Reverse Nearest Neighbor Queries Research Articles

Efficient Processing of Continuous Reverse k Nearest Neighbor on Moving Objects in Road Networks

A reverse k nearest neighbor (RkNN) query retrieves all the data points that have q as one of their k closest points. In recent years, considerable research has been conducted into monitoring reverse k nearest neighbor queries. In this paper, we study the problem of continuous reverse nearest neighbor queries where both the query object q and data objects are moving. Existing state-of-the-art techniques are sensitive towards the movement of data objects, e.g., a candidate object must be verified whenever it changes its location. Further, insufficient attention has been given to the monitoring of RNN queries in dynamic road networks where the network weight changes depending on the traffic conditions. In this paper, we address these problems by proposing a new safe exit-based algorithm called CORE-X for efficiently computing the safe exit points of both query and data objects. The safe exit point of an object indicates the point at which its safe region and non-safe region meet, thus a set of safe exit points represents the border of the safe region. Within the safe region, the query result remains unchanged provided the query and data objects remain inside their respective safe regions. The results of extensive experiments conducted using real road maps indicate that the proposed algorithm significantly reduces communication and computation costs compared to the state-of-the-art algorithm.

DART+: Direction-aware bichromatic reverse k nearest neighbor query processing in spatial databases

This article presents a novel type of queries in spatial databases, called the direction-aware bichromatic reverse k nearest neighbor(DBRkNN) queries, which extend the bichromatic reverse nearest neighbor queries. Given two disjoint sets, P and S, of spatial objects, and a query object q in S, the DBRkNN query returns a subset P? of P such that k nearest neighbors of each object in P? include q and each object in P? has a direction toward q within a pre-defined distance. We formally define the DBRkNN query, and then propose an efficient algorithm, called DART, for processing the DBRkNN query. Our method utilizes a grid-based index to cluster the spatial objects, and the B+-tree to index the direction angle. We adopt a filter-refinement framework that is widely used in many algorithms for reverse nearest neighbor queries. In the filtering step, DART eliminates all the objects that are away from the query object more than a pre-defined distance, or have an invalid direction angle. In the refinement step, remaining objects are verified whether the query object is actually one of the k nearest neighbors of them. As a major extension of DART, we also present an improved algorithm, called DART+, for DBRkNN queries. From extensive experiments with several datasets, we show that DART outperforms an R-tree-based naive algorithm in both indexing time and query processing time. In addition, our extension algorithm, DART+, also shows significantly better performance than DART.

Finding shortest paths on terrains by killing two birds with one stone

With the increasing availability of terrain data, e.g., from aerial laser scans, the management of such data is attracting increasing attention in both industry and academia. In particular, spatial queries, e.g., k -nearest neighbor and reverse nearest neighbor queries, in Euclidean and spatial network spaces are being extended to terrains. Such queries all rely on an important operation, that of finding shortest surface distances. However, shortest surface distance computation is very time consuming. We propose techniques that enable efficient computation of lower and upper bounds of the shortest surface distance, which enable faster query processing by eliminating expensive distance computations. Empirical studies show that our bounds are much tighter than the best-known bounds in many cases and that they enable speedups of up to 43 times for some well-known spatial queries.

Parallel approach for processing itinerary-based RNN queries in object tracking WSNs

Reverse Nearest Neighbor (RNN) query is to find the set of objects that are closer to the Q than any other objects in dataset D. Owing to the wide application spectrum, there have been great demands for effective RNN query processing in the circumstance where the sensor nodes are deployed over a wide geographical area and track the location of objects. However, relentless energy and computing resource depletion are inevitable by the maintaining the infrastructures in the existing researches. Motivated by these issues, we propose a novel approach, named the parallel itinerary-based RNN (PIRNN) query processing algorithm which does not rely on any kind of infrastructures. PIRNN disseminates multiple itineraries concurrently and it prunes the search area to increase performance. Furthermore, we extend PIRNN with two optimization heuristics, called Peri-Segment Completion (PSC) and Look Forward (LF) to minimize the area to be searched. In order to evaluate the performance of PIRNN query processing, we compare PIRNN with itinerary-based SAA and TPL. The extensive simulation results show that the PIRNN method outperforms SAA and TPL in terms of network traffic.

