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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 24 (11 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 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 23 (14 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.
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 16 (5 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.
Highperformance multilevel graphs
 IN: 9TH DIMACS IMPLEMENTATION CHALLENGE
, 2006
"... Shortestpath computation is a frequent task in practice. Owing to evergrowing realworld graphs, there is a constant need for faster algorithms. In the course of time, a large number of techniques to heuristically speed up Dijkstra’s shortestpath algorithm have been devised. This work reviews the ..."
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Cited by 15 (4 self)
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Shortestpath computation is a frequent task in practice. Owing to evergrowing realworld graphs, there is a constant need for faster algorithms. In the course of time, a large number of techniques to heuristically speed up Dijkstra’s shortestpath algorithm have been devised. This work reviews the multilevel technique to answer shortestpath queries exactly [SWZ02, HSW06], which makes use of a hierarchical decomposition of the input graph and precomputation of supplementary information. We develop this preprocessing to the maximum and introduce several ideas to enhance this approach considerably, by reorganizing the precomputed data in partial graphs and optimizing them individually. To answer a given query, certain partial graphs are combined to a search graph, which can be explored by a simple and fast procedure. Experiments confirm query times of less than 200 µs for a road graph with over 15 million vertices.
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.
Bidirectional A ∗ Search for TimeDependent Fast Paths
"... Abstract. The computation of pointtopoint shortest paths on timedependent road networks has many practical applications, but there have been very few works that propose efficient algorithms for large graphs. One of the difficulties of route planning on timedependent graphs is that we do not know ..."
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Cited by 11 (6 self)
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Abstract. The computation of pointtopoint shortest paths on timedependent road networks has many practical applications, but there have been very few works that propose efficient algorithms for large graphs. One of the difficulties of route planning on timedependent graphs is that we do not know the exact arrival time at the destination, hence applying bidirectional search is not straightforward; we propose a novel approach based on A ∗ with landmarks (ALT) that starts a search from both the source and the destination node, where the backward search is used to bound the set of nodes that have to be explored by the forward search. Extensive computational results show that this approach is very effective in practice if we are willing to accept a small approximation factor, resulting in a speedup of several times with respect to Dijkstra’s algorithm while finding only slightly suboptimal solutions. 1
HighPerformance MultiLevel Routing
 DIMACS SERIES IN DISCRETE MATHEMATICS AND THEORETICAL COMPUTER SCIENCE
, 2008
"... Shortestpath computation is a frequent task in practice. Owing to evergrowing realworld graphs, there is a constant need for faster algorithms. In the course of time, a large number of techniques to heuristically speed up Dijkstra’s shortestpath algorithm have been devised. This work reviews the ..."
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Cited by 4 (3 self)
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Shortestpath computation is a frequent task in practice. Owing to evergrowing realworld graphs, there is a constant need for faster algorithms. In the course of time, a large number of techniques to heuristically speed up Dijkstra’s shortestpath algorithm have been devised. This work reviews the multilevel technique to answer shortestpath queries exactly [24, 9], which makes use of a hierarchical decomposition of the input graph and precomputation of supplementary information. We develop this preprocessing to the maximum and introduce several ideas to enhance this approach considerably, by reorganizing the precomputed data in partial graphs and optimizing them individually. To answer a given query, certain partial graphs are combined to a search graph, which can be explored by a simple and fast procedure. The concept behind the construction of the search graph is such that query times depend mainly on the number of partial graphs included. This is confirmed by experiments with different road graphs, each containing several million vertices, and time, distance, and unit metrics. Our query algorithm computes the distance between any pair of vertices in no more than 40 µs, however, a lengthy preprocessing is required to achieve this query performance.
On kskip Shortest Paths
"... Given two vertices s, t in a graph, let P be the shortest path (SP) from s to t, and P ⋆ a subset of the vertices in P. P ⋆ is a kskip shortest path from s to t, if it includes at least a vertex out of every k consecutive vertices in P. In general, P ⋆ succinctly describes P by sampling the vertice ..."
