Bichromatic Reverse Nearest Neighbor Research Articles

Finding optimal region for bichromatic reverse nearest neighbor in two- and three-dimensional spaces

The MaxBRNN problem is to find an optimal region such that setting up a new service within this region might attract the maximum number of customers by proximity. The MaxBRNN problem has many practical applications such as service location planning and emergency schedule. In typical real-life applications the data volume of the problem is huge, thus an efficient solution is highly desired. In this paper, we propose two efficient algorithms, namely, OptRegion, and 3D-OptRegion to tackle the MaxBRNN problem and MaxBRkNN in two- and three-dimensional spaces, especially for the 3D-OptRegion, we propose a powerful pruning strategy Fine-grained Pruning Strategy to reduce the searching space. Our method employs three optimization techniques, i.e., sweep line (sweep plane in a three-dimensional space), pruning strategy (based on upper bound estimation), and influence value computation (of candidate points), to improve the search performance. In a three-dimensional space, we additionally use a fine-grained pruning strategy to further improve the pruning effect. Extensive experimental evaluation using both real and synthetic datasets confirms that both OptRegion and 3D-OptRegion outperform the existing algorithms significantly under all problem instances.

Capacity constrained maximizing bichromatic reverse nearest neighbor search

When planning a new development (facility/service site), location decisions are always the major issue. In this paper we introduce a novel query capacity constraint MaxBRNN, which can solve the facility location selection problem efficiently.The MaxBRNN (maximizing BRNN) query is based on bichromatic reverse nearest neighbor (BRNN) query which uses the number of reverse nearest customers to model the influence of a facility location. The MaxBRNN query has been appreciated extensively in spatial database studies because of its great potential in real life applications, such as, markets decision, sensor network clustering and the design of GSM (global system for mobile communication). The existing researches mostly suppose that the service facility's capacity is unlimited. However, in real cases, facilities are inevitably constrained by designed capacities. For example, if the government wants to select a new place to set up an emergency center to share the existing centers’ patients, they need to know the current emergency centers’ capacity so that they can estimate the new center's scale. Thus, the capacity constrained MaxBRNN query is significantly important in planning a new development. As far as we know, the capacity constrained MaxBRNN query has not been studied yet, so, we formulate this problem, propose a basic solution and develop some efficient algorithms for the query.Our major contributions are as follows: (1) we propose a novel query capacity constraint MaxBRNN which can solve the facility location selection problem effectively and efficiently; (2) we develop a basic algorithm CCMB and two improved algorithms which can find out the optimal region in terms of building a new facility, maximize its impact and deal with the complicated reassignment when adding new facilities into the dataset; (3) we prove the algorithms’ effectiveness and efficiency by extensive experiments using both real and synthetic data sets.

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.

A new approach for maximizing bichromatic reverse nearest neighbor search

Maximizing bichromatic reverse nearest neighbor (MaxBRNN) is a variant of bichromatic reverse nearest neighbor (BRNN). The purpose of the MaxBRNN problem is to find an optimal region that maximizes the size of BRNNs. This problem has lots of real applications such as location planning and profile-based marketing. The best-known algorithm for the MaxBRNN problem is called MaxOverlap. In this paper, we study the MaxBRNN problem and propose a new approach called MaxSegment for a two-dimensional space when the \(L_2\)-norm is used. Then, we extend our algorithm to other variations of the MaxBRNN problem such as the MaxBRNN problem with other metric spaces, and a three-dimensional space. Finally, we conducted experiments on real and synthetic datasets to compare our proposed algorithm with existing algorithms. The experimental results verify the efficiency of our proposed approach.

Method for Maximizing Bichromatic Reverse Nearest Neighbor in Road Networks

Method for Maximizing Bichromatic Reverse Nearest Neighbor in Road Networks

Maximizing bichromatic reverse nearest neighbor for L p -norm in two- and three-dimensional spaces

Bichromatic reverse nearest neighbor (BRNN) has been extensively studied in spatial database literature. In this paper, we study a related problem called MaxBRNN: find an optimal region that maximizes the size of BRNNs for L p -norm in two- and three- dimensional spaces. Such a problem has many real-life applications, including the problem of finding a new server point that attracts as many customers as possible by proximity. A straightforward approach is to determine the BRNNs for all possible points that are not feasible since there are a large (or infinite) number of possible points. To the best of our knowledge, there are no existing algorithms which solve MaxBRNN for any L p -norm space of two- and three-dimensionality. Based on some interesting properties of the problem, we come up with an efficient algorithm called MaxOverlap for to solve this problem. Extensive experiments are conducted to show that our algorithm is efficient.

Bichromatic Reverse Nearest-Neighbor Search in Mobile Systems

In traditional reverse nearest-neighbor (RNN) search, the goal is to find the set of interest objects taking the query object as the nearest neighbor given that the interest objects and the query object have the same type. However, when the interest objects and the query object are of different types, this problem is called <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">bichromatic reverse nearest neighbor</i> (BRNN) search. The BRNN query has an increasing number of mobile applications and requires efficient algorithms for processing. In this paper, we present a novel approach for the BRNN search in the context of spatial network databases (SNDB). The main idea behind our approaches is to use Euclidean-based range search to prune the search space and use Euclidean distance in addition to network distance to minimize processing time. Finally, the experimental results confirm that our proposed algorithm have good performance on different network densities.

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.

Efficient method for maximizing bichromatic reverse nearest neighbor

Bichromatic reverse nearest neighbor (BRNN) has been extensively studied in spatial database literature. In this paper, we study a related problem called MaxBRNN: find an optimal region that maximizes the size of BRNNs. Such a problem has many real life applications, including the problem of finding a new server point that attracts as many customers as possible by proximity. A straightforward approach is to determine the BRNNs for all possible points that are not feasible since there are a large (or infinite) number of possible points. To the best of our knowledge, the fastest known method has exponential time complexity on the data size. Based on some interesting properties of the problem, we come up with an efficient algorithm called MaxOverlap. Extensive experiments are conducted to show that our algorithm is many times faster than the best-known technique.