Spatial query processing in road networks for wireless data broadcast

Recently, wireless broadcast environments have attracted significant attention due to its high scalability to broadcast information to a large number of mobile subscribers. It is especially a promising and desirable dissemination method for the heavily loaded environment where a great number of the same type of requests are sent from the users. There have been many studies on processing spatial queries via broadcast model recently. However, not much attention is paid to the spatial queries in road networks on wireless broadcast environments. In this paper, we focus on three common types of spatial queries, namely, k nearest neighbor (kNN) queries, range queries and reverse nearest neighbor (RNN) queries in spatial networks for wireless data broadcast. Specially, we propose a novel index for spatial queries in wireless broadcast environments (ISW). With the reasonable organization and the effectively pre-computed bounds, ISW provides a powerful framework for spatial queries. Furthermore, efficient algorithms are designed to cope with kNN, range and RNN queries separately based on ISW. The search space can be obviously reduced and subsequently the client can download as less as possible data for query processing, which can conserve the energy while not significantly influence the efficiency. The detailed theory analysis of cost model and the experimental results are presented for verifying the efficiency and effectiveness of ISW and our methods.

On multi-type reverse nearest neighbor search

This paper presents a study of the Multi-Type Reverse Nearest Neighbor (MTRNN) query problem. Traditionally, a reverse nearest neighbor (RNN) query finds all the objects that have the query point as their nearest neighbor. In contrast, an MTRNN query finds all the objects that have the query point in their multi-type nearest neighbors. Existing RNN queries find an influence set by considering only one feature type. However, the influence from multiple feature types is often critical for strategic decision making in many business scenarios, such as site selection for a new shopping center. To that end, we first formalize the notion of the MTRNN query by considering the influence of multiple feature types. We also propose R-tree based algorithms to find the influence set for a given query point and multiple feature types. Finally, experimental results are provided to show the strength of the proposed algorithms as well as design decisions related to performance tuning.

Effectiveness of NAQ-tree in handling reverse nearest-neighbor queries in high-dimensional metric space

Reverse nearest-neighbor (RNN) query processing is important for many applications such as decision-support systems, profile-based marketing and molecular biology; consequently, RNN query processing has attracted considerable attention in the research community in recent years. Most existing approaches for RNN query processing either rely on nearest-neighbor pre-computation or work for specific data space (e.g., the Euclidean space). The only method for RNN query processing in metric space is based on the M-tree. In this paper, we propose an approach for RNN query processing in high-dimensional metric space using distance-based index structure (in particular, NAQ-tree that outperforms the other distance-based index structures as we have already verified in a previous study). In high-dimensional space, the properties of distance-based index structure provide strong pruning rules than the M-tree. In addition, unlike the previous work, our approach integrates the filtering and verification steps and uses the information obtained in the verification stage to further improve the filtering rate. Our approach delivers results incrementally and hence well serves real-time applications. The reported experimental results demonstrate the applicability and effectiveness of the proposed NAQ-tree-based RNN approach.

Spatial Network RNN Queries in GIS

Geographical information systems (GIS) and applications assist us in commuting, traveling and locating our points of interests. The efficient implementation and support of spatial queries in those systems is of particular interest and importance. The use of a Voronoi diagram has traditionally been applied to computational geometry. In this paper, we will show how a Voronoi diagram can be applied to support spatial queries in GIS systems, and in particular to reverse nearest neighbor (RNN) queries. An RNN query retrieves the set of interest objects having the query object as the nearest neighbor among other objects. Two cases of RNN queries are: monochromatic (MRNN) and bichromatic (BRNN). In the MRNN, the interest objects and the query object are of the same type, whereas in the BRNN they are of two different types. Due to the shortcomings of solutions for BRNN in the literature, we develop a new approach and algorithm, named the ‘2Vor BRNN algorithm’, for processing this query type in the context of the spatial network database (SNDB). Our novel approach extends the previous work and uses the ‘order-2 network Voronoi diagram’ to provide a more efficient solution for the BRNN. In addition, we experimentally confirm that the proposed algorithm outperforms the previous one in terms of memory used and response time.

