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22
Reach for A∗: Efficient pointtopoint shortest path algorithms
 IN WORKSHOP ON ALGORITHM ENGINEERING & EXPERIMENTS
, 2006
"... We study the pointtopoint shortest path problem in a setting where preprocessing is allowed. We improve the reachbased approach of Gutman [16] in several ways. In particular, we introduce a bidirectional version of the algorithm that uses implicit lower bounds and we add shortcut arcs which reduc ..."
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Cited by 62 (5 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 [16] in several ways. In particular, we introduce a bidirectional version of the algorithm that uses implicit lower bounds and we add shortcut arcs which reduce vertex reaches. Our modifications greatly reduce both preprocessing and query times. The resulting algorithm is as fast as the best previous method, due to Sanders and Schultes [27]. However, our algorithm is simpler and combines in a natural way with A∗ search, which yields significantly better query times.
Geometric SpeedUp Techniques for Finding Shortest Paths in Large Sparse Graphs
, 2003
"... In this paper, we consider Dijkstra's algorithm for the single source single target shortest paths problem in large sparse graphs. The goal is to reduce the response time for online queries by using precomputed information. For the result of the preprocessing, we admit at most linear space. ..."
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Cited by 53 (14 self)
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In this paper, we consider Dijkstra's algorithm for the single source single target shortest paths problem in large sparse graphs. The goal is to reduce the response time for online queries by using precomputed information. For the result of the preprocessing, we admit at most linear space. We assume that a layout of the graph is given. From this layout, in the preprocessing, we determine for each edge a geometric object containing all nodes that can be reached on a shortest path starting with that edge. Based on these geometric objects, the search space for online computation can be reduced significantly. We present an extensive experimental study comparing the impact of different types of objects. The test data we use are traffic networks, the typical field of application for this scenario.
Computing ManytoMany Shortest Paths Using Highway Hierarchies
, 2007
"... We present a fast algorithm for computing all shortest paths between source nodes s ∈ S and target nodes t ∈ T. This problem is important as an initial step for many operations research problems (e.g., the vehicle routing problem), which require the distances between S and T as input. Our approach i ..."
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Cited by 16 (5 self)
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We present a fast algorithm for computing all shortest paths between source nodes s ∈ S and target nodes t ∈ T. This problem is important as an initial step for many operations research problems (e.g., the vehicle routing problem), which require the distances between S and T as input. Our approach is based on highway hierarchies, which are also used for the currently fastest speedup techniques for shortest path queries in road networks. We show how to use highway hierarchies so that for example, a 10 000 × 10 000 distance table in the European road network can be computed in about one minute. These results are based on a simple basic idea, several refinements, and careful engineering of the approach. We also explain how the approach can be parallelized and how the computation can be restricted to computing only the k closest connections.
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 15 (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.
Route Planning and Map Inference with Global Positioning Traces
 In Computer Science in Perspective
"... Abstract. Navigation systems assist almost any kind of motion in the physical world including sailing, flying, hiking, driving and cycling. On the other hand, traces supplied by global positioning systems (GPS) can track actual time and absolute coordinates of the moving objects. Consequently, this ..."
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Cited by 13 (2 self)
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Abstract. Navigation systems assist almost any kind of motion in the physical world including sailing, flying, hiking, driving and cycling. On the other hand, traces supplied by global positioning systems (GPS) can track actual time and absolute coordinates of the moving objects. Consequently, this paper addresses efficient algorithms and data structures for the route planning problem based on GPS data; given a set of traces and a current location, infer a short(est) path to the destination. The algorithm of Bentley and Ottmann is shown to transform geometric GPS information directly into a combinatorial weighted and directed graph structure, which in turn can be queried by applying classical and refined graph traversal algorithms like Dijkstras ’ singlesource shortest path algorithm or A*. For highprecision map inference especially in car navigation, algorithms for road segmentation, map matching and lane clustering are presented. 1
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 12 (6 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.
In Transit to Constant Time ShortestPath Queries in Road Networks
"... When you drive to somewhere ‘far away’, you will leave your current location via one of only a few ‘important’ traffic junctions. Starting from this informal observation, we develop an algorithmic approach—transit node routing— that allows us to reduce quickestpath queries in road networks to a sma ..."
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Cited by 10 (2 self)
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When you drive to somewhere ‘far away’, you will leave your current location via one of only a few ‘important’ traffic junctions. Starting from this informal observation, we develop an algorithmic approach—transit node routing— that allows us to reduce quickestpath queries in road networks to a small number of table lookups. We present two implementations of this idea, one based on a simple grid data structure and one based on highway hierarchies. For the road map of the United States, our best query times improve over the best previously published figures by two orders of magnitude. Our results exhibit various tradeoffs between average query time (5 µs to 63 µs), preprocessing time (59 min to 1200 min), and storage overhead (21 bytes/node to 244 bytes/node).
Goal directed shortest path queries using Precomputed Cluster Distances
 IN 5TH WORKSHOP ON EXPERIMENTAL ALGORITHMS (WEA), NUMBER 4007 IN LNCS
, 2006
"... We demonstrate how Dijkstra’s algorithm for shortest path queries can be accelerated by using precomputed shortest path distances. Our approach allows a completely flexible tradeoff between query time and space consumption for precomputed distances. In particular, sublinear space is sufficient to g ..."
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Cited by 8 (2 self)
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We demonstrate how Dijkstra’s algorithm for shortest path queries can be accelerated by using precomputed shortest path distances. Our approach allows a completely flexible tradeoff between query time and space consumption for precomputed distances. In particular, sublinear space is sufficient to give the search a strong “sense of direction”. We evaluate our approach experimentally using large, realworld road networks.
PointtoPoint Shortest Path Algorithms with Preprocessing
"... Abstract. This is a survey of some recent results on pointtopoint shortest path algorithms. This classical optimization problem received a lot of attention lately and significant progress has been made. After an overview of classical results, we study recent heuristics that solve the problem while ..."
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Cited by 4 (0 self)
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Abstract. This is a survey of some recent results on pointtopoint shortest path algorithms. This classical optimization problem received a lot of attention lately and significant progress has been made. After an overview of classical results, we study recent heuristics that solve the problem while examining only a small portion of the input graph; the graph can be very big. Note that the algorithms we discuss find exact shortest paths. These algorithms are heuristic because they perform well only on some graph classes. While their performance has been good in experimental studies, no theoretical bounds are known to support the experimental observations. Most of these algorithms have been motivated by finding paths in large road networks. We start by reviewing the classical Dijkstra’s algorithm and its bidirectional variant, developed in 1950’s and 1960’s. Then we review A* search, an AI technique developed in 1970’s. Next we turn our attention to modern results which are based on preprocessing the graph. To be practical, preprocessing needs to be reasonably fast and not use too much space. We discuss landmark and reachbased algorithms as well as their combination. 1
Geometric Travel Planning
, 2003
"... This paper provides a novel approach for optimal route planning making efficient use of the underlying geometrical structure. It combines classical AI exploration with computational geometry. Given a set ..."
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Cited by 4 (2 self)
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This paper provides a novel approach for optimal route planning making efficient use of the underlying geometrical structure. It combines classical AI exploration with computational geometry. Given a set