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.

Abstract- We present an access method for timeslice queries that reconstructs a past state s(t) of a time-evolving collection of objects, in O(log,, n + Is(t)l/b) I/O ‘8, where Is(t)1 denotes the size of the collection at time t, n is the total number of changes in the collection’s evolution and b is the size of an I/O transfer. Changes include the addition, deletion or attribute modification of objects; they are assumed to occur in increasing time order and always affect the most current state of the collection (thus our index supports transaction-time.) The space used is 0 n/b) while the update processing is constant per change, i.e., independent of n. This is the first I I O-optimal access method for this problem using O(n/b) space and O(1) updating (in the expected amortized sense due to the use of hashing.) This performance is also achieved for interval intersection temporal queries. An advantage of our approach is that its performance can be tuned to match particular application needs (trading space for query time and vice versa). In addition, the Snapshot Index can naturally migrate data on a write-once optical medium while maintaining the same performance bounds.

. We propose an asymptotically optimal multiversion B-tree. In our setting, insertions and deletions of data items are allowed only for the present version, whereas range queries and exact match queries are allowed for any version, present or past. The technique we present for transforming a (usual single version) B-tree into a multiversion B-tree is more general: it applies to a number of spatial and non-spatial hierarchical external access structures with certain properties directly, and it can be modified for others. For the B-tree and several other hierarchical external access structures, multiversion capabilities come at no extra cost, neither for storage space nor for runtime, asymptotically in the worst case. The analysis of the behavior of the multiversion B-tree shows that the constant loss of efficiency is low enough to make our suggestion not only a theoretical, but also a practical one. 1 Introduction The importance of maintaining data not only in their latest version, but ...

Managing multiple versions of XML documents represents a critical requirement for many applications. Recently, there has been much work on supporting complex queries on XML data (e.g., regular path expressions, structural projections, etc.). In this paper, we examine the problem of implementing efficiently such complex queries on multiversion XML documents. Our approach relies on a numbering scheme whereby durable node numbers (DNNs) are used to preserve the order among the nodes of the XML tree while remaining invariant with respect to updates. Using the document’s DNNs, we show that many complex queries are reduced to combinations of range version retrieval queries. We thus examine three alternative storage organizations/indexing schemes to efficiently evaluate range version retrieval queries in this environment. A thorough performance analysis is then presented to reveal the advantages of each scheme.

We present a practical and asymptotically optimal indexing structure for a versioned timestamped database with step-wise constant data. Three version operations, insertions, updates, and deletes are allowed for the present version, whereas query operations are allowed for any version, present or past. Snapshot and time-range queries can be answered optimally with this structure. As a two-level index, attribute-search and attribute-history queries can be solved in time proportional to the output size plus an additive logarithmic term. The time index uses linear storage; this improves upon previous work which either had logarithmic query overhead time and quadratic space, or linear space and linear query overhead time. The tradeoff is a small increase in the time for version operations from constant to logarithmic. All measures are worst-case. The index has a natural structure for archiving in write-once storage media like optical disks. Research supported in part by NSF grants CCR90103...

A new variation of Overlapping B+-trees is presented, which provides efficient indexing of transaction time and keys in a two dimensional key-time space. Modification operations (i.e. insertions, deletions and updates) are allowed at the current version, whereas queries are allowed to any temporal version, i.e. either in the current or in past versions. Using this structure, snapshot and range-timeslice queries can be answered optimally. However, the fundamental objective of the proposed method is to deliver efficient performance in case of a general pure-key query (i.e. "history of a key"). The trade-off is a small increase in time cost for version operations and storage requirements.

this paper, we combine the ideas of time-varying data and branching versions to produce and compare two new indexing structures: the BT (Branched and Temporal) Forest and the PBT-Tree (the Persistent Branched and Temporal Tree).

We present an asymptotically optimal and practically efficient multiversion access structure (MVAS) for a versioned timestamped database with step-wise constant data. The structure combines an enhanced B+-tree with access lists in a novel way. This allows for both key history and version range queries to be answered optimally, while still maintaining linear storage. In our model, three version operations, insertions, updates, and deletes are allowed for the present version, whereas query operations are allowed for any version, present or past. The following query operations are supported optimally: key search, key range search, key history search (or time range search), snapshot of the database, and time range view. The bounds on storage space and query operations are worst case bounds per operation, while those for version operations are amortized over a sequence of version operations. Partially supported by NSF and DARPA Grant CCR 9006300 and NSF Grant CCR 9010366. y Dept. of EC...

Given a set of n objects, each characterized by d attributes speci ed at m xed time instances, we are interested in the problem of designing space e cient indexing structures such that arbitrary temporal range search queries can be handled e ciently. Whenm =1, our problem reduces to the d-dimensional orthogonal search problem. We establish e cient data structures to handle several classes of the general problem. Our results include a linear size data structure that enables a query time of O(log n log m = log log n + f) for one-sided queries when d = 1, where f is the number of objects satisfying the query. A similar result is shown for counting queries. We alsoshow that the most general problem can be solved with a polylogarithmic query time using nonlinear space data structures. 1

We consider the problem of dynamically indexing temporal observations about a collection of objects, each observation consisting of a key identifying the object, a list of attribute values and a timestamp indicating the time at which these values were recorded. We make no assumptions about the rates at which these observations are collected, nor do we assume that the various objects have about the same number of observations. We develop indexing structures that are almost linear in the total number of observations available at any given time instant, and that support dynamic insertions in polylogarithmic time. Moreover, these structures allow the quick handling of queries to identify objects whose attribute values fall within a certain range at every time instance of a speci ed time interval. Provably good bounds are established. 1