Probabilistic Reverse Nearest Neighbor Queries on Uncertain Data

Uncertain data are inherent in various important applications and reverse nearest neighbor (RNN) query is an important query type for many applications. While many different types of queries have been studied on uncertain data, there is no previous work on answering RNN queries on uncertain data. In this paper, we formalize probabilistic reverse nearest neighbor query that is to retrieve the objects from the uncertain data that have higher probability than a given threshold to be the RNN of an uncertain query object. We develop an efficient algorithm based on various novel pruning approaches that solves the probabilistic RNN queries on multidimensional uncertain data. The experimental results demonstrate that our algorithm is even more efficient than a sampling-based approximate algorithm for most of the cases and is highly scalable.

Facility location problems in the plane based on reverse nearest neighbor queries

For a finite set of points S, the (monochromatic) reverse nearest neighbor (RNN) rule associates with any query point q the subset of points in S that have q as its nearest neighbor. In the bichromatic reverse nearest neighbor (BRNN) rule, sets of red and blue points are given and any blue query is associated with the subset of red points that have it as its nearest blue neighbor. In this paper we introduce and study new optimization problems in the plane based on the bichromatic reverse nearest neighbor (BRNN) rule. We provide efficient algorithms to compute a new blue point under criteria such as: (1) the number of associated red points is maximum (MAXCOV criterion); (2) the maximum distance to the associated red points is minimum (MINMAX criterion); (3) the minimum distance to the associated red points is maximum (MAXMIN criterion). These problems arise in the competitive location area where competing facilities are established. Our solutions use techniques from computational geometry, such as the concept of depth of an arrangement of disks or upper envelope of surface patches in three dimensions.

Voronoi-based reverse nearest neighbor query processing on spatial networks

The use of Voronoi diagram has traditionally been applied to computational geometry and multimedia problems. In this paper, we will show how Voronoi diagram can be applied to spatial query processing, and in particular to Reverse Nearest Neighbor (RNN) queries. Spatial and geographical query processing, in general, and RNN in particular, are becoming more important, as online maps are now widely available. In this paper, using the concept of Voronoi diagram, we classify RNN into four types depending on whether the query point and the interest objects are the generator points of the Voronoi Polygon or not. Our approach is based on manipulating Network Voronoi Diagram properties and applying a progressive incremental network expansion for finding the polygon inner network distances required to solve RNN queries. Our experimentation results show that our approaches have good response times in answering RNN queries.

Visible Reverse k-Nearest Neighbor Query Processing in Spatial Databases

Reverse nearest neighbor (RNN) queries have a broad application base such as decision support, profile-based marketing, resource allocation, etc. Previous work on RNN search does not take obstacles into consideration. In the real world, however, there are many physical obstacles (e.g., buildings) and their presence may affect the visibility between objects. In this paper, we introduce a novel variant of RNN queries, namely, visible reverse nearest neighbor (VRNN) search, which considers the impact of obstacles on the visibility of objects. Given a data set P, an obstacle set O, and a query point q in a 2D space, a VRNN query retrieves the points in P that have q as their visible nearest neighbor. We propose an efficient algorithm for VRNN query processing, assuming that P and O are indexed by R-trees. Our techniques do not require any preprocessing and employ half-plane property and visibility check to prune the search space. In addition, we extend our solution to several variations of VRNN queries, including: 1) visible reverse k-nearest neighbor (VRkNN) search, which finds the points in P that have q as one of their k visible nearest neighbors; 2) \delta-VRkNN search, which handles VRkNN retrieval with the maximum visible distance \delta constraint; and 3) constrained VRkNN (CVRkNN) search, which tackles the VRkNN query with region constraint. Extensive experiments on both real and synthetic data sets have been conducted to demonstrate the efficiency and effectiveness of our proposed algorithms under various experimental settings.

