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

– 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-...

In a variety of applications, we need to keep track of the development of a data set over time. For maintaining and querying these multiversion data efficiently, external storage structures are an absolute necessity. We propose a multiversion B-tree that supports insertions and deletions of data items at the current version and range queries and exact match queries for any version, current or past. Our multiversion B-tree is asymptotically optimal in the sense that the time and space bounds are asymptotically the same as those of the (single-version) B-tree in the worst case. The technique we present for transforming a (single-version) Btree into a multiversion B-tree is quite general: it applies to a number of hierarchical external access structures with certain properties directly, and it can be modified for others.

We consider the problem of exploiting parallelism to accelerate the performance of spatial access methods and specifically, R-trees [11]. Our goal is to design a server for spatial data, so that to maximize the throughput of range queries. This can be achieved by (a) maximizing parallelism for large range queries, and (b) by engaging as few disks as possible on point queries [22]. We propose a simple hardware architecture consisting of one processor with several disks attached to it. On this architecture, we propose to distribute the nodes of a traditional R-tree, with cross-disk pointers (`Multiplexed' R-tree). The R-tree code is identical to the one for a single-disk R-tree, with the only addition that we have to decide which disk a newly created R-tree node should be stored in. We propose and examine several criteria to choose a disk for a new node. The most successful one, termed `proximity index' or PI, estimates the similarity of the new node with the other R-tree nodes already o...

Multimedia applications usually involve a large number of multimedia objects (texts, images, sounds etc.). Spatial and temporal relationships among these objects should be efficiently supported and retrieved within a multimedia authoring tool. In this paper we present severol spatial, temporal and spatia-temporal relationships of inierest and propose efficient indexing schenzes, based on multidimensional (spatial) data structures, for large multimedia applications that involve thousands of objects. Evaluation models of the proposed schemes are also presented as well as hints for the selection of the most appropriate one, according to the multimedia author’s requiremeni‘s. 1.

We consider the problems of computing aggregation queries in temporal databases, and of maintaining materialized temporal aggregate views efficiently. The latter problem is particularly challenging since a single data update can cause aggregate results to change over the entire time line. We introduce a new index structure called the SBtree, which incorporates features from both segment-trees and B-trees. SB-trees support fast lookup of aggregate results based on time, and can be maintained efficiently when the data changes. We also extend the basic SB-tree index to handle cumulative (also called moving-window) aggregates. For materialized aggregate views in a temporal database or warehouse, we propose building and maintaining SB-tree indices instead of the views themselves. 1.

Abstract—An efficient multiversion access structure for a transaction-time database is presented. Our method requires optimal storage and query times for several important queries and logarithmic update times. Three version operations}inserts, updates, and deletes}are allowed on the current database, while queries are allowed on any version, present or past. The following query operations are performed in optimal query time: key range search, key history search, and time range view. The key-range query retrieves all records having keys in a specified key range at a specified time; the key history query retrieves all records with a given key in a specified time range; and the time range view query retrieves all records that were current during a specified time interval. Special cases of these queries include the key search query, which retrieves a particular version of a record, and the snapshot query which reconstructs the database at some past time. To the best of our knowledge no previous multiversion access structure simultaneously supports all these query and version operations within these time and space bounds. The bounds on query operations are worst case per operation, while those for storage space and version operations are (worst-case) amortized over a sequence of version operations. Simulation results show that good storage utilization and query performance is obtained. Index Terms—Transaction-time database, multidimensional data, access methods, data structures, indexing, I/O complexity.

Spatiotemporal objects, i.e., objects which change their position and/or extent over time appear in many applications. In this paper we examine the problem of indexing large volumes of such data. Important in this environment is how the spatiotemporal objects move and/or change. We consider a rather general case where object movements/changes are defined by combinations of polynomial functions. We further concentrate on "snapshot" as well as small "interval" queries as these are quite common when examining the history of the gathered data. The obvious approach that approximates each spatiotemporal object by an MBR and uses a traditional multidimensional access method to index them is inefficient. Objects that "live" for long time intervals have large MBRs which introduce a lot of empty space. Clustering long intervals has been dealt in temporal databases by the use of partially persistent indices. What differentiates this problem from traditional temporal indexing, is that objects are allowed to move/change during their lifetime. Better ways are thus needed to approximate general spatiotemporal objects. One obvious solution is to introduce artificial splits: the lifetime of a long-lived object is split into smaller consecutive pieces. This decreases the empty space but increases the number of indexed MBRs. We first give an optimal algorithm and a heuristic for splitting a given spatiotemporal object in a predefined number of pieces. Then, given an upper bound on the total number of possible splits, we present three algorithms that decide how the splits are distributed among all the objects so that the total empty space is minimized. The number of splits cannot be increased indefinitely since the extra objects will eventually affect query performance. Usi...

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