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 new access meth d, called M-tree, is proposed to organize and search large data sets from a generic "metric space", i.e. whE4 object proximity is only defined by a distance function satisfyingth positivity, symmetry, and triangle inequality postulates. We detail algorith[ for insertion of objects and split management, whF h keep th M-tree always balanced - severalheralvFV split alternatives are considered and experimentally evaluated. Algorithd for similarity (range and k-nearest neigh bors) queries are also described. Results from extensive experimentationwith a prototype system are reported, considering as th performance criteria th number of page I/O's and th number of distance computations. Th results demonstratethm th Mtree indeed extendsth domain of applicability beyond th traditional vector spaces, performs reasonably well inhE[94Kv#E44V[vh data spaces, and scales well in case of growing files. 1

We introduce the problem of mining association rules in large relational tables containing both quantitative and categorical attributes. An example of such an association might be "10% of married people between age 50 and 60 have at least 2 cars". We deal with quantitative attributes by finepartitioning the values of the attribute and then combining adjacent partitions as necessary. We introduce measures of partial completeness which quantify the information lost due to partitioning. A direct application of this technique can generate too many similar rules. We tackle this problem by using a "greater-than-expected-value" interest measure to identify the interesting rules in the output. We give an algorithm for mining such quantitative association rules. Finally, we describe the results of using this approach on a real-life dataset. 1 Introduction Data mining, also known as knowledge discovery in databases, has been recognized as a new area for database research. The problem of discove...

The coming years will witness dramatic advances in wireless communications as well as positioning technologies. As a result, tracking the changing positions of objects capable of continuous movement is becoming increasingly feasible and necessary. The present paper proposes a novel, R # -tree based indexing technique that supports the efficient querying of the current and projected future positions of such moving objects. The technique is capable of indexing objects moving in one-, two-, and three-dimensional space. Update algorithms enable the index to accommodate a dynamic data set, where objects may appear and disappear, and where changes occur in the anticipated positions of existing objects. A comprehensive performance study is reported.

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...

Abstract—Collision detection is of paramount importance for many applications in computer graphics and visualization. Typically, the input to a collision detection algorithm is a large number of geometric objects comprising an environment, together with a set of objects moving within the environment. In addition to determining accurately the contacts that occur between pairs of objects, one needs also to do so at real-time rates. Applications such as haptic force-feedback can require over 1,000 collision queries per second. In this paper, we develop and analyze a method, based on bounding-volume hierarchies, for efficient collision detection for objects moving within highly complex environments. Our choice of bounding volume is to use a “discrete orientation polytope” (“k-dop”), a convex polytope whose facets are determined by halfspaces whose outward normals come from a small fixed set of k orientations. We compare a variety of methods for constructing hierarchies (“BV-trees”) of bounding k-dops. Further, we propose algorithms for maintaining an effective BV-tree of k-dops for moving objects, as they rotate, and for performing fast collision detection using BV-trees of the moving objects and of the environment. Our algorithms have been implemented and tested. We provide experimental evidence showing that our approach yields substantially faster collision detection than previous methods. Index Terms—Collision detection, intersection searching, bounding volume hierarchies, discrete orientation polytopes, bounding boxes, virtual reality, virtual environments. 1

We introduce a new model of similarity of time sequences that captures the intuitive notion that two sequences should be considered similar if they have enough non-overlapping time-ordered pairs of subsequences thar are similar. The model allows the amplitude of one of the two sequences to be scaled by any suitable amount and its offset adjusted appropriately. Two subsequences are considered similar if one can be enclosed within an envelope of a specified width drawn around the other. The model also allows non-matching gaps in the matching subsequences. The matching subsequences need not be aligned along the time axis. Given this model of similarity,we present fast search techniques for discovering all similar sequences in a set of sequences. These techniques can also be used to find all (sub)sequences similar to a given sequence. We applied this matching system to the U.S. mutual funds data and discovered interesting matches.

In this paper, we propose a novel formulation for distance-based outliers that is based on the distance of a point from its k th nearest neighbor. We rank each point on the basis of its distance to its k th nearest neighbor and declare the top n points in this ranking to be outliers. In addition to developing relatively straightforward solutions to finding such outliers based on the classical nestedloop join and index join algorithms, we develop a highly efficient partition-based algorithm for mining outliers. This algorithm first partitions the input data set into disjoint subsets, and then prunes entire partitions as soon as it is determined that they cannot contain outliers. This results in substantial savings in computation. We present the results of an extensive experimental study on real-life and synthetic data sets. The results from a real-life NBA database highlight and reveal several expected and unexpected aspects of the database. The results from a study on synthetic data sets demonstrate that the partition-based algorithm scales well with respect to both data set size and data set dimensionality. 1

Users often can not easily express their queries. For example, in a multimedia/image by content setting, the user might want photographs with sunsets; in current systems, like QBIC, the user has to give a sample query, and to specify the relative importance of color, shape and texture. Even worse, the user might want correlations between attributes, like, for example, in a traditional, medical record database, a medical researcher might want to find "mildly overweight patients", where the implied query would be "weight/height ≈ 4 lb/inch". Our goal is to provide a user-friendly, but theoretically solid method, to handle such queries. We allow the user to give several examples, and, optionally, their 'goodness' scores, and we propose a novel method to "guess" which attributes are important, which correlations are important, and with what weight. Our contributions are twofold: (a) we formalize the problem as a minimization problem and show how to solve for the optimal solution, completely av...

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...