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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 13 (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.
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 13 (7 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.
Path Oracles for Spatial Networks
, 2009
"... The advent of locationbased services has led to an increased demand for performing operations on spatial networks in real time. The challenge lies in being able to cast operations on spatial networks in terms of relational operators so that they can be performed in the context of a database. A line ..."
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Cited by 11 (5 self)
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The advent of locationbased services has led to an increased demand for performing operations on spatial networks in real time. The challenge lies in being able to cast operations on spatial networks in terms of relational operators so that they can be performed in the context of a database. A linearsized construct termed a path oracle is introduced that compactly encodes the n2 shortest paths between every pair of vertices in a spatial network having n vertices thereby reducing each of the paths to a single tuple in a relational database and enables finding shortest paths by repeated application of a single SQL SELECT operator. The construction of the path oracle is based on the observed coherence between the spatial positions of both source and destination vertices and the shortest paths between them which facilitates the aggregation of source and destination vertices into groups that share common vertices or edges on the shortest paths between them. With the aid of the WellSeparated Pair (WSP) technique, which has been applied to spatial networks using the network distance measure, a path oracle is proposed that takes O(sdn) space, where s is empirically estimated to be around 12 for road networks, but that can retrieve an intermediate link in a shortest path in O(logn) time using a Btree. An additional construct termed the pathdistance oracle of size O(n · max(sd, 1 d ε)) (empirically (n · max(122, 2.5 2 ε))) is proposed that can retrieve an intermediate vertex as well as an εapproximation of the network distances in O(logn) time using a Btree. Experimental results indicate that the proposed oracles are linear in n which means that they are scalable and can enable complicated query processing scenarios on massive spatial network datasets.
Approximate distance oracles for geometric spanners
 Submitted
, 2002
"... Given an arbitrary real constant ε> 0, and a geometric graph G in ddimensional Euclidean space with n points, O(n) edges, and constant dilation, our main result is a data structure that answers (1 + ε)approximate shortest path length queries in constant time. The data structure can be constructed ..."
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Cited by 11 (2 self)
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Given an arbitrary real constant ε> 0, and a geometric graph G in ddimensional Euclidean space with n points, O(n) edges, and constant dilation, our main result is a data structure that answers (1 + ε)approximate shortest path length queries in constant time. The data structure can be constructed in O(n log n) time using O(n log n) space. This represents the first data structure that answers (1 + ε)approximate shortest path queries in constant time, and hence functions as an approximate distance oracle. The data structure is also applied to several other problems. In particular, we also show that approximate shortest path queries between vertices in a planar polygonal domain with “rounded ” obstacles can be answered in constant time. Other applications include query versions of closest pair problems, and the efficient computation of the approximate dilations of geometric graphs. Finally, we show how to extend the main result to answer (1 + ε)approximate shortest path length queries in constant time for geometric spanner graphs with m = ω(n) edges. The resulting data structure can be constructed in O(m + n log n) time using O(n log n) space.
Distance Oracles for Spatial Networks
"... Abstract — The popularity of locationbased services and the need to do realtime processing on them has led to an interest in performing queries on transportation networks, such as finding shortest paths and finding nearest neighbors. The challenge is that these operations involve the computation o ..."
