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

A frequently encountered type of query in Geographic Information Systems is to find the k nearest neighbor objects to a given point in space. Processing such queries requires substantially different search algorithms than those for location or range queries. In this paper we present an efficient branch-and-bound R-tree traversal algorithm to find the nearest neighbor object to a point, and then generalize it to finding the k nearest neighbors. We also discuss metrics for an optimistic and a pessimistic search ordering strategy as well as for pruning. Finally, we present the results of several experiments obtained using the implementation of our algorithm and examine the behavior of the metrics and the scalability of the algorithm.

Two different techniques of browsing through a collection of spatial objects stored in an R-tree spatial data structure on the basis of their distances from an arbitrary spatial query object are compared. The conventional approach is one that makes use of a k-nearest neighbor algorithm where k is known prior to the invocation of the algorithm. Thus if m#kneighbors are needed, the k-nearest neighbor algorithm needs to be reinvoked for m neighbors, thereby possibly performing some redundant computations. The second approach is incremental in the sense that having obtained the k nearest neighbors, the k +1 st neighbor can be obtained without having to calculate the k +1nearest neighbors from scratch. The incremental approach finds use when processing complex queries where one of the conditions involves spatial proximity (e.g., the nearest city to Chicago with population greater than a million), in which case a query engine can make use of a pipelined strategy. A general incremental nearest neighbor algorithm is presented that is applicable to a large class of hierarchical spatial data structures. This algorithm is adapted to the R-tree and its performance is compared to an existing k-nearest neighbor algorithm for R-trees [45]. Experiments show that the incremental nearest neighbor algorithm significantly outperforms the k-nearest neighbor algorithm for distance browsing queries in a spatial database that uses the R-tree as a spatial index. Moreover, the incremental nearest neighbor algorithm also usually outperforms the k-nearest neighbor algorithm when applied to the k-nearest neighbor problem for the R-tree, although the improvement is not nearly as large as for distance browsing queries. In fact, we prove informally that, at any step in its execution, the incremental...

We propose a file structure to index high-dimensionality data, typically, points in some feature space. The idea is to use only a few of the features, utilizing additional features whenever the additional discriminatory power is absolutely necessary. We present in detail the design of our tree structure and the associated algorithms that handle such `varying length' feature vectors. Finally we report simulation results, comparing the proposed structure with the R -tree, which is one of the most successful methods for low-dimensionality spaces. The results illustrate the superiority of our method, with up to 80% savings in disk accesses. Type of Contribution: New Index Structure, for high-dimensionality feature spaces. Algorithms and performance measurements. Keywords: Spatial Index, Similarity Retrieval, Query by Content 1 Introduction Many applications require enhanced indexing, capable of performing similarity searching on several, non-traditional (`exotic') data types. The targ...

In this paper we present an analytical model that predicts the performance of R-trees (and its variants) when a range query needs to be answered. The cost model uses knowledge of the dataset only, i.e., the proposed formula that estimates the number of disk accesses is a function of data properties, namely, the amount of data and their density in the work space. In other words, the proposed model is applicable even before the construction of the R-tree index, a fact that makes it a useful tool for dynamic spatial databases. Several experiments on synthetic and real datasets show that the proposed analytical model is very accurate, the relative error being usually around 10%-15%, for uniform and non-uniform distributions. We believe that this error is involved with the gap between efficient R-tree variants, like the R*-tree, and an optimum, not implemented yet, method. Our work extends previous research concerning R-tree analysis and constitutes a useful tool for spatial query optimiz...

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...

In this paper we present the results from an extensive comparison study of three R-tree packing algorithms, including a new easy to implement algorithm. The algorithms are evaluated using both synthetic and actual data from various application domains including VLSI design, GIS (tiger), and computational fluid dynamics. Our studies also consider the impact that various degrees of buffering have on query performance. Experimental results indicate that none of the algorithms is best for all types of data. In general, our new algorithm requires up to 50% fewer disk accesses than the best previously proposed algorithm for point and region queries on uniformly distributed or mildly skewed point and region data, and approximately the same for highly skewed point and region data.

. An efficient benchmarking environment for spatiotemporal access methods should at least include modules for generating synthetic datasets, storing datasets (real datasets included), collecting and running access structures, and visualizing experimental results. Focusing on the dataset repository module, a collection of synthetic data that would simulate a variety of real life scenarios is required. Several algorithms have been implemented in the past to generate static spatial (point or rectangular) data, for instance, following a predefined distribution in the workspace. However, by introducing motion, and thus temporal evolution in spatial object definition, generating synthetic data tends to be a complex problem. In this paper, we discuss the parameters to be considered by a generator for such type of data, propose an algorithm, called "Generate_Spatio_Temporal_Data" (GSTD), which generates sets of moving point or rectangular data that follow an extended set of distri...

Nearest neighbor search in high dimensional spaces is an interesting and important problem which is relevant for a wide variety of novel database applications. As recent results show, however, the problem is a very difficult one, not only with regards to the performance issue but also to the quality issue. In this paper, we discuss the quality issue and identify a new generalized notion of nearest neighbor search as the relevant problem in high dimensional space. In contrast to previous approaches, our new notion of nearest neighbor search does not treat all dimensions equally but uses a quality criterion to select relevant dimensions (projections) with respect to the given query. As an example for a useful quality criterion, we rate how well the data is clustered around the query point within the selected projection. We then propose an efficient and effective algorithm to solve the generalized nearest neighbor problem. Our experiments based on a number of real and synthetic data sets show that our new approach provides new insights into the nature of nearest neighbor search on high dimensional data.

We propose a novel index structure, A-tree (Approximation tree), for similarity search of high-dimensional data. The basic idea of the A-tree is the introduction of Virtual Bounding Rectangles (VBRs), which contain and approximate MBRs and data objects. VBRs can be represented rather compactly, and thus affect the tree configuration both quantitatively and qualitatively. Firstly, since tree nodes can install large number of entries of VBRs, fanout of nodes becomes large, thus leads to fast search. More importantly, we have a free hand in arranging MBRs and VBRs in tree nodes. In the A-trees, nodes contain entries of an MBR and its children VBRs. Therefore, by fetching a node of an A-tree, we can obtain the information of exact position of a parent MBR and approximate position of its children. We have performed experiments using both synthetic and real data sets. For the real data sets, the A-tree outperforms the SR-tree and the VA-File in all range of dimensionality up to 64 dimension, which is the highest dimension in our experiments. The A-tree achieves 77.3 % (77.7%, resp.) savings in page accesses compared to the SR-tree (the VA-File, resp.) for 64-dimensional real data.