest detail of movement possible in a game map, but can be applied to the high-level 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 location-based 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 location-based 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 large-scale 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 previously-existing indexing technique which could solve this problem without additional preprocessing. 1.
Distributed Time-Dependent 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 time-dependent 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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Cited by 12 (7 self)
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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 time-dependent 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 re-preprocessing that takes the current traffic situation into account. By giving a distributed memory parallelization of the arguably best current technique – time-dependent 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: time-dependent shortest paths, distributed computation, message passing, algorithm en-gineering 1
HLDB: Location-based 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 net-works entirely within a database. HLDB is based on hub la-bels (HL), the fastest point-to-point algorithm for road net-works, and its queries are implemented (quite naturally) in stan ..."
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Cited by 7 (4 self)
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This paper introduces HLDB, the first practical system that can answer exact spatial queries on continental road net-works entirely within a database. HLDB is based on hub la-bels (HL), the fastest point-to-point algorithm for road net-works, and its queries are implemented (quite naturally) in standard SQL. Within the database, HLDB answers exact distance queries and retrieves full shortest-path descriptions in real time, even on networks with tens of millions of ver-tices. 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 fast-food restaurants. We also introduce efficient new HL-based 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 shortest-path 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 single-pair shortest-path 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 single-pair shortest-path 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 pre-computation, but only on given road network properties. In that we specifically target large road networks that exhibit a high degree of change (e.g., Open-StreetMap). 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.
Design and Implementation of a Practical I/O-efficient Shortest Paths Algorithm
"... We report on initial experimental results for a practical I/O-efficient Single-Source Shortest-Paths (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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Cited by 5 (1 self)
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We report on initial experimental results for a practical I/O-efficient Single-Source Shortest-Paths (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 average-case efficiency, i.e., assuming randomly chosen edge-weights, it turns out that its performance on real-world instances with non-random edge weights is actually even better than on the respective inputs with random weights. Furthermore, compared to the currently best implementation for external-memory 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/O-efficient implementation for the classic general SSSP in a (semi) external setting: in two recent projects [10, 23], Kumar/Schwabe-like 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 semi-external 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 real-world 24 million node street graph, our implementation was over 40 times faster. Even larger gains of over 500 can be estimated for ran-
On computational models for flash memory devices
- in Experimental Algorithms, 2009
"... Abstract. Flash memory-based solid-state disks are fast becoming the dominant form of end-user storage devices, partly even replacing the traditional hard-disks. Existing two-level memory hierarchy models fail to realize the full potential of flash-based storage devices. We propose two new computati ..."
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Cited by 4 (1 self)
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Abstract. Flash memory-based solid-state disks are fast becoming the dominant form of end-user storage devices, partly even replacing the traditional hard-disks. Existing two-level memory hierarchy models fail to realize the full potential of flash-based storage devices. We propose two new computation models, the general flash model and the unit-cost 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 external-memory algorithms and data structures based on the merging paradigm can be adapted efficiently into the unit-cost model. Our experiments show that the theoretical analysis of algorithms on our models corresponds to the empirical behavior of algorithms when using solid-state disks as external memory. 1
Space-Efficient SHARC-Routing
, 2009
"... Accelerating the computation of quickest paths in road networks has been undergoing a rapid development during the last years. The breakthrough idea for handling road networks with tens of millions of nodes was the concept of shortcuts, i.e., additional arcs that represent long paths in the input. V ..."
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Cited by 3 (1 self)
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Accelerating the computation of quickest paths in road networks has been undergoing a rapid development during the last years. The breakthrough idea for handling road networks with tens of millions of nodes was the concept of shortcuts, i.e., additional arcs that represent long paths in the input. Very recently, this concept has been transferred to time-dependent road networks where travel times on arcs are given by functions. Unfortunately, the concept of shortcuts yields a high increase in space consumption for time-dependent road networks since the travel time functions assigned to the shortcuts may become quite complex. In this work, we present how the space overhead induced by time-dependent SHARC, a technique relying on shortcuts as well, can be reduced significantely. As a result, we are able to reduce the overhead stemming from SHARC by a factor of up to 11.5 for the price of a loss in query performance of a factor of 4. The methods we present allow a flexible trade-off between space consumption and query performance.
