Search operations in databases require special support at the physical level. This is true for conventional databases as well as spatial databases, where typical search operations include the point query (find all objects that contain a given search point) and the region query (find all objects that overlap a given search region). More

We present an efficient indexing method to locate 1-dimensional subsequences witbin a collection of sequences, such that the subsequences match a given (query) pattern within a specified tolerance. The idea is to map each data sequence into a small set of multidimensional rectangles in feature space. Then, these rectangles can be readily indexed using traditional spatial access methods, like the R*-tree [9]. In more deteil, we use a sliding window over the data sequence and extract its features; the result is a trail in feature space. We propose an efficient and effective algorithm to divide such trails into sub-trails, which are subsequently represented by their Minimum Bounding Rectangles (MBRs). We also examine queries of varying lengths, and we show how to handle each case efficiently. We implemented our method and carried out experiments on synthetic and real data (stock price movements). We compared the method to sequential scanning, which is the only obvious competitor. The results were excellent: our method accelerated the search time from 3 times up to 100 times.

The problem of indexing multidimensional objects is considered. First, a classification of existing methods is given along with a discussion of the major issues involved in multidimensional data indexing. Second, a variation to Guttman’s R-trees (R +-trees) that avoids overlapping rectangles in intermediate nodes of the tree is introduced. Algorithms for searching, updating, initial packing and reorganization of the structure are discussed in detail. Finally, we provide analytical results indicating that R +-trees achieve up to 50 % savings in disk accesses compared to an R-tree when searching files of thousands of rectangles. 1

The problem of indexing multidimensional objects is considered. First, a classification of existing methods is given along with a discussion of the major issues involved in multidimensional data indexing. Second, a variation to Guttman's R-trees (R -trees) that avoids overlapping rectangles in intermediate nodes of the tree is introduced. Algorithms for searching, updating, initial packing and reorganization of the structure are discussed in detail. Finally, we provide analytical results indicating that R -trees achieve up to 50% savings in disk accesses compared to an R-tree when searching files of thousands of rectangles. 1 Also with University of Maryland Systems Research Center. 2 Also with University of Maryland Institute for Advanced Computer Studies (UMIACS). This research was sponsored partialy by the National Science Foundation under Grant CDR-85-00108. 1. Introduction It has been recognized in the past that existing Database Management Systems (DBMSs) do not ...

– main idea; file structure – algorithms: insertion/split – deletion – search: range, nn, spatial joins – performance analysis – variations (packed; hilbert;...) 15-721 Copyright: C. Faloutsos (2001) 2 Problem • Given a collection of geometric objects (points, lines, polygons,...) • organize them on disk, to answer spatial queries (range, nn, etc) 15-721 Copyright: C. Faloutsos (2001) 3 1 (Who cares?)

We propose a new R-tree structure that outperforms all the older ones. The heart of the idea is to facilitate the deferred splitting approach in R-trees. This is done by proposing an ordering on the R-tree nodes. This ordering has to be 'good', in the sense that it should group 'similar' data rectangles together, to minimize the area and perimeter of the resulting minimum bounding rectangles (MBRs). Following [19] we have chosen the so-called '2D-c' method, which sorts rectangles according to the Hilbert value of the center of the rectangles. Given the ordering, every node has a welldefined set of sibling nodes; thus, we can use deferred splitting. By adjusting the split policy, the Hilbert R-tree can achieve as high utilization as desired. To the contrary, the R -tree has no control over the space utilization, typically achieving up to 70%. We designed the manipulation algorithms in detail, and we did a full implementation of the Hilbert R-tree. Our experiments show that the '2-to-...

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This paper describes PBSM (Partition Based Spatial--Merge), a new algorithm for performing spatial join operation. This algorithm is especially effective when neither of the inputs to the join have an index on the joining attribute. Such a situation could arise if both inputs to the join are intermediate results in a complex query, or in a parallel environment where the inputs must be dynamically redistributed. The PBSM algorithm partitions the inputs into manageable chunks, and joins them using a computational geometry based plane--sweeping technique. This paper also presents a performance study comparing the the traditional indexed nested loops join algorithm, a spatial join algorithm based on joining spatial indices, and the PBSM algorithm. These comparisons are based on complete implementations of these algorithms in Paradise, a database system for handling GIS applications. Using real data sets, the performance study examines the behavior of these spatial join algorithms in a vari...

We propose the concept of fractal dimension of a set of points, in order to quantify the deviation from the uniformity distribution. Using measurements on real data sets (road intersections of U.S. counties, star coordinates from NASA's Infrared-Ultraviolet Explorer etc.) we provide evidence that real data indeed are skewed, and, moreover, we show that they behave as mathematical fractals, with a measurable, non-integer fractal dimension. Armed with this tool, we then show its practical use in predicting the performance of spatial access methods, and specifically of the R-trees. We provide the first analysis of R-trees for skewed distributions of points: We develop a formula that estimates the number of disk accesses for range queries, given only the fractal dimension of the point set, and its count. Experiments on real data sets show that the formula is very accurate: the relative error is usually below 5%, and it rarely exceeds 10%. We believe that the fractal dimension will help rep...

Spatial joins are one of the most importaot operations for combining spatial objects of several relations. IO this paper, spatial join processing is studied in detail for extended spatial objects in two-dimensional data space. We present an approach for spatial join processing that is based on three steps. First, a spatial join is performed on the minimum bounding rectangles of the objects returning a set of candidates. Various approaches for accelerating this step of join processing have been examined at the last year’s conference [BKS 93a]. In this paper, we focus on the problem how to compute the answers from the set of candidates which is handled by the foliowing two steps. First of all, sophisticated approximations are used to identify answers as well as to filter out false hits from the set of candidates. For this purpose, we investigate various types of conservative and progressive approximations. In the last step, the exact geometry of the remaioing candidates has to be tested against the join predicate. The time required for computing spatial joio predicates can essentially be reduced when objects are adequately organized in main memory. IO our approach, objects are fiist decomposed into simple components which are exclusively organized by a main-memory resident spatial data structure. Overall, we present a complete approach of spatial join processing on complex spatial objects. The performance of the individual steps of our approach is evaluated with data sets from real cartographic applications. The results show that our approach reduces the total execution time of the spatial join by factors.