Efficient processing of probabilistic reverse nearest neighbor queries over uncertain data

Reverse nearest neighbor (RNN) search is very crucial in many real applications. In particular, given a database and a query object, an RNN query retrieves all the data objects in the database that have the query object as their nearest neighbors. Often, due to limitation of measurement devices, environmental disturbance, or characteristics of applications (for example, monitoring moving objects), data obtained from the real world are uncertain (imprecise). Therefore, previous approaches proposed for answering an RNN query over exact (precise) database cannot be directly applied to the uncertain scenario. In this paper, we re-define the RNN query in the context of uncertain databases, namely probabilistic reverse nearest neighbor (PRNN) query, which obtains data objects with probabilities of being RNNs greater than or equal to a user-specified threshold. Since the retrieval of a PRNN query requires accessing all the objects in the database, which is quite costly, we also propose an effective pruning method, called geometric pruning (GP), that significantly reduces the PRNN search space yet without introducing any false dismissals. Furthermore, we present an efficient PRNN query procedure that seamlessly integrates our pruning method. Extensive experiments have demonstrated the efficiency and effectiveness of our proposed GP-based PRNN query processing approach, under various experimental settings.

Ranked Reverse Nearest Neighbor Search

Given a set of data points P and a query point q in a multidimensional space, reverse nearest neighbor (RNN) query finds data points in P whose nearest neighbors are q. Reverse k-nearest neighbor (RkNN) query (where k ges 1) generalizes RNN query to find data points whose kNNs include q. For RkNN query semantics, q is said to have influence to all those answer data points. The degree of q's influence on a data point p (isin P) is denoted by kappap where q is the kappap-th NN of p. We introduce a new variant of RNN query, namely, ranked reverse nearest neighbor (RRNN) query, that retrieves t data points most influenced by q, i.e., the t data points having the smallest kappa's with respect to q. To answer this RRNN query efficiently, we propose two novel algorithms, kappa-counting and kappa-browsing that are applicable to both monochromatic and bichromatic scenarios and are able to deliver results progressively. Through an extensive performance evaluation, we validate that the two proposed RRNN algorithms are superior to solutions derived from algorithms designed for RkNN query.

Influence sets based on reverse nearest neighbor queries

Inherent in the operation of many decision support and continuous referral systems is the notion of the “influence” of a data point on the database. This notion arises in examples such as finding the set of customers affected by the opening of a new store outlet location, notifying the subset of subscribers to a digital library who will find a newly added document most relevant, etc. Standard approaches to determining the influence set of a data point involve range searching and nearest neighbor queries. In this paper, we formalize a novel notion of influence based on reverse neighbor queries and its variants. Since the nearest neighbor relation is not symmetric, the set of points that are closest to a query point ( i.e. , the nearest neighbors) differs from the set of points that have the query point as their nearest neighbor (called the reverse nearest neighbors). Influence sets based on reverse nearest neighbor (RNN) queries seem to capture the intuitive notion of influence from our motivating examples. We present a general approach for solving RNN queries and an efficient R-tree based method for large data sets, based on this approach. Although the RNN query appears to be natural, it has not been studied previously. RNN queries are of independent interest, and as such should be part of the suite of available queries for processing spatial and multimedia data. In our experiments with real geographical data, the proposed method appears to scale logarithmically, whereas straightforward sequential scan scales linearly. Our experimental study also shows that approaches based on range searching or nearest neighbors are ineffective at finding influence sets of our interest.