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.
Given a point q, a reverse k nearest neighbor (RkNN) query retrieves all the data points that have q as one of their k nearest neighbors. Existing methods for processing such queries have at least one of the following deficiencies: (i) they do not support arbitrary values of k (ii) they cannot deal efficiently with database updates, (iii) they are applicable only to 2D data (but not to higher dimensionality), and (iv) they retrieve only approximate results. Motivated by these shortcomings, we develop algorithms for exact processing of RkNN with arbitrary values of k on dynamic multidimensional datasets. Our methods utilize a conventional data-partitioning index on the dataset and do not require any pre-computation. In addition to their flexibility, we experimentally verify that the proposed algorithms outperform the existing ones even in their restricted focus. Reverse Nearest Neighbor (RNN) queries are of particular interest in a wide range of applications such as decision support systems, profile based marketing, data streaming, document databases, and bioinformatics. The earlier approaches to solve this problem mostly deal with two dimensional data. However most of the above applications inherently involve high dimensions and high dimensional RNN problem is still unexplored. In this paper, we propose an approximate solution to answer RNN queries in high dimensions. Our approach is based on the strong correlation in practice between k-NN and RNN. It works in two phases. In the first phase the k-NN of a query point is found and in the next phase they are further analyzed using a novel type of query Boolean Range Query (BRQ). Experimental results show that BRQ is much more efficient than both NN and range queries, and can be effectively used to answer RNN queries. Performance is further improved by running multiple BRQ simultaneously. The proposed approach can also be used to answer other variants of RNN queries such as RNN of order k, bichromatic RNN, and Matching Query which has many applications of its own. Our technique can efficiently answer NN, RNN, and its variants with approximately same number of I O as running a NN query. In this paper we propose an algorithm for answering reverse nearest neighbor RNN queries a problem formulated only recently This class of queries is strongly related to that of nearest neighbor NN queries although the two are not necessarily complementary Unlike nearest neighbor queries RNN queries nd the set of database points that have the query point as the nearest neighbor There is no other proposal we are aware of that provides an algorithmic approach to answer RNN queries The earlier approach for RNN queries KM is based on the pre computation of neighborhood information that is organized in terms of auxiliary data structures It can be argued that the pre computation of the RNN information for all points in the database can be too restrictive In the case of dynamic databases insert and update operations are expensive and can lead to modi cations of large parts of the auxiliary data structures Also answers to RNN queries for a set of data points depend on the number of dimensions taken in considerations when initializing the data structures We propose an algorithmic approach that is exible enough to support a larger class of RNN queries and in order to support them we also extend the current method of nearest neighbor search to that of conditional nearest neighbor