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Cited by 2 (0 self)
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Given two vertices s, t in a graph, let P be the shortest path (SP) from s to t, and P ⋆ a subset of the vertices in P. P ⋆ is a kskip shortest path from s to t, if it includes at least a vertex out of every k consecutive vertices in P. In general, P ⋆ succinctly describes P by sampling the vertices in P with a rate of at least 1/k. This makes P ⋆ a natural substitute in scenarios where reporting every single vertex of P is unnecessary or even undesired. This paper studies kskip SP computation in the context of spatial network databases (SNDB). Our technique has two properties crucial for realtime query processing in SNDB. First, our solution is able to answer kskip queries significantly faster than finding the original SPs in their entirety. Second, the previous objective is achieved with a structure that occupies less space than storing the underlying road network. The proposed algorithms are the outcome of a careful theoretical analysis that reveals valuable insight into the characteristics of the kskip SP problem. Their efficiency has been confirmed by extensive experiments with real data.
Continuous Monitoring of Nearest Neighbors on Land Surface
"... As georealistic rendering of land surfaces is becoming commonplace in geographical information systems (GIS), games and online Earth visualization platforms, a new type of k Nearest Neighbor (kNN) queries, “surface ” k Nearest Neighbor (skNN) queries, has emerged and been investigated recently, whi ..."
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Cited by 2 (1 self)
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As georealistic rendering of land surfaces is becoming commonplace in geographical information systems (GIS), games and online Earth visualization platforms, a new type of k Nearest Neighbor (kNN) queries, “surface ” k Nearest Neighbor (skNN) queries, has emerged and been investigated recently, which extends the traditional kNN queries to a constrained third dimension (i.e., land surface). All existing techniques, however, assume a static environment, limiting their utility in emerging applications (e.g., Locationbased Services) where objects move. In this paper, for the first time, we propose two exact methods that can continuously answer skNN queries in a highly dynamic environment which allows for arbitrary movements of data objects. The first method, inspired by the existing techniques in monitoring kNN in road networks [7] maintains an analogous counterpart of the Dijkstra Expansion Tree on land surface, called Surface Expansion Tree (SETree). However, we show the concept of expansion tree for land surface does not work as SEtree suffers from intrinsic defects: it is fat and short, and hence does not improve the query efficiency. Therefore, we propose a superior approach that partitions SETree into hierarchical chunks of precomputed surface distances, called Angular Surface Index Tree (ASITree). Unlike SEtree, ASITree is a well balanced thin and tall tree. With ASITree, we can continuously monitor skNN queries efficiently with low CPU and I/O overheads by both speeding up the surface shortest path computations and localizing the searches. We experimentally verify the applicability and evaluate the efficiency of the proposed methods with both real world and synthetic data sets. ASITree consistently and significantly outperforms SETree in all cases. 1.
Combining Speedup Techniques based on Landmarks and Containers with parallelised preprocessing in Random and Planar Graphs
"... The Dijkstra’s algorithm is applied in many real world problems like mobile routing, road maps, railway networks, etc,. There are many techniques available to speedup the algorithm while guaranteeing the optimality of the solution. Almost all of the speedup techniques have a substantial amount of pa ..."
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The Dijkstra’s algorithm is applied in many real world problems like mobile routing, road maps, railway networks, etc,. There are many techniques available to speedup the algorithm while guaranteeing the optimality of the solution. Almost all of the speedup techniques have a substantial amount of parallelism that can be exploited to decrease its running time. By suitably modifying portions of the existing system various degrees of parallelism can be achieved. The rapidly growing field of multiprocessing systems and multicore processors provide many opportunities for such improvements. In these techniques there’s always a demand for the running time and the time required for preprocessing. Space requirements for the preprocessing also have a major influence on the running time of the algorithm. The main focus of the work is to implement landmark technique and to identify the segment of the code in landmark preprocessing which can be parallelized to obtain better speedup. The results are applied to the combined speedup technique which is based on landmarks and containers. The experimental results were compared and analysed for determining better performance improvements in random graphs and planar graphs.