Traditional spatial queries return, for a given query object @math , all database objects that satisfy a given predicate, such as epsilon range and @math -nearest neighbors. This paper defines and studies inverse spatial queries, which, given a subset of database objects @math and a query predicate, return all objects which, if used as query objects with the predicate, contain @math in their result. We first show a straightforward solution for answering inverse spatial queries for any query predicate. Then, we propose a filter-and-refinement framework that can be used to improve efficiency. We show how to apply this framework on a variety of inverse queries, using appropriate space pruning strategies. In particular, we propose solutions for inverse epsilon range queries, inverse @math -nearest neighbor queries, and inverse skyline queries. Our experiments show that our framework is significantly more efficient than naive approaches.
Mutual-pruning approaches such as @cite_8 @cite_6 @cite_7 use other points to prune a given index entry @math . TPL @cite_7 is the most general and efficient approach. It uses an R-tree to compute a nearest neighbor ranking of the query point @math . The key idea is to iteratively construct Voronoi hyper-planes around @math using the retrieved neighbors. TPL can be used for inverse @math NN queries where @math , by simply performing a reverse @math NN query for each query point and then intersecting the results (i.e., the brute-force approach).
@cite_7 @cite_6 @cite_8
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A very important class of spatial queries consists of nearest-neighbor (NN) query and its variations. Many studies in the past decade utilize R-trees as their underlying index structures to address NN queries efficiently. The general approach is to use R-tree in two phases. First, R-tree's hierarchical structure is used to quickly arrive to the neighborhood of the result set. Second, the R-tree nodes intersecting with the local neighborhood (Search Region) of an initial answer are investigated to find all the members of the result set. While R-trees are very efficient for the first phase, they usually result in the unnecessary investigation of many nodes that none or only a small subset of their including points belongs to the actual result set. On the other hand, several recent studies showed that the Voronoi diagrams are extremely efficient in exploring an NN search region, while due to lack of an efficient access method, their arrival to this region is slow. In this paper, we propose a new index structure, termed VoR-Tree that incorporates Voronoi diagrams into R-tree, benefiting from the best of both worlds. The coarse granule rectangle nodes of R-tree enable us to get to the search region in logarithmic time while the fine granule polygons of Voronoi diagram allow us to efficiently tile or cover the region and find the result. Utilizing VoR-Tree, we propose efficient algorithms for various Nearest Neighbor queries, and show that our algorithms have better I O complexity than their best competitors. Group nearest neighbor (GNN) queries are a relatively new type of operations in spatial database applications. Different from a traditional kNN query which specifies a single query point only, a GNN query has multiple query points. Because of the number of query points and their arbitrary distribution in the data space, a GNN query is much more complex than a kNN query. In this paper, we propose two pruning strategies for GNN queries which take into account the distribution of query points. Our methods employ an ellipse to approximate the extent of multiple query points, and then derive a distance or minimum bounding rectangle (MBR) using that ellipse to prune intermediate nodes in a depth-first search via an R @math -tree. These methods are also applicable to the best-first traversal paradigm. We conduct extensive performance studies. The results show that the proposed pruning strategies are more efficient than the existing methods. The nearestor near-neighbor query problems arise in a large variety of database applications, usually in the context of similarity searching. Of late, there has been increasing interest in building search index structures for performing similarity search over high-dimensional data, e.g., image databases, document collections, time-series databases, and genome databases. Unfortunately, all known techniques for solving this problem fall prey to the of dimensionality." That is, the data structures scale poorly with data dimensionality; in fact, if the number of dimensions exceeds 10 to 20, searching in k-d trees and related structures involves the inspection of a large fraction of the database, thereby doing no better than brute-force linear search. It has been suggested that since the selection of features and the choice of a distance metric in typical applications is rather heuristic, determining an approximate nearest neighbor should su ce for most practical purposes. In this paper, we examine a novel scheme for approximate similarity search based on hashing. The basic idea is to hash the points Supported by NAVY N00014-96-1-1221 grant and NSF Grant IIS-9811904. Supported by Stanford Graduate Fellowship and NSF NYI Award CCR-9357849. Supported by ARO MURI Grant DAAH04-96-1-0007, NSF Grant IIS-9811904, and NSF Young Investigator Award CCR9357849, with matching funds from IBM, Mitsubishi, Schlumberger Foundation, Shell Foundation, and Xerox Corporation. Permission to copy without fee all or part of this material is granted provided that the copies are not made or distributed for direct commercial advantage, the VLDB copyright notice and the title of the publication and its date appear, and notice is given that copying is by permission of the Very Large Data Base Endowment. To copy otherwise, or to republish, requires a fee and or special permission from the Endowment. Proceedings of the 25th VLDB Conference, Edinburgh, Scotland, 1999. from the database so as to ensure that the probability of collision is much higher for objects that are close to each other than for those that are far apart. We provide experimental evidence that our method gives signi cant improvement in running time over other methods for searching in highdimensional spaces based on hierarchical tree decomposition. Experimental results also indicate that our scheme scales well even for a relatively large number of dimensions (more than 50). In many applications involving spatial objects, we are only interested in objects that are directly visible from query points. In this paper, we formulate the visible k nearest neighbor (VkNN) query and present incremental algorithms as a solution, with two variants differing in how to prune objects during the search process. One variant applies visibility pruning to only objects, whereas the other variant applies visibility pruning to index nodes as well. Our experimental results show that the latter outperforms the former. We further propose the aggregate VkNN query that finds the visible k nearest objects to a set of query points based on an aggregate distance function. We also propose two approaches to processing the aggregate VkNN query. One accesses the database via multiple VkNN queries, whereas the other issues an aggregate k nearest neighbor query to retrieve objects from the database and then re-rank the results based on the aggregate visible distance metric. With extensive experiments, we show that the latter approach consistently outperforms the former one.