Data structures for retrieval on integer grids

A family of data structures is presented for retrieval of the sum of values of points within a half-plane or polygon, given that the points are on integer coordinates in the plane. Fredman has shown that the problem has a lower bound of Ω(N^2/3) for intermixed updates and retrievals. Willard has shown an upper bound of O(N^2log6^4) for the case where the points are not restricted to integer coordinates.We have developed families of related data structures for retrievals of half-planes or polygons. One of the data structures permits intermixed updates and half-plane retrievals in O(N^2/3log N) time, where N is the size of the grid.We use a technique we call "Rotation" to permit a better match of a portion of the data structure to the particular problem. Rotations appear to be an effective method for trading-off storage redundancy against retrieval time for certain classes of problems

Query processing of geometric objects with free form boundarie sin spatial databases

The increasing demand for the use of database systems as an integrating factor in CAD/CAM applications has necessitated the development of database systems with appropriate modelling and retrieval capabilities. One essential problem is the treatment of geometric data which has led to the development of spatial databases. Unfortunately, most proposals only deal with simple geometric objects like multidimensional points and rectangles. On the other hand, there has been a rapid development in the field of representing geometric objects with free form curves or surfaces, initiated by engineering applications such as mechanical engineering, aviation or astronautics. Therefore, we propose a concept for the realization of spatial retrieval operations on geometric objects with free form boundaries, such as B-spline or Bezier curves, which can easily be integrated in a database management system. The key concept is the encapsulation of geometric operations in a so-called query processor. First, this enables the definition of an interface allowing the integration into the data model and the definition of the query language of a database system for complex objects. Second, the approach allows the use of an arbitrary representation of the geometric objects. After a short description of the query processor, we propose some representations for free form objects determined by B-spline or Bezier curves. The goal of efficient query processing in a database environment is achieved using a combination of decomposition techniques and spatial access methods. Finally, we present some experimental results indicating that the performance of decomposition techniques is clearly superior to traditional query processing strategies for geometric objects with free form boundaries

Reverse spatial visual top-k query

With the wide application of mobile Internet techniques an location-based services (LBS), massive multimedia data with geo-tags has been generated and collected. In this paper, we investigate a novel type of spatial query problem, named reverse spatial visual top- $k$ query (RSVQ k ) that aims to retrieve a set of geo-images that have the query as one of the most relevant geo-images in both geographical proximity and visual similarity. Existing approaches for reverse top- $k$ queries are not suitable to address this problem because they cannot effectively process unstructured data, such as image. To this end, firstly we propose the definition of RSVQ k problem and introduce the similarity measurement. A novel hybrid index, named VR 2 -Tree is designed, which is a combination of visual representation of geo-image and R-Tree. Besides, an extension of VR 2 -Tree, called CVR 2 -Tree is introduced and then we discuss the calculation of lower/upper bound, and then propose the optimization technique via CVR 2 -Tree for further pruning. In addition, a search algorithm named RSVQ k algorithm is developed to support the efficient RSVQ k query. Comprehensive experiments are conducted on four geo-image datasets, and the results illustrate that our approach can address the RSVQ k problem effectively and efficiently