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54
Contraction hierarchies: Faster and simpler . . .
, 2008
"... We present a route planning technique solely based on the concept of node contraction. We contract or remove one node at a time out of the graph and add shortcut edges to the remaining graph to preserve shortest paths distances. The resulting contraction hierarchy (CH), the original graph plus short ..."
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Cited by 120 (34 self)
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We present a route planning technique solely based on the concept of node contraction. We contract or remove one node at a time out of the graph and add shortcut edges to the remaining graph to preserve shortest paths distances. The resulting contraction hierarchy (CH), the original graph plus shortcuts, also defines an order of “importance ” among all nodes through the node selection. We apply a modified bidirectional Dĳkstra algorithm that takes advantage of this node order to obtain shortest paths. The search space is reduced by relaxing only edges leading to more important nodes in the forward search and edges coming from more important nodes in the backward search. Both search scopes eventually meet at the most important node on a shortest path. We use a simple but extensible heuristic to obtain the node order: a priority queue whose priority function for each node is a linear combination of several terms, e.g. one term weights nodes depending on the sparsity of the remaining graph after the contraction. Another term regards the already contracted nodes to allow a more uniform contraction. Depending on the application we can select the combination of the priority terms to obtain the required hierarchy.
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.
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.
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
A computational study of externalmemory BFS algorithms
 In SODA
, 2006
"... Breadth First Search (BFS) traversal is an archetype for many important graph problems. However, computing a BFS level decomposition for massive graphs was considered nonviable so far, because of the large number of I/Os it incurs. This paper presents the first experimental evaluation of recent exte ..."
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Cited by 25 (3 self)
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Breadth First Search (BFS) traversal is an archetype for many important graph problems. However, computing a BFS level decomposition for massive graphs was considered nonviable so far, because of the large number of I/Os it incurs. This paper presents the first experimental evaluation of recent externalmemory BFS algorithms for general graphs. With our STXXL based implementations exploiting pipelining and diskparallelism, we were able to compute the BFS level decomposition of a webcrawl based graph of around 130 million nodes and 1.4 billion edges in less than 4 hours using single disk and 2.3 hours using 4 disks. We demonstrate that some rather simple externalmemory algorithms perform significantly better (minutes as compared to hours) than internalmemory BFS, even if more than half of the input resides internally. 1
A Flexible OpenSource Toolbox for Scalable Complex Graph Analysis
, 2011
"... The Knowledge Discovery Toolbox (KDT) enables domain experts to perform complex analyses of huge datasets on supercomputers using a highlevel language without grappling with the difficulties of writing parallel code, calling parallel libraries, or becoming a graph expert. KDT provides a flexible Py ..."
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Cited by 21 (3 self)
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The Knowledge Discovery Toolbox (KDT) enables domain experts to perform complex analyses of huge datasets on supercomputers using a highlevel language without grappling with the difficulties of writing parallel code, calling parallel libraries, or becoming a graph expert. KDT provides a flexible Python interface to a small set of highlevel graph operations; composing a few of these operations is often sufficient for a specific analysis. Scalability and performance are delivered by linking to a stateoftheart backend compute engine that scales from laptops to large HPC clusters. KDT delivers very competitive performance from a generalpurpose, reusable library for graphs on the order of 10 billion edges and greater. We demonstrate speedup of 1 and 2 orders of magnitude over PBGL and Pegasus, respectively, on some tasks. Examples from simple use cases and key graphanalytic benchmarks illustrate the productivity and performance realized by KDT users. Semantic graph abstractions provide both flexibility and high performance for realworld use cases. Graphalgorithm researchers benefit from the ability to develop algorithms quickly using KDT’s graph and underlying matrix abstractions for distributed memory. KDT is available as opensource code to foster experimentation.
Reach for A∗: Shortest Path Algorithms with Preprocessing
 DIMACS SERIES IN DISCRETE MATHEMATICS AND THEORETICAL COMPUTER SCIENCE
, 2009
"... We study the pointtopoint shortest path problem with preprocessing. Given an input graph, we preprocess it so as to be able to answer a series of sourcetodestination queries efficiently. Our work is motivated by an algorithm of Gutman [ALENEX’04], based on the notion of reach, which measures ho ..."
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Cited by 21 (12 self)
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We study the pointtopoint shortest path problem with preprocessing. Given an input graph, we preprocess it so as to be able to answer a series of sourcetodestination queries efficiently. Our work is motivated by an algorithm of Gutman [ALENEX’04], based on the notion of reach, which measures how important each vertex is with respect to shortest paths. We present a simplified version of his algorithm that does not require explicit lower bounds during queries. We also show how the addition of shortcuts to the graph greatly improves the performance of both preprocessing and queries. Finally, we combine a reachbased algorithm with landmarkbased A∗ search to obtain a wide range of spacetime tradeoffs. For our motivating application, driving directions for road networks, the resulting algorithm is very efficient and practical. The road networks of the USA and Western Europe have roughly 20 million vertices, but on average our algorithm must visit fewer than a thousand to find the distance between two points. Our algorithm also works reasonably well on 2dimensional grid graphs with random arc weights.
Better landmarks within reach
 IN THE 9TH DIMACS IMPLEMENTATION CHALLENGE: SHORTEST PATHS
, 2007
"... We present significant improvements to a practical algorithm for the pointtopoint shortest path problem on road networks that combines A∗ search, landmarkbased lower bounds, and reachbased pruning. Through reachaware landmarks, better use of cache, and improved algorithms for reach computation ..."
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Cited by 19 (1 self)
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We present significant improvements to a practical algorithm for the pointtopoint shortest path problem on road networks that combines A∗ search, landmarkbased lower bounds, and reachbased pruning. Through reachaware landmarks, better use of cache, and improved algorithms for reach computation, we make preprocessing and queries faster while reducing the overall space requirements. On the road networks of the USA or Europe, the shortest path between two random vertices can be found in about one millisecond after one or two hours of preprocessing. The algorithm is also effective on twodimensional grids.
Mobile Route Planning
"... We provide an implementation of an exact route planning algorithm on a mobile device that answers shortestpath queries in a road network of a whole continent instantaneously, i.e., with a delay of about 100ms, which is virtually not observable for a human user. We exploit spatial and hierarchical ..."
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Cited by 19 (2 self)
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We provide an implementation of an exact route planning algorithm on a mobile device that answers shortestpath queries in a road network of a whole continent instantaneously, i.e., with a delay of about 100ms, which is virtually not observable for a human user. We exploit spatial and hierarchical locality properties to design a significantly compressed externalmemory graph representation, which can be traversed efficiently and which occupies only a few hundred megabytes for road networks with up to 34 million nodes. Next to the accuracy, the computational speed, and the low space requirements, the simplicity of our approach is a fourth argument that suggests an application of our implementation in car navigation systems.