Effective Decompositioning of Complex Spatial Objects into Intervals Hans-Peter Kriegel, Peter Kunath, Martin Pfeifle, Matthias Renz University of Munich, Germany, {kriegel, kunath, pfeifle, renz}@dbs.informatik.uni-muenchen.de ABSTRACT In order to guarantee efficient query processing together with industrial strength, spatial index structures have to be integrated into fully-fledged object-relational database management systems (ORDBMSs). A promising way to cope with spatial data can be found somewhere in between replicating and non-replicating spatial index structures. In this paper, we use the concept of gray intervals which helps to range between these two extremes. Based on the gray in- tervals, we introduce a cost-based decomposition method for accelerating the Relational Interval Tree (RI-tree). Our approach uses compression algorithms for the effective storage of the decomposed spatial objects. The experimen- tal evaluation on real-world test data points out that our new concept outperforms the RI-tree by up to two orders of magnitude with respect to overall query response time and secondary storage space. KEY WORDS Relational Indexing, Spatial Objects, Decompositioning. 1. Introduction The efficient management of spatially extended objects has become an enabling technology for many novel database applications. As a common and successful approach, spa- tial objects can conservatively be approximated by a set of voxels, i.e. cells of a grid covering the complete data space. By means of space filling curves, each voxel can be encod- ed by a single integer and, thus, an extended object is repre- sented by a set of enumerated voxels. These voxels can fur- ther be grouped together to intervals, which can be organized by spatial index structures. By expressing spatial region queries as intersections of these spatial primitives, vital operations for two-dimen- sional GIS and environmental information systems [11] can be supported. Efficient and scalable database solutions are also required for three-dimensional CAD applications to cope with rapidly growing amounts of dynamic data. Such applications include the digital mock-up of vehicles and airplanes, virtual reality applications, e.g. haptic simula- tions in virtual product environments. For these applica- tions suitable index structures, which guarantee efficient spatial query processing, are indispensable. For commercial use, a seamless and capable integra- tion of temporal and spatial indexing into industrial- strength databases is essential. Fortunately, a lot of tradi- tional database servers have evolved into Object-Relational Database Management Systems (ORDBMS). This means that in addition to the efficient and secure management of data ordered under the relational model, these systems now also provide support for data organized under the object model. Object types and other features, such as binary large objects (BLOBs), external procedures, extensible indexing, user-defined aggregate functions and query optimization, can be used to build powerful, reusable server-based com- ponents. An important new requirement for large spatial objects is a high approximation quality which is primarily influ- enced by the resolution of the grid covering the data space. A promising way to cope with high resolution spatial data may be found somewhere in between replicating and non- replicating spatial index structures. In the case of replicat- ing access methods, e.g. the Relational Interval Tree [9], the number of the simple spatial primitives used to approxi- mate the objects can become very high, resulting in a stor- age and query processing overhead. On the other hand, many of the non-replicating access methods, e.g. R-trees [5], use simple spatial primitives such as rectilinear hyper- rectangles for one-value approximations of extended ob- jects. Although providing the minimal storage complexity, one-value approximations of spatially extended objects of- ten are far too coarse. In many GIS applications, objects feature a very complex and fine-grained geometry. A non- replicating storage of such data causes region queries to produce too many false hits that have to be eliminated by subsequent filter steps. For such applications, the accuracy can be improved by decomposing the objects. 1.1 Related Work In this section, we will shortly discuss different aspects re- lated to an effective decompositioning of complex spatial objects for efficient relational indexing. Complex Spatial Objects. Gaede pointed out that the number of voxels representing a spatially extended object exponentially depends on the granularity of the grid ap- proximation [3]. Furthermore, the extensive analysis given in [10] and [2] shows that the asymptotic redundancy of an interval- and tile-based decomposition is proportional to the surface of the approximated object. Thus, in the case of large high-resolution parts, e.g. wings of an airplane, the number of tiles or intervals can become unreasonably high. Relational Spatial Indexing. A wide variety of access methods for spatially extended objects has been published so far. For a general overview on spatial index structures, we refer the reader to the surveys of Manolopoulos, The- odoridis and Tsotras [12] or Gaede and Günther [4]. We use the Relational Interval Tree (RI-tree) in this paper because it outperforms competing index structures by factors of up IASTED Int. Conf. on Databases and Applications (DBA'04)