On Using B + -Tree for Efficient Processing for the Boundary Neighborhood Problem AZZAM SLEIT Department of Computer Science, King Abdulla II School for Information Technology University of Jordan, P.O. Box 13898, Amman 11942, JORDAN azzam.sleit@ju.edu.jo Abstract: - A spatial data set is a collection of spatially referenced objects. The boundary neighborhood problem (i.e. BN problem) in spatial database systems is defined as finding all boundary neighbors for a given object based on special dimensions. This problem arises in several applications mainly in GIS systems such as finding all countries that surround a given lake or sea. Spatial objects can be represented and indexed by their minimum bounding rectangles (i.e. MBR’s) which give rough indication for the existence of an object. This paper proposes a solution for the BN problem, based on indexing the space using B + -tree. Key-Words: - B + -tree, Boundary Neighborhood Operator, Spatial Database, Rectangular Object 1 Introduction Management of spatial data is a requirement for various fields. Space of interest can be two dimensional geographical planes such as a geographic information systems, man-designed space like a layout of a VLSI design or conceptual information space like an electro-magnetic field. Systems of spatial data types or spatial algebras capture the abstractions for points, lines, rectangles and regions that provide the basis for modeling the structure of geometric entities in space together with their relationships, properties and operations. The key function of all spatial systems is the ability to query the database for specific relationships between objects especially topological relations such as the nearest, intersection and adjacency. The processing of such queries depends on the efficiency with which the objects are stored and indexed and how the query utilizes the stored objects. A point in space may represent the location of an object in space. Cities can be modeled as points in space while lines can be viewed as the basic abstraction for moving through space, or connections such as roads, rivers, or cables. Regions can be considered as the abstraction for objects having extent in 2d-space such as countries, lakes, or parks. Rectangles are often used in approximating regional spatial objects to serve as the minimum rectilinear enclosing objects or more commonly called the minimum bounding rectangles (i.e. MBRs) [4]. In such a case, the approximation gives a rough indication for an object existence within the MBR. A spatial query is then processed in two steps [5]. Firstly, a filter step employs an index to retrieve all MBRs that satisfy the query and possibly some false hits. Secondly, a refinement step uses the exact geometry of the objects to dismiss the false hits. Consequently, proposing that the spatial system represents and indexes regional objects in a two- dimensional space as MBRs, we define the boundary neighborhood problem (BN) as finding all MBRs which surround and touch the MBR of a particular object. Providing an efficient solution for large databases of MBRs has obvious applications in areas such as Geographic Information Systems, VLSI, and wireless computing. Several indexing structures have been proposed to facilitate accessing regions in multi-dimensional space. The quad-tree [7, 13, 14] which is one of the oldest methods used to index spatial data is a generalization of binary search tree to higher dimensions. It represents recursive subdivision of space into subspaces using iso-oriented hyper planes. In quad-tree variants, each interior node has four descendants, each corresponds to a rectangle. The rectangles are referred to using the compass points: NW, NE, SW, and SE quadrants. The decomposition of the space is performed until the number of points in a rectangle is smaller than a given threshold. Consequently, quad-trees are not necessarily balanced. This decomposition turns out WSEAS TRANSACTIONS on SYSTEMS Azzam Sleit ISSN: 1109-2777 711 Issue 7, Volume 7, July 2008