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85
Query Processing in Spatial Network Databases
 In VLDB
, 2003
"... Despite the importance of spatial networks in reallife 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 ..."
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Cited by 137 (7 self)
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Despite the importance of spatial networks in reallife 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.
Scalable Network Distance Browsing in Spatial Databases
, 2008
"... An algorithm is presented for finding the k nearest neighbors in a spatial network in a bestfirst manner using network distance. The algorithm is based on precomputing the shortest paths between all possible vertices in the network and then making use of an encoding that takes advantage of the fact ..."
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Cited by 80 (8 self)
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An algorithm is presented for finding the k nearest neighbors in a spatial network in a bestfirst manner using network distance. The algorithm is based on precomputing the shortest paths between all possible vertices in the network and then making use of an encoding that takes advantage of the fact that the shortest paths from vertex u to all of the remaining vertices can be decomposed into subsets based on the first edges on the shortest paths to them from u. Thus, in the worst case, the amount of work depends on the number of objects that are examined and the number of links on the shortest paths to them from q, rather than depending on the number of vertices in the network. The amount of storage required to keep track of the subsets is reduced by taking advantage of their spatial coherence which is captured by the aid of a shortest path quadtree. In particular, experiments on a number of large road networks as
Finding fastest paths on a road network with speed patterns
 In Proc. Int. Conf. on Data Engineering (ICDE’06
, 2006
"... This paper proposes and solves the TimeInterval All Fastest Path (allFP) query. Given a userdefined 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 subinterval of I. Note that the query algorithm should fin ..."
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Cited by 45 (0 self)
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This paper proposes and solves the TimeInterval All Fastest Path (allFP) query. Given a userdefined 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 subinterval of I. Note that the query algorithm should find a partitioning of I into subintervals. 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 traveltime functions are provided to expand a path. A novel lowerbound estimator for travel time is proposed. Performance results reveal that our method is more efficient and more accurate than the discretetime approach. 1
Aggregate nearest neighbor queries in road networks
 TKDE
, 2005
"... Abstract—Aggregate nearest neighbor queries return the object that minimizes an aggregate distance function with respect to a set of query points. Consider, for example, several users at specific locations (query points) that want to find the restaurant (data point), which leads to the minimum sum o ..."
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Cited by 44 (0 self)
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Abstract—Aggregate nearest neighbor queries return the object that minimizes an aggregate distance function with respect to a set of query points. Consider, for example, several users at specific locations (query points) that want to find the restaurant (data point), which leads to the minimum sum of distances that they have to travel in order to meet. We study the processing of such queries for the case where the position and accessibility of spatial objects are constrained by spatial (e.g., road) networks. We consider alternative aggregate functions and techniques that utilize Euclidean distance bounds, spatial access methods, and/or network distance materialization structures. Our algorithms are experimentally evaluated with synthetic and real data. The results show that their relative performance depends on the problem characteristics. Index Terms—Query processing, spatial databases, spatial databases and GIS, locationdependent and sensitive. 1
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 35 (7 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.
Finding timedependent shortest paths over large graphs
 In Proc. EDBT
, 2008
"... The spatial and temporal databases have been studied widely and intensively over years. In this paper, we study how to answer queries of finding the best departure time that minimizes the total travel time from a place to another, over a road network, where the traffic conditions dynamically change ..."
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Cited by 35 (1 self)
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The spatial and temporal databases have been studied widely and intensively over years. In this paper, we study how to answer queries of finding the best departure time that minimizes the total travel time from a place to another, over a road network, where the traffic conditions dynamically change from time to time. We study a generalized form of this problem, called the timedependent shortestpath problem. A timedependent graph GT is a graph that has an edgedelay function, wi,j(t), associated with each edge (vi, vj), to be stored in a database. The edgedelay function wi,j(t) specifies how much time it takes to travel from node vi to node vj, if it departs from vi at time t. A userspecified query is to ask the minimumtraveltime path, from a source node, vs, to a destination node, ve, over the timedependent graph, GT, with the best departure time to be selected from a time interval T. We denote this user query as LTT(vs, ve, T) over GT. The challenge of this problem is the added complexity due to the time dependency in the timedependent graph. That is, edge delays are not constants, and can vary from time to time. In this paper, we propose a novel algorithm to find the minimumtraveltime path with the best departure time for a LTT(vs, ve, T) query over a large graph GT. Our approach outperforms existing algorithms in terms of both time complexity in theory and efficiency in practice. We will discuss the design of our algorithm, together with its correctness and complexity. We conducted extensive experimental studies over large graphs and will report our findings. 1.
Efficient query processing on spatial networks
 In Proceedings of the 13th ACM International Symposium on Advances in Geographic Information Systems
, 2005
"... A framework for determining the shortest path and the distance between every pair of vertices on a spatial network is presented. The framework, termed SILC, uses path coherence between the shortest path and the spatial positions of vertices on the spatial network, thereby, resulting in an encoding t ..."
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Cited by 30 (14 self)
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A framework for determining the shortest path and the distance between every pair of vertices on a spatial network is presented. The framework, termed SILC, uses path coherence between the shortest path and the spatial positions of vertices on the spatial network, thereby, resulting in an encoding that is compact in representation and fast in path and distance retrievals. Using this framework, a wide variety of spatial queries such as incremental nearest neighbor searches and spatial distance joins can be shown to work on datasets of locations residing on a spatial network of sufficiently large size. The suggested framework is suitable for both main memory and diskresident datasets. Categories and Subject Descriptors
Combining SpeedUp Techniques for ShortestPath Computations
 In Proc. 3rd Workshop on Experimental and Efficient Algorithms. LNCS
, 2004
"... Computing a shortest path from one node to another in a directed graph is a very common task in practice. This problem is classically solved by Dijkstra's algorithm. Many techniques are known to speed up this algorithm heuristically, while optimality of the solution can still be guaranteed. ..."
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Cited by 29 (7 self)
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Computing a shortest path from one node to another in a directed graph is a very common task in practice. This problem is classically solved by Dijkstra's algorithm. Many techniques are known to speed up this algorithm heuristically, while optimality of the solution can still be guaranteed. In most studies, such techniques are considered individually.
Reverse Nearest Neighbors in Large Graphs
"... 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 fundam ..."
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Cited by 23 (1 self)
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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
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 22 (6 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.