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

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 examine the estimation of selectivities for range and spatial join queries in real spatial databases. As we have shown earlier [FK94a], real point sets: (a) violate consistently the "uniformity" and "independence" assumptions, (b) can often be described as "fractals", with non-integer (fractal) dimension. In this paper we show that, among the infinite family of fractal dimensions, the so called "Correlation Dimension" D 2 is the one that we need to predict the selectivity of spatial join. The main contribution is that, for all the real and synthetic point-sets we tried, the average number of neighbors for a given point of the point-set follows a power law, with D 2 as the exponent. This immediately solves the selectivity estimation for spatial joins, as well as for "biased" range queries (i.e., queries whose centers prefer areas of high point density). We present the formulas to estimate the selectivity for the biased queries, including an integration constant (K `shape 0 ) for ea...

The hash-join paradigm works well for relational joins, but is hard to apply to spatial joins. Relational hash-joins can guarantee that items in different hash buckets are irrelevant to each other for the purpose of join, but complexities intrinsic to spatial join predicates preclude such guarantees. It is also difficult to design spatial partition functions that produce equal-sized buckets. We examine how to apply the hash-join paradigm to spatial joins, and define a new framework for spatial hash-joins. Our spatial partition functions have two components: a set of bucket extents and an assignment function, which may map a data item into multiple buckets. Furthermore, the partition functions for the two input datasets may be different. We have designed and tested a spatial hashjoin method based on this framework. The partition function for the inner dataset is initialized by sampling the dataset, and evolves as data are inserted. The partition function for the outer dataset is immutab...

In many massive dataset applications the data must be stored in space and query efficient data structures on external storage devices. Often the data needs to be changed dynamically. In this chapter we discuss recent advances in the development of provably worst-case efficient external memory dynamic data structures. We also briefly discuss some of the most popular external data structures used in practice.

In this paper, we consider the filter step of the spatial join problem, for the case where neither of the inputs are indexed. We present a new algorithm, Scalable Sweeping-Based Spatial Join (SSSJ), that achieves both efficiency on real-life data and robustness against highly skewed and worst-case data sets. The algorithm combines a method with theoretically optimal bounds on I/O transfers based on the recently proposed distribution-sweeping technique with a highly optimized implementation of internal-memory plane-sweeping. We present experimental results based on an efficient implementation of the SSSJ algorithm, and compare it to the state-ofthe-art Partition-Based Spatial-Merge (PBSM) algorithm of Pate1 and DeWitt.

AbstractÐWe present a new approach for indexing animated objects and efficiently answering queries about their position in time and space. In particular, we consider an animated movie as a spatiotemporal evolution. A movie is viewed as an ordered sequence of frames, where each frame is a 2D space occupied by the objects that appear in that frame. The queries of interest are range queries of the form, ªfind the objects that appear in area S between frames fi and fjº as well as nearest neighbor queries such as, ªfind the q nearest objects to a given position A between frames fi and fj.º The straightforward approach to index such objects considers the frame sequence as another dimension and uses a 3D access method (such as, an R-Tree or its variants). This, however, assigns long ªlifetimeº intervals to objects that appear through many consecutive frames. Long intervals are difficult to cluster efficiently in a 3D index. Instead, we propose to reduce the problem to a partial-persistence problem. Namely, we use a 2D access method that is made partially persistent. We show that this approach leads to faster query performance while still using storage proportional to the total number of changes in the frame evolution. What differentiates this problem from traditional temporal indexing approaches is that objects are allowed to move and/or change their extent continuously between frames. We present novel methods to approximate such object evolutions. We formulate an optimization problem for which we provide an optimal solution for the case where objects move linearly. Finally, we present an extensive experimental study of the proposed methods. While we concentrate on animated movies, our approach is general and can be applied to other spatiotemporal applications as well. Index TermsÐAccess methods, spatiotemporal databases, animated objects, multimedia. 1

Existing Database Management Systems (DBMSs) do not handle efficiently multi-dimensional data such as boxes, polygons, or even points in a multi-dimensional space. We examine access methods for these data with two design goals in mind: (a) efficiency in terms of search speed and space overhead and (b) ability to be integrated in a DBMS easily. We propose a method to map multidimensional objects into points in a 1-dimensional space; thus, traditional primary-key access methods can be applied, with very few extensions on the part of the DBMS. We propose such mappings based on fractals; we implemented the whole method on top of a B +-tree, along with several mappings. Simulation experiments on several distributions of the input data show

. In dynamic spatio-temporal environments where objects may continuously move in space, maintaining consistent information about the location of objects and processing motion-specific queries is a challenging problem. In this paper, we focus on indexing and query processing techniques for mobile objects. Specifically, we develop a classification of different types of selection queries that arise in mobile environments and explore efficient algorithms to evaluate them. Query processing algorithms are developed for both native space and parametric space indexing techniques. A performance study compares the two indexing strategies for different types of queries. 1

A box-tree is a bounding-volume hierarchy that uses axis-aligned boxes as bounding volumes. The query complexity of a box-tree with respect to a given type of query is the maximum number of nodes visited when answering such a query. We describe several new algorithms for constructing box-trees with small worst-case query complexity with respect to queries with axisparallel boxes and with points. We also prove lower bounds on the worst-case query complexity for box-trees, which show that our results are optimal or close to optimal. Finally, we present algorithms to convert box-trees to R-trees, resulting in R-trees with (almost) optimal query complexity. 1