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UVDiagram: A Voronoi Diagram for Uncertain Data
, 2009
"... The Voronoi diagram is an important technique for answering nearestneighbor queries for spatial databases. In this paper, we study how the Voronoi diagram can be used on uncertain data, which are inherent in scientific and business applications. In particular, we propose the UncertainVoronoi Diagr ..."
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Cited by 14 (5 self)
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The Voronoi diagram is an important technique for answering nearestneighbor queries for spatial databases. In this paper, we study how the Voronoi diagram can be used on uncertain data, which are inherent in scientific and business applications. In particular, we propose the UncertainVoronoi Diagram (or UVdiagram in short). Conceptually, the data space is divided into distinct “UVpartitions”, where each UVpartition P is associated with a set S of objects; any point q located in P has the set S as its nearest neighbor with nonzero probabilities. The UVdiagram facilitates queries that inquire objects for having nonzero chances of being the nearest neighbor of a given query point. It also allows analysis of nearest neighbor information, e.g., finding out how many objects are the nearest neighbors in a given area. However, a UVdiagram requires exponential construction and storage costs. To tackle these problems, we devise an alternative representation for UVpartitions, and develop an adaptive index for the UVdiagram. This index can be constructed in polynomial time. We examine how it can be extended to support other related queries. We also perform extensive experiments to validate the effectiveness of our approach.
Scalable Processing of Snapshot and Continuous NearestNeighbor Queries over OneDimensional Uncertain Data
"... In several emerging and important applications, such as locationbased services, sensor monitoring and biological databases, the values of the data items are inherently imprecise. A useful query class for these data is the Probabilistic NearestNeighbor Query (PNN), which yields the IDs of objects ..."
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In several emerging and important applications, such as locationbased services, sensor monitoring and biological databases, the values of the data items are inherently imprecise. A useful query class for these data is the Probabilistic NearestNeighbor Query (PNN), which yields the IDs of objects for being the closest neighbor of a query point, together with the objects’ probability values. Previous studies showed that this query takes a long time to evaluate. To address this problem, we propose the Constrained NearestNeighbor Query (CPNN), which returns the IDs of objects whose probabilities are higher than some threshold, with a given error bound in the answers. We show that the CPNN can be answered efficiently with verifiers. These are methods that derive the lower and upper bounds of answer probabilities, so that an object can be quickly decided on whether it should be included in the answer. We design five verifiers, which can be used on uncertain data with arbitrary probability density functions. We further develop a partial evaluation technique, so that a user can obtain some answers quickly, without waiting
Probabilistic Voronoi Diagrams for Probabilistic Moving Nearest Neighbor Queries
"... A large spectrum of applications such as location based services and environmental monitoring demand efficient query processing on uncertain databases. In this paper, we propose the probabilistic Voronoi diagram (PVD) for processing moving nearest neighbor queries on uncertain data, namely the proba ..."
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A large spectrum of applications such as location based services and environmental monitoring demand efficient query processing on uncertain databases. In this paper, we propose the probabilistic Voronoi diagram (PVD) for processing moving nearest neighbor queries on uncertain data, namely the probabilistic moving nearest neighbor (PMNN) queries. A PMNN query finds the most probable nearest neighbor of a moving query point continuously. To process PMNN queries efficiently, we provide two techniques: a precomputation approach and an incremental approach. In the precomputation approach, we develop an algorithm to efficiently evaluate PMNN queries based on the precomputed PVD for the entire data set. In the incremental approach, we propose an incremental probabilistic safe region based technique that does not require to precompute the whole PVD to answer the PMNN query. In this incremental approach, we exploit the knowledge for a known region to compute the lower bound of the probability of an object being the nearest neighbor. Experimental results show that our approaches significantly outperform a sampling based approach by orders of magnitude in terms of I/O, query processing time, and communication overheads.
Voronoibased Nearest Neighbor Search for MultiDimensional Uncertain Databases
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Efficient Rank Based KNN Query Processing Over Uncertain Data
"... Abstract — Uncertain data are inherent in many applications such as environmental surveillance and quantitative economics research. As an important problem in many applications, KNN query has been extensively investigated in the literature. In this paper, we study the problem of processing rank base ..."
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Abstract — Uncertain data are inherent in many applications such as environmental surveillance and quantitative economics research. As an important problem in many applications, KNN query has been extensively investigated in the literature. In this paper, we study the problem of processing rank based KNN query against uncertain data. Besides applying the expected rank semantic to compute KNN, we also introduce the median rank which is less sensitive to the outliers. We show both ranking methods satisfy nice topk properties such as exactk, containment, unique ranking, value invariance, stability and fairfulness. For given query q, IO and CPU efficient algorithms are proposed in the paper to compute KNN based on expected (median) ranks of the uncertain objects. To tackle the correlations of the uncertain objects and high IO cost caused by large number of instances of the uncertain objects, randomized algorithms are proposed to approximately compute KNN with theoretical guarantees. Comprehensive experiments are conducted on both real and synthetic data to demonstrate the efficiency of our techniques. I.
DOI 10.1007/s007780120290x REGULAR PAPER UVdiagram: a voronoi diagram for uncertain spatial databases
"... © The Author(s) 2012. This article is published with open access at Springerlink.com Abstract The Voronoi diagram is an important technique for answering nearestneighbor queries for spatial databases. We study how the Voronoi diagram can be used for uncertain spatial data, which are inherent in sc ..."