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Cited by 10 (4 self)
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Abstract — The popularity of locationbased services and the need to do realtime processing on them has led to an interest in performing queries on transportation networks, such as finding shortest paths and finding nearest neighbors. The challenge is that these operations involve the computation of distance along a spatial network rather than “as the crow flies. ” In many applications an estimate of the distance is sufficient, which can be achieved by use of an oracle. An approximate distance oracle is proposed for spatial networks that exploits the coherence between the spatial position of vertices and the network distance between them. Using this observation, a distance oracle is introduced that is able to obtain the εapproximate network distance between two vertices of the spatial network. The network distance between every pair of vertices in the spatial network is efficiently represented by adapting the wellseparated pair technique to spatial networks. Initially, use is made of an εapproximate distance oracle of size O ( n εd) that is capable of retrieving the approximate network distance in O(logn) time using a Btree. The retrieval time can be theoretically reduced to O(1) time by proposing another εapproximate distance oracle of size O ( nlogn εd) that uses a hash table. Experimental results indicate that the proposed technique is scalable and can be applied to sufficiently large road networks. A 10%approximate oracle (ε = 0.1) on a large network yielded an average error of 0.9 % with 90 % of the answers making an error of 2 % or less and an average retrieval time of 68µ seconds. Finally, a strategy for the integration of the distance oracle into any relational database system as well as using it to perform a variety of spatial queries such as region search, knearest neighbor search, and spatial joins on spatial networks is discussed. I.
Drawing Graphs to Speed Up ShortestPath Computations
, 2005
"... We consider the problem of (repeatedly) computing singlesource singletarget shortest paths in large, sparse graphs. Previous investigations have shown the practical usefulness of geometric speedup techniques that guarantee the correctness of the result for shortestpath computations. However, such ..."
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Cited by 9 (2 self)
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We consider the problem of (repeatedly) computing singlesource singletarget shortest paths in large, sparse graphs. Previous investigations have shown the practical usefulness of geometric speedup techniques that guarantee the correctness of the result for shortestpath computations. However, such speedup techniques utilize a layout of the graph which typically comes from geographic information. This paper examines the question how geometric speedup techniques can be used in case there is no layout given. We present an extensive computational study analyzing the usefulness of methods from graph drawing as foundation for such techniques. It turns out that using appropriate layout algorithms, a significant speedup can be achieved.
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 9 (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).
Engineering the LabelConstrained Shortest Path Algorithm NDSSL
, 2007
"... We consider a generalization of the pointtopoint (and singlesource) shortest path problem to instances where the shortest path must satisfy a formal language constraint. Given an alphabet Σ, a (directed) network G whose edges are weighted and Σlabeled, and a regular grammar L ⊆ Σ ∗ , the Regular ..."
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Cited by 9 (1 self)
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We consider a generalization of the pointtopoint (and singlesource) shortest path problem to instances where the shortest path must satisfy a formal language constraint. Given an alphabet Σ, a (directed) network G whose edges are weighted and Σlabeled, and a regular grammar L ⊆ Σ ∗ , the Regular Language Constrained Shortest Path problem consists of finding a shortest path p in G complying with the additional constraint that l(p) ∈ L. Here l(p) denotes the unique word given by concatenating the Σlabels of the edges along the path p. In this chapter, we summarize our recent results and present new theoretical and experimental results for the Regular Language Constrained Shortest problem. We also present extensions of several speedup techniques developed earlier for the standard pointtopoint shortest path problem. These speedup techniques are integrated within the basic algorithmic framework to yield new algorithms for the problem. In order to evaluate the performance of the basic algorithm and its extensions, we have performed preliminary experimental analysis. Through our experiments, we study the scalability of the algorithm with respect to the network size as well as with respect to the constraining language complexity. Further, we study the effectiveness of speedup techniques such as goaldirected and bidirectional search when applied to the Regular Language Constrained Shortest problem. 1
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.
Dynamic Shortest Paths Containers
, 2003
"... Using a set of geometric containers to speed up shortest path queries in a weighted graph has been proven a useful tool for dealing with large sparse graphs. Given a layout of a graph G = (V, E), we store, for each edge (u, v) E, the bounding box of all nodes t V for which a shortest utpath ..."
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Cited by 7 (3 self)
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Using a set of geometric containers to speed up shortest path queries in a weighted graph has been proven a useful tool for dealing with large sparse graphs. Given a layout of a graph G = (V, E), we store, for each edge (u, v) E, the bounding box of all nodes t V for which a shortest utpath starts with (u, v). Shortest path queries can then be answered by Dijkstra's algorithm restricted to edges where the corresponding bounding box contains the target. In this