A Self-adjusting Indexing Structure for Spatial Data

This paper introduces a spatial indexing structure that adjusts itself so as to provide faster access to spatially referenced data most in demand. The structure is a hybrid of a splay tree and a quadtree. The quadtree is a well-known spatial data structure that successively segments a spatial data area into quadrants, preserving the spatial arrangement of the data. Access to data is based on a traversal of the tree according to a featureÕs containment within a specific quadrant. The splay tree, on the other hand, is a binary search tree that adjusts itself through the use of a splay operation to promote frequently accessed data to the top of the tree where it can be more quickly accessed during future operations. Because users of spatial data tend to concentrate on a specific area for querying, the combination of features from both of these data structures should provide efficient access time to the region of interest. The research includes an object-oriented implementation of the structure as part of the Object Vector Product Format (OVPF) project. This paper examines the data structure and associated operations, and gives an outline of the object-oriented implementation and preliminary experimental results. INTRODUCTION The data structure introduced in this paper was developed specifically to provide near-optimal performance for interactive access to spatial data. That is, we undertook this research to provide an efficient means of accessing data for the way in which end users of a spatial information system such as a GIS would generally be expected to require retrieval of such information. The paradigm with which we are concerned is one in which the user first loads a large quantity of spatial data (e.g., coastlines of the world), then consecutively zooms in to the area of interest (e.g., Australian coastline, eastern Australian coastline, etc.). It is this area of interest in which most of the userÕs queries are concentrated. This can be considered the userÕs Òworking setÓ in a way analogous to that of the operating systems concept. By that, we mean that the userÕs access pattern will stabilize at some level to involve primarily data from only one region or quad cell. The background section immediately following this section provides information on both quadtrees and splay trees, along with a brief discussion on our view of the interactive user paradigm, which motivated this work. Following that is an introduction to the spatial splay tree (SS-tree), the hybrid data structure developed to enhance performance of interactive user queries. This section includes a discussion of the creation of the SS-tree, as well as various operations on the tree. An object-oriented implementation of the SS-tree in the Object Vector Product Format (OVPF) prototype is discussed next, followed by the conclusion and directions for future work. BACKGROUND Indexing of spatial data is essential to provide efficient access to the data. Several indexing schemes have been developed, including the quadtree (Hunter 1978), the Rtree (Guttman 1984) and its variations (Beckmann 1990, Sellis 1987), and k-d-B-trees (Robinson 1981), to name a few. A taxonomy and discussion of issues in spatial indexing can be found in (Lu 1993), while a more in-depth look at spatial data structures as a whole is given in (Samet 1989). The following sub-section gives a general overview of the quadtree structure and its use in spatial query processing. Readers interested in more details are referred to (Samet 1984). Following the quadtree discussion is an introduction to the splay tree, its operations and potential advantages. Quadtrees The quadtree is probably the most cited and used spatial indexing method at this time. The reasons for this are due to the fact that the quadtree provides a simple, intuitive method of organizing spatial data that also provides efficient access to the data. The quadtree can be used for indexing both vector and raster data. The principle upon which it is based is simply the regular recursive subdivision of blocks of spatial data into four equal-sized cells, or quadrants. Cells are successively subdivided until some criterion is met, usually either: (1) each cell contains homogeneous data, e.g., a single ÒfeatureÓ for vector data, or rasters containing the same value (known as a region quadtree), or (2) a preset number of decomposition iterations has been performed. Thus, the cells of a quadtree are of a standard size (in powers of two) and are nonoverlapping in terms of areal representation. A tree structure is constructed by arranging each cell as the parent of its component quadrant cells. This structuring leads to a tree whose nodes at any level of the tree are all of the same size, that size being exactly one fourth the size of the nodes at the next higher level of the tree. An example of a quad-based subdivision of an image and its associated tree structure is shown below in Figure 1. Figure 1. Subdivision of an image into quadrants (a), and quadtree representation (b). b. a b