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© The Author(s) 2012. This article is published with open access at Springerlink.com Abstract The Voronoi diagram is an important technique for answering nearestneighbor queries for spatial databases. We study how the Voronoi diagram can be used for uncertain spatial data, which are inherent in scientific and business applications. Specifically, we propose the UncertainVoronoi diagram (or UVdiagram), which divides the data space into disjoint “UVpartitions”. Each UVpartition P is associated with a set S of objects, such that any point q located in P has the set S as its nearest neighbor with nonzero probabilities. The UVdiagram enables queries that return objects with nonzero chances of being the nearest neighbor (NN) of a given point q. It supports “continuous nearestneighbor search”, which refreshes the set of NN objects of q, as the position of q changes. It also allows the analysis of nearestneighbor information, for example, to find out the number
PlaneSweep Algorithms for the K Group NearestNeighbor Query
"... Abstract: One of the most representative and studied queries in Spatial Databases is the (K) NearestNeighbor (NNQ), that discovers the (K) nearest neighbor(s) to a query point. An extension that is important for practical applications is the (K) Group Nearest Neighbor Query (GNNQ), that discovers ..."
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Abstract: One of the most representative and studied queries in Spatial Databases is the (K) NearestNeighbor (NNQ), that discovers the (K) nearest neighbor(s) to a query point. An extension that is important for practical applications is the (K) Group Nearest Neighbor Query (GNNQ), that discovers the (K) nearest neighbor(s) to a group of query points (considering the sum of distances to all the members of the query group). This query has been studied during the recent years, considering data sets indexed by efficient spatial data structures. We study (K) GNNQs, considering nonindexed data sets, since this case is frequent in practical applications. And we present two (RAMbased) PlaneSweep algorithms, that apply optimizations emerging from the geometric properties of the problem. By extensive experimentation, using real and synthetic data sets, we highlight the most efficient algorithm. 1
1Scalable Evaluation of Trajectory Queries over Imprecise Location Data
"... Abstract—Trajectory queries, which retrieve nearby objects for every point of a given route, can be used to identify alerts of potential threats along a vessel route, or monitor the adjacent rescuers to a travel path. However, the locations of these objects (e.g., threats, succours) may not be preci ..."
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Abstract—Trajectory queries, which retrieve nearby objects for every point of a given route, can be used to identify alerts of potential threats along a vessel route, or monitor the adjacent rescuers to a travel path. However, the locations of these objects (e.g., threats, succours) may not be precisely obtained due to hardware limitations of measuring devices, as well as complex natures of the surroundings. For such data, we consider a common model, where the possible locations of an object are bounded by a closed region, called “imprecise region”. Ignoring or coarsely wrapping imprecision can render low query qualities, and cause undesirable consequences such as missing alerts of threats and poor response rescue time. Also, the query is quite timeconsuming, since all points on the trajectory are considered. In this paper, we study how to efficiently evaluate trajectory queries over imprecise objects, by proposing a novel concept, ubisector, which is an extension of bisector specified for imprecise data. Based on the ubisector, we provide an efficient and versatile solution which supports different shapes of commonlyused imprecise regions (e.g., rectangles, circles, and line segments). Extensive experiments on real datasets show that our proposal achieves better efficiency, quality, and scalability than its competitors. Index Terms—Trajectory query, possible nearest neighbor, imprecise object, ubisector F 1
Noname manuscript No. (will be inserted by the editor) UVDiagram: A Voronoi Diagram for Uncertain Spatial Databases
"... the date of receipt and acceptance should be inserted later Abstract The Voronoi diagram is an important technique for answering nearestneighbor queries for spatial databases. We study how the Voronoi diagram can be used for uncertain spatial data, which are inherent in scientific and business a ..."
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the date of receipt and acceptance should be inserted later Abstract The Voronoi diagram is an important technique for answering nearestneighbor queries for spatial databases. We study how the Voronoi diagram can be used for uncertain spatial data, which are inherent in scientific and business applications. Specifically, we propose the UncertainVoronoi Diagram (or UVdiagram), which divides the data space into disjoint “UVpartitions”. Each UVpartition P is associated with a set S of objects, such that any point q located in P has the set S as its nearest neighbor with nonzero probabilities. The UVdiagram enables queries that return objects with nonzero chances of being the nearest neighbor (NN) of a given point q. It supports “continuous nearest neighbor search”, which refreshes the set of NN objects of q, as the position of q changes. It also allows the analysis of nearest neighbor information, e.g., to find out the number of objects that are the nearest neighbors of any point in a given area. A UVdiagram requires exponential construction and storage costs. To tackle these problems, we devise
Scalable Evaluation of Trajectory Queries over Imprecise Location Data
"... Abstract—Trajectory queries, which retrieve nearby objects for every point of a given route, can be used to identify alerts of potential threats along a vessel route, or monitor the adjacent rescuers to a travel path. However, the locations of these objects (e.g., threats, succours) may not be preci ..."
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Abstract—Trajectory queries, which retrieve nearby objects for every point of a given route, can be used to identify alerts of potential threats along a vessel route, or monitor the adjacent rescuers to a travel path. However, the locations of these objects (e.g., threats, succours) may not be precisely obtained due to hardware limitations of measuring devices, as well as complex natures of the surroundings. For such data, we consider a common model, where the possible locations of an object are bounded by a closed region, called “imprecise region”. Ignoring or coarsely wrapping imprecision can render low query qualities, and cause undesirable consequences such as missing alerts of threats and poor response rescue time. Also, the query is quite timeconsuming, since all points on the trajectory are considered. In this paper, we study how to efficiently evaluate trajectory queries over imprecise objects, by proposing a novel concept, ubisector, which is an extension of bisector specified for imprecise data. Based on the ubisector, we provide an efficient and versatile solution which supports different shapes of commonlyused imprecise regions (e.g., rectangles, circles, and line segments). Extensive experiments on real datasets show that our proposal achieves better efficiency, quality, and scalability than its competitors. Index Terms—Trajectory query, possible nearest neighbor, imprecise object, ubisector 1