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16
SHARC: Fast and robust unidirectional routing
 IN: WORKSHOP ON ALGORITHM ENGINEERING AND EXPERIMENTS (ALENEX
, 2008
"... During the last years, impressive speedup techniques for Dijkstra’s algorithm have been developed. Unfortunately, the most advanced techniques use bidirectional search which makes it hard to use them in scenarios where a backward search is prohibited. Even worse, such scenarios are widely spread, e ..."
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Cited by 27 (14 self)
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During the last years, impressive speedup techniques for Dijkstra’s algorithm have been developed. Unfortunately, the most advanced techniques use bidirectional search which makes it hard to use them in scenarios where a backward search is prohibited. Even worse, such scenarios are widely spread, e.g., timetableinformation systems or timedependent networks. In this work, we present a unidirectional speedup technique which competes with bidirectional approaches. Moreover, we show how to exploit the advantage of unidirectional routing for fast exact queries in timetable information systems and for fast approximative queries in timedependent scenarios. By running experiments on several inputs other than road networks, we show that our approach is very robust to the input.
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 25 (12 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.
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 22 (6 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.
Adaptive fastest path computation on a road network: A traffic mining approach
 In Proc. 2007 Int. Conf. on Very Large Data Bases (VLDB’07
, 2007
"... Efficient fastest path computation in the presence of varying speed conditions on a large scale road network is an essential problem in modern navigation systems. Factors affecting road speed, such as weather, time of day, and vehicle type, need to be considered in order to select fast routes that m ..."
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Cited by 20 (2 self)
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Efficient fastest path computation in the presence of varying speed conditions on a large scale road network is an essential problem in modern navigation systems. Factors affecting road speed, such as weather, time of day, and vehicle type, need to be considered in order to select fast routes that match current driving conditions. Most existing systems compute fastest paths based on road Euclidean distance and a small set of predefined road speeds. However, “History is often the best teacher”. Historical traffic data or driving patterns are often more useful than the simple Euclidean distancebased computation because people must have good reasons to choose these routes, e.g., they may want to avoid those that pass through high crime areas at night or that likely encounter accidents, road construction, or traffic jams. In this paper, we present an adaptive fastest path algorithm capable of efficiently accounting for important driving and speed patterns mined from a large set of traffic data. The algorithm is based on the following observations: (1) The hierarchy of roads can be used to partition the road network into areas, and different path precomputation strategies can be used at the area level, (2) we can limit our route search strategy to edges and path segments that are actually frequently traveled in the data, and (3) drivers usually traverse the road network through the largest roads available given the distance of the trip, except if there are small roads with a significant speed advantage over the large ones. Through an extensive experimental evaluation on real road networks we show that our algorithm provides desirable (short and wellsupported) routes, and that it is significantly faster than competing methods.
Landmarkbased routing in dynamic graphs
 IN: 6TH WORKSHOP ON EXPERIMENTAL ALGORITHMS
, 2007
"... Many speedup techniques for route planning in static graphs exist, only few of them are proven to work in a dynamic scenario. Most of them use preprocessed information, which has to be updated whenever the graph is changed. However, goal directed search based on landmarks (ALT) still performs cor ..."
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Cited by 17 (6 self)
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Many speedup techniques for route planning in static graphs exist, only few of them are proven to work in a dynamic scenario. Most of them use preprocessed information, which has to be updated whenever the graph is changed. However, goal directed search based on landmarks (ALT) still performs correct queries as long as an edge weight does not drop below its initial value. In this work, we evaluate the robustness of ALT with respect to traffic jams. It turns out that—by increasing the efficiency of ALT—we are able to perform fast (down to 20 ms on the Western European network) random queries in a dynamic scenario without updating the preprocessing as long as the changes in the network are moderate. Furthermore, we present how to update the preprocessed data without any additional space consumption and how to adapt the ALT algorithm to a timedependent scenario. A timedependent scenario models predictable changes in the network, e.g. traffic jams due to rush hour.
TRANSIT— ultrafast shortestpath queries with lineartime preprocessing
 In 9th DIMACS Implementation Challenge [1
, 2006
"... {bast,funke,dmatijev} at mpiinf dot mpg dot de We introduce the concept of transit nodes, as a means for preprocessing a road network, with given coordinates for each node and a travel time for each edge, such that pointtopoint shortestpath queries can be answered extremely fast. The transit nod ..."
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Cited by 14 (1 self)
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{bast,funke,dmatijev} at mpiinf dot mpg dot de We introduce the concept of transit nodes, as a means for preprocessing a road network, with given coordinates for each node and a travel time for each edge, such that pointtopoint shortestpath queries can be answered extremely fast. The transit nodes are a set of nodes, as small as possible, with the property that every shortest path that is nonlocal in the sense that it covers a certain not too small euclidean distance passes through at least on of these nodes. With such a set and precomputed distances from each node in the graph to its few, closest transit nodes, every nonlocal shortest path query becomes a simple matter of combining information from a few table lookups. For the US road network, which has about 24 million nodes and 58 million edges, we achieve a worstcase query processing time of about 10 microseconds (not milliseconds) for 99 % of all queries. This improves over the best previously reported times by two orders of magnitude. 1
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 14 (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.
Experimental Study on SpeedUp Techniques for Timetable Information Systems
 PROCEEDINGS OF THE 7TH WORKSHOP ON ALGORITHMIC APPROACHES FOR TRANSPORTATION MODELING, OPTIMIZATION, AND SYSTEMS (ATMOS 2007
, 2007
"... During the last years, impressive speedup techniques for DIJKSTRA’s algorithm have been developed. Unfortunately, recent research mainly focused on road networks. However, fast algorithms are also needed for other applications like timetable information systems. Even worse, the adaption of recentl ..."
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Cited by 11 (7 self)
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During the last years, impressive speedup techniques for DIJKSTRA’s algorithm have been developed. Unfortunately, recent research mainly focused on road networks. However, fast algorithms are also needed for other applications like timetable information systems. Even worse, the adaption of recently developed techniques to timetable information is more complicated than expected. In this work, we check whether results from road networks are transferable to timetable information. To this end, we present an extensive experimental study of the most prominent speedup techniques on different types of inputs. It turns out that recently developed techniques are much slower on graphs derived from timetable information than on road networks. In addition, we gain amazing insights into the behavior of speedup techniques in general.
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).
Statistical Density Prediction in Traffic Networks
, 2008
"... Recently, modern tracking methods started to allow capturing the position of massive numbers of moving objects. Given this information, it is possible to analyze and predict the traffic density in a network which offers valuable information for traffic control, congestion prediction and prevention. ..."
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Cited by 7 (2 self)
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Recently, modern tracking methods started to allow capturing the position of massive numbers of moving objects. Given this information, it is possible to analyze and predict the traffic density in a network which offers valuable information for traffic control, congestion prediction and prevention. In this paper, we propose a novel statistical approach to predict the density on any edge of such a network at some time in the future. Our method is based on shorttime observations of the traffic history. Therefore, knowing the destination of each traveling individual is not required. Instead, we assume that the individuals will act rationally and choose the shortest path from their starting points to their destinations. Based on this assumption, we introduce a statistical approach to describe the likelihood of any given individual in the network to be located at a certain position at a certain time. Since determining this likelihood is quite expensive when done in a straightforward way, we propose an efficient method to speed up the prediction which is based on a suffixtree. In our experiments, we show the capability of our approach to make useful predictions about the traffic density and illustrate the efficiency of our new algorithm when calculating these predictions.