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16
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 26 (8 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.
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 14 (6 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.
Query processing using distance oracles for spatial networks
 Best Papers of ICDE 2009 Special Issue
"... 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 here is that the efficient execution of spatial oper ..."
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Cited by 10 (3 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 here is that the efficient execution of spatial operations usually involves the computation of distance along a spatial network instead of “as the crow flies, ” which is not simple. Techniques are described that enable the determination of the network distance between any pair of points (i.e., vertices) with as little as OðnÞ space rather than having to store the n2 distances between all pairs. This is done by being willing to expend a bit more time to achieve this goal such as Oðlog nÞ instead of Oð1Þ, as well as by accepting an error " in the accuracy of the distance that is provided. The strategy that is adopted reduces the space requirements and is based on the ability to identify groups of source and destination vertices for which the distance is approximately the same within some ". The reductions are achieved by introducing a construct termed a distance oracle that yields an estimate of the network distance (termed the "approximate distance) between any two vertices in the spatial network. The distance oracle is obtained by showing how to adapt the wellseparated pair technique from computational geometry to spatial networks. Initially, an "approximate distance oracle of size Oð n " dÞ is used that is capable of retrieving the approximate network distance in Oðlog nÞ time using a Btree. The retrieval time can be theoretically reduced n log n further to Oð1Þ time by proposing another "approximate distance oracle of size Oð
Approximate shortest distance computing: A querydependent local landmark scheme
 In ICDE
, 2012
"... Abstract—Shortest distance query between two nodes is a fundamental operation in largescale networks. Most existing methods in the literature take a landmark embedding approach, which selects a set of graph nodes as landmarks and computes the shortest distances from each landmark to all nodes as an ..."
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Cited by 7 (1 self)
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Abstract—Shortest distance query between two nodes is a fundamental operation in largescale networks. Most existing methods in the literature take a landmark embedding approach, which selects a set of graph nodes as landmarks and computes the shortest distances from each landmark to all nodes as an embedding. To handle a shortest distance query between two nodes, the precomputed distances from the landmarks to the query nodes are used to compute an approximate shortest distance based on the triangle inequality. In this paper, we analyze the factors that affect the accuracy of the distance estimation in the landmark embedding approach. In particular we find that a globally selected, queryindependent landmark set plus the triangulation based distance estimation introduces a large relative error, especially for nearby query nodes. To address this issue, we propose a querydependent local landmark scheme, which identifies a local landmark close to the specific query nodes and provides a more accurate distance estimation than the traditional global landmark approach. Specifically, a local landmark is defined as the least common ancestor of the two query nodes in the shortest path tree rooted at a global landmark. We propose efficient local landmark indexing and retrieval techniques, which are crucial to achieve low offline indexing complexity and online query complexity. Two optimization techniques on graph compression and graph online search are also proposed, with the goal to further reduce index size and improve query accuracy. Our experimental results on largescale social networks and road networks demonstrate that the local landmark scheme reduces the shortest distance estimation error significantly when compared with global landmark embedding. I.
Querying Shortest Path Distance with Bounded Errors in Large Graphs
"... Abstract. Shortest paths and shortest path distances are important primary queries for users to query in a large graph. In this paper, we propose a new approach to answer shortest path and shortest path distance queries efficiently with an error bound. The error bound is controlled by a userspecif ..."
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Cited by 5 (3 self)
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Abstract. Shortest paths and shortest path distances are important primary queries for users to query in a large graph. In this paper, we propose a new approach to answer shortest path and shortest path distance queries efficiently with an error bound. The error bound is controlled by a userspecified parameter, and the online query efficiency is achieved with prepossessing offline. In the offline preprocessing, we take a reference node embedding approach which computes the singlesource shortest paths from each reference node to all the other nodes. To guarantee the userspecified error bound, we design a novel coveragebased reference node selection strategy, and show that selecting the optimal set of reference nodes is NPhard. We propose a greedy selection algorithm which exploits the submodular property of the formulated objective function, and use a graph partitioningbased heuristic to further reduce the offline computational complexity of reference node embedding. In the online query answering, we use the precomputed distances to provide a lower bound and an upper bound of the true shortest path distance based on the triangle inequality. In addition, we propose a linear algorithm which computes the approximate shortest path between two nodes within the error bound. We perform extensive experimental evaluation on a largescale road network and a social network and demonstrate the effectiveness and efficiency of our proposed methods. 1
1Joint Search by Social and Spatial Proximity
"... Abstract—The diffusion of social networks introduces new challenges and opportunities for advanced services, especially so with their ongoing addition of locationbased features. We show how applications like company and friend recommendation could significantly benefit from incorporating social and ..."
