B-trees have become, de facto, a standard for file organization. File indexes of users, dedicated database systems, and general-purpose access methods have all been proposed and nnplemented using B-trees This paper reviews B-trees and shows why they have been so successful It discusses the major variations of the B-tree, especially the B+-tree,

Abstract. As a contribution to the recent debate on simple implementations of dictionaries, we present new maintenance algorithms for balanced trees. In terms of code simplicity, our algorithms compare favourably with those for deterministic and probabilistic skip lists.

Information retrieval research usually deals with globally visible, static document collections. Practical applications, in contrast, like file system search and enterprise search, have to cope with highly dynamic text collections and have to take into account user-specific access permissions when generating the results to a search query. The goal of this thesis is to close the gap between information retrieval research and the requirements exacted by these real-life applications. The algorithms and data structures presented in this thesis can be used to implement a file system search engine that is able to react to changes in the file system by updating its index data in real time. File changes (in-sertions, deletions, or modifications) are reflected by the search results within a few seconds,

Abstract. Since the invention of AVL trees in 1962, a wide variety of ways to balance binary search trees have been proposed. Notable are red-black trees, in which bottom-up rebalancing after an insertion or deletion takes O(1) amortized time and O(1) rotations worst-case. But the design space of balanced trees has not been fully explored. We introduce the rank-balanced tree, a relaxation of AVL trees. Rank-balanced trees can be rebalanced bottom-up after an insertion or deletion in O(1) amortized time and at most two rotations worst-case, in contrast to red-black trees, which need up to three rotations per deletion. Rebalancing can also be done top-down with fixed lookahead in O(1) amortized time. Using a novel analysis that relies on an exponential potential function, we show that both bottom-up and top-down rebalancing modify nodes exponentially infrequently in their heights. 1

We address the vexing issue of deletions in balanced trees. Rebalancing after a deletion is generally more complicated than rebalancing after an insertion. Textbooks neglect deletion rebalancing, and many database systems do not do it. We describe a relaxation of AVL trees in which rebalancing is done after insertions but not after deletions, yet access time remains logarithmic in the number of insertions. For many applications of balanced trees, our structure offers performance competitive with that of classical balanced trees. With the addition of periodic rebuilding, the performance of our structure is theoretically superior to that of many if not all classic balanced tree structures. Our structure needs O(log log m) bits of balance information per node, where m is the number of insertions, or O(log log n) with periodic rebuilding, where n is the number of nodes. An insertion takes up to two rotations and O(1) amortized time. Using an analysis that relies on an exponential potential function, we show that rebalancing steps occur with a frequency that is exponentially small in the height of the affected node. 1

Many applications of spatio-temporal databases require support for sequenced spatio-temporal (SST) aggregation, e.g., when analyzing traffic density in a city. Conceptually, an SST aggregation produces one aggregate value for each point in time and space. This paper is the first to propose a method to efficiently evaluate SST aggregation queries for the COUNT, SUM, and AVG aggregation functions. Based on a discrete time model and a discrete, 1.5 dimensional space model that represents a road network, we generalize the concept of (temporal) constant intervals towards constant rectangles that represent maximal rectangles in the space-time domain over which the aggregation result is constant. We propose a new data structure, termed SST-tree, which extends the Balanced Tree for one-dimensional temporal aggregation towards the support for two-dimensional, spatio-temporal aggregation. The main feature of the Balanced Tree to store constant intervals in a compact way by using two counters is extended towards a compact representation of constant rectangles in the space-time domain. We propose and evaluate two variants of the SST-tree. The SST T-tree and SST H-tree use trees and hashmaps to manage spacestamps, respectively. Our experiments show that both solutions outperform a brute force approach in terms of memory and time. The SST H-tree is more efficient in terms of memory, whereas the SST T-tree is more efficient in terms of time. 1.

Mobile devices equipped with wireless technologies to communicate and positioning systems to locate objects of interest are common place today, providing the impetus to develop location-aware applications. At the heart of location-aware applications are moving objects or objects that continuously change location over time, such as cars in transportation networks or pedestrians or postal packages. Location-aware applications tend to support the tracking of very large numbers of such moving objects as well as many users that are interested in finding out about the locations of other moving objects. Such location-aware applications rely on support from database management systems to model, store, and query moving object data. The management of moving object data exposes the limitations of traditional (spatial) database management systems as well as their index structures designed to keep track of objects ' locations. Spatial index structures that have been designed for geographic objects in the past primarily assume data are foremost of static nature (e.g., land parcels, road networks, or airport locations), thus requiring a limited amount of index structure updates and reorganization over a period of time. While handling moving objects however, there is an incumbent need for continuous

Abstract In this chapter, we propose a distributed multimedia data management architecture, which can efficiently store and retrieve multimedia data across several nodes of a Grid environment. The main components of the proposed system comprises of a distributed multidimensional index structure, a distributed query manager handling content-based information retrievals and a load balancing technology. The proposed distributed query manager embeds the high-level semantic relationships among the multimedia data objects into the k-NN based similarity search, thus bridging the semantic gap and increasing the relevance of query results manifold. This research has two major usabilities. First, it models a web environment where each node of the Grid can be considered as the nodes or sources of data in the world-wide-web. This should help to investigate and understand the challenges and requirements of future search paradigms based on content of multimedia data rather than on text annotations, as used currently. Second, it provides the foundation to develop content-based information retrievals as a possible Grid service. Extensive experiments were conducted with varied data sizes and different number of distribution nodes. Encouraging results are obtained that makes this endeavor a potential architecture to manage complex multimedia data over a distributed environment. 1

Abstract. Many database systems that use a B + tree as the underlying data structure do not do rebalancing on deletion. This means that a bad sequence of deletions can create a very unbalanced tree. Yet such databases perform well in practice. Avoidance of rebalancing on deletion has been justified empirically and by average-case analysis, but to our knowledge no worst-case analysis has been done. We do such an analysis. We show that the tree height remains logarithmic in the number of insertions, independent of the number of deletions. Furthermore the amortized time for an insertion or deletion, excluding the search time, is O(1), and nodes are modified by insertions and deletions with a frequency that is exponentially small in their height. The latter results do not hold for standard B + trees. By adding periodic rebuilding of the tree, we obtain a data structure that is theoretically superior to standard B + trees in many ways. We conclude that rebalancing on deletion can be considered harmful. 1