Despite the importance of spatial networks in real-life applications, most of the spatial database literature focuses on Euclidean spaces. In this paper we propose an architecture that integrates network and Euclidean information, capturing pragmatic constraints. Based on this architecture, we develop a Euclidean restriction and a network expansion framework that take advantage of location and connectivity to efficiently prune the search space. These frameworks are successfully applied to the most popular spatial queries, namely nearest neighbors, range search, closest pairs and edistance joins, in the context of spatial network databases.

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.

Abstract not found

In many fields of application shortest path finding problems in very large graphs arise. Scenarios where large numbers ofonW##O queries for shortest paths have to be processedin real-time appear for examplein tra#cinc5###HF5 systems.In such systems, the techn5Ww# con sidered to speed up the shortest pathcomputation are usually basedon precomputed incomputed5 On approach proposedoften in thiscon text is a spacereduction where precomputed shortest paths are replaced by sin## edges with weight equal to thelenOq of the corresponres shortest path.In this paper, we give a first systematic experimen tal study of such a spacereduction approach. Wein troduce theconOkW of multi-level graph decomposition Foron specificapplication scenica from the field of timetable information in public tranc ort, we perform a detailed anai ysisan experimen tal evaluation of shortest path computation based on multi-level graph decomposition.

Shortest-path computation is a frequent task in practice. Owing to ever-growing real-world 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 shortest-path algorithm have been devised. This work reviews the multi-level technique to answer shortest-path 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.

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 distance-based 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 pre-computation 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 well-supported) routes, and that it is significantly faster than competing methods.

This paper proposes and solves the Time-Interval All Fastest Path (allFP) query. Given a user-defined leaving or arrival time interval I, a source node s and an end node e, allFP asks for a set of all fastest paths from s to e, one for each sub-interval of I. Note that the query algorithm should find a partitioning of I into sub-intervals. Existing methods can only be used to solve a very special case of the problem, when the leaving time is a single time instant. A straightforward solution to the allFP query is to run existing methods many times, once for every time instant in I. This paper proposes a solution based on novel extensions to the A * algorithm. Instead of expanding the network many times, we expand once. The travel time on a path is kept as a function of leaving time. Methods to combine travel-time functions are provided to expand a path. A novel lower-bound estimator for travel time is proposed. Performance results reveal that our method is more efficient and more accurate than the discrete-time approach. 1

Abstract—A reverse nearest neighbor (RNN) query returns the data objects that have a query point as their nearest neighbor (NN). Although such queries have been studied quite extensively in Euclidean spaces, there is no previous work in the context of large graphs. In this paper, we provide a fundamental lemma, which can be used to prune the search space while traversing the graph in search for RNN. Based on it, we develop two RNN methods; an eager algorithm that attempts to prune network nodes as soon as they are visited and a lazy technique that prunes the search space when a data point is discovered. We study retrieval of an arbitrary number k of reverse nearest neighbors, investigate the benefits of materialization, cover several query types, and deal with cases where the queries and the data objects reside on nodes or edges of the graph. The proposed techniques are evaluated in various practical scenarios involving spatial maps, computer networks, and the DBLP coauthorship graph. Index Terms — Query processing, spatial databases, graphs and networks. 1

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 short-time 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 suffix-tree. 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.

This paper proposes and solves a-autonomy and k-stops shortest path problems in large spatial databases. Given a source s and a destination d, anaautonomy query retrieves a sequence of data points connecting s and d, such that the distance between any two consecutive points in the path is not greater than a. Ak-stops query retrieves a sequence that contains exactly k intermediate data points. In both cases our aim is to compute the shortest path subject to these constraints. Assuming that the dataset is indexed by a data-partitioning method, the proposed techniques initially compute a sub-optimal path by utilizing the Euclidean distance information provided by the index. The length of the retrieved path is used to prune the search space, filtering out large parts of the input dataset. In a final step, the optimal (a-autonomy or k-stops) path is computed (using only the non-eliminated data points) by an exact algorithm. We discuss several processing methods for both problems, and evaluate their efficiency through extensive experiments.