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59
Scalable Network Distance Browsing in Spatial Databases
, 2008
"... An algorithm is presented for finding the k nearest neighbors in a spatial network in a bestfirst manner using network distance. The algorithm is based on precomputing the shortest paths between all possible vertices in the network and then making use of an encoding that takes advantage of the fact ..."
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Cited by 84 (10 self)
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An algorithm is presented for finding the k nearest neighbors in a spatial network in a bestfirst manner using network distance. The algorithm is based on precomputing the shortest paths between all possible vertices in the network and then making use of an encoding that takes advantage of the fact that the shortest paths from vertex u to all of the remaining vertices can be decomposed into subsets based on the first edges on the shortest paths to them from u. Thus, in the worst case, the amount of work depends on the number of objects that are examined and the number of links on the shortest paths to them from q, rather than depending on the number of vertices in the network. The amount of storage required to keep track of the subsets is reduced by taking advantage of their spatial coherence which is captured by the aid of a shortest path quadtree. In particular, experiments on a number of large road networks as
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.
Reach for A∗: Efficient PointtoPoint Shortest Path Algorithms
, 2006
"... We study the pointtopoint shortest path problem in a setting where preprocessing is allowed. We improve the reachbased approach of Gutman [17] in several ways. In particular, we introduce a bidirectional version of the algorithm that uses implicit lower bounds and we add shortcut arcs to reduce v ..."
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Cited by 77 (6 self)
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We study the pointtopoint shortest path problem in a setting where preprocessing is allowed. We improve the reachbased approach of Gutman [17] in several ways. In particular, we introduce a bidirectional version of the algorithm that uses implicit lower bounds and we add shortcut arcs to reduce vertex reaches. Our modifications greatly improve both preprocessing and query times. The resulting algorithm is as fast as the best previous method, due to Sanders and Schultes [28]. However, our algorithm is simpler and combines in a natural way with A∗ search, which yields significantly better query times.
Engineering Highway Hierarchies
, 2006
"... Highway hierarchies exploit hierarchical properties inherent in realworld road networks to allow fast and exact pointtopoint shortestpath queries. A fast preprocessing routine iteratively performs two steps: first, it removes edges that only appear on shortest paths close to source or target; s ..."
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Cited by 69 (6 self)
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Highway hierarchies exploit hierarchical properties inherent in realworld road networks to allow fast and exact pointtopoint shortestpath queries. A fast preprocessing routine iteratively performs two steps: first, it removes edges that only appear on shortest paths close to source or target; second, it identifies lowdegree nodes and bypasses them by introducing shortcut edges. The resulting hierarchy of highway networks is then used in a Dijkstralike bidirectional query algorithm to considerably reduce the search space size without losing exactness. The crucial fact is that ‘far away ’ from source and target it is sufficient to consider only highlevel edges. Various experiments with realworld road networks confirm the performance of our approach. On a 2.0 GHz machine, preprocessing the network of Western Europe, which consists of about 18 million nodes, takes 13 minutes and yields 48 bytes of additional data per node. Then, random queries take 0.61 ms on average. If we are willing to accept slower query times (1.10 ms), the memory usage can be decreased to 17 bytes per node. We can guarantee that at most 0.014 % of all nodes are visited during any query. Results for US road networks are similar. Highway hierarchies can be combined with goaldirected search, they can be extended to answer manytomany queries, and they are a crucial ingredient for other speedup techniques, namely for transitnode routing and highwaynode routing.
Computing PointtoPoint Shortest Paths from External Memory
"... We study the ALT algorithm [19] for the pointtopoint shortest path problem in the context of road networks. We suggest improvements to the algorithm itself and to its preprocessing stage. We also develop a memoryefficient implementation of the algorithm that runs on a Pocket PC. It stores graph d ..."
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Cited by 54 (6 self)
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We study the ALT algorithm [19] for the pointtopoint shortest path problem in the context of road networks. We suggest improvements to the algorithm itself and to its preprocessing stage. We also develop a memoryefficient implementation of the algorithm that runs on a Pocket PC. It stores graph data in a flash memory card and uses RAM to store information only for the part of the graph visited by the current shortest path computation. The implementation works even on very large graphs, including that of the North America road network, with almost 30 million vertices.
Engineering multilevel overlay graphs for shortestpath queries
 IN: PROCEEDINGS OF THE EIGHT WORKSHOP ON ALGORITHM ENGINEERING AND EXPERIMENTS (ALENEX06), SIAM
, 2006
"... An overlay graph of a given graph G =(V,E) on a subset S ⊆ V is a graph with vertex set S that preserves some property of G. In particular, we consider variations of the multilevel overlay graph used in [21] to speed up shortestpath computations. In this work, we follow up and present general verte ..."
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Cited by 35 (7 self)
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An overlay graph of a given graph G =(V,E) on a subset S ⊆ V is a graph with vertex set S that preserves some property of G. In particular, we consider variations of the multilevel overlay graph used in [21] to speed up shortestpath computations. In this work, we follow up and present general vertex selection criteria and strategies of applying these criteria to determine a subset S inducing an overlay graph. The main contribution is a systematic experimental study where we investigate the impact of selection criteria and strategies on multilevel overlay graphs and the resulting speedup achieved for shortestpath queries. Depending on selection strategy and graph type, a centrality index criterion, a criterion based on planar separators, and vertex degree turned out to be good selection criteria.
Efficient query processing on spatial networks
 In Proceedings of the 13th ACM International Symposium on Advances in Geographic Information Systems
, 2005
"... A framework for determining the shortest path and the distance between every pair of vertices on a spatial network is presented. The framework, termed SILC, uses path coherence between the shortest path and the spatial positions of vertices on the spatial network, thereby, resulting in an encoding t ..."
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Cited by 34 (15 self)
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A framework for determining the shortest path and the distance between every pair of vertices on a spatial network is presented. The framework, termed SILC, uses path coherence between the shortest path and the spatial positions of vertices on the spatial network, thereby, resulting in an encoding that is compact in representation and fast in path and distance retrievals. Using this framework, a wide variety of spatial queries such as incremental nearest neighbor searches and spatial distance joins can be shown to work on datasets of locations residing on a spatial network of sufficiently large size. The suggested framework is suitable for both main memory and diskresident datasets. Categories and Subject Descriptors
Engineering Fast Route Planning Algorithms
, 2007
"... Algorithms for route planning in transportation networks have recently undergone a rapid development, leading to methods that are up to one million times faster than Dijkstra’s algorithm. We outline ideas, algorithms, implementations, and experimental methods behind this development. We also explai ..."
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Cited by 33 (4 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 one million times faster than Dijkstra’s algorithm. We outline ideas, algorithms, implementations, and experimental methods behind this development. We also explain why the story is not over yet because dynamically changing networks, flexible objective functions, and new applications pose a lot of interesting challenges.
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. ..."
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Cited by 29 (7 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.