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Cited by 2 (0 self)
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Abstract—The diffusion of social networks introduces new challenges and opportunities for advanced services, especially so with their ongoing addition of locationbased features. We show how applications like company and friend recommendation could significantly benefit from incorporating social and spatial proximity, and study a query type that captures these twofold semantics. We develop highly scalable algorithms for its processing, and enhance them with elaborate optimizations. Finally, we use real social network data to empirically verify the efficiency and efficacy of our solutions. F 1
Best Upgrade Plans for Large Road Networks
"... Abstract. In this paper, we consider a new problem in the context of road network databases, named Resource Constrained Best Upgrade Plan computation (BUP, for short). Consider a transportation network (weighted graph) G where a subset of the edges are upgradable, i.e., for each such edge there is a ..."
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Abstract. In this paper, we consider a new problem in the context of road network databases, named Resource Constrained Best Upgrade Plan computation (BUP, for short). Consider a transportation network (weighted graph) G where a subset of the edges are upgradable, i.e., for each such edge there is a cost, which if spent, the weight of the edge can be reduced to a specific new value. Given a source and a destination in G, and a budget (resource constraint) B, the BUP problem is to identify which upgradable edges should be upgraded so that the shortest path distance between source and destination (in the updated network) is minimized, without exceeding the available budget for the upgrade. In addition to transportation networks, the BUP query arises in other domains too, such as telecommunications. We propose a framework for BUP processing and evaluate it with experiments on large, real road networks. 1
RouteSaver: Leveraging Route APIs for Accurate and Efficient Query Processing at LocationBased Services
 IEEE TRANSACTIONS ON KNOWLEDGE AND DATA ENGINEERING (TKDE)
"... Locationbased services (LBS) enable mobile users to query pointsofinterest (e.g., restaurants, cafes) on various features (e.g., price, quality, variety). In addition, users require accurate query results with uptodate travel times. Lacking the monitoring infrastructure for road traffic, the LB ..."
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Locationbased services (LBS) enable mobile users to query pointsofinterest (e.g., restaurants, cafes) on various features (e.g., price, quality, variety). In addition, users require accurate query results with uptodate travel times. Lacking the monitoring infrastructure for road traffic, the LBS may obtain live travel times of routes from online route APIs in order to offer accurate results. Our goal is to reduce the number of requests issued by the LBS significantly while preserving accurate query results. First, we propose to exploit recent routes requested from route APIs to answer queries accurately. Then, we design effective lower/upper bounding techniques and ordering techniques to process queries efficiently. Also, we study parallel route requests to further reduce the query response time. Our experimental evaluation shows that our solution is 3 times more efficient than a competitor, and yet achieves high result accuracy (above 98%).
Simple, Fast, and Scalable Reachability Oracle
"... A reachability oracle (or hop labeling) assigns each vertex v two sets of vertices: Lout(v) and Lin(v), such that u reaches v iff Lout(u) ∩ Lin(v) = ∅. Despite their simplicity and elegance, reachability oracles have failed to achieve efficiency in more than ten years since their introduction: The ..."
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A reachability oracle (or hop labeling) assigns each vertex v two sets of vertices: Lout(v) and Lin(v), such that u reaches v iff Lout(u) ∩ Lin(v) = ∅. Despite their simplicity and elegance, reachability oracles have failed to achieve efficiency in more than ten years since their introduction: The main problem is high construction cost, which stems from a setcover framework and the need to materialize transitive closure. In this paper, we present two simple and efficient labeling algorithms, HierarchicalLabeling and DistributionLabeling, which can work on massive realworld graphs: Their construction time is an order of magnitude faster than the setcover based labeling approach, and transitive closure materialization is not needed. On large graphs, their index sizes and their query performance can now beat the stateoftheart transitive closure compression and online search approaches.