An analysis of B-trees and their variants

Information Processing Letters, 1986

A recent paper by has presented a new simple derivation of the approximate average utilization of B-trees. This paper presents two weaknesses of that derivation and shows how these might be overcome.

Foundations and Trends in Databases, 2010

Invented about 40 years ago and called ubiquitous less than 10 years later, B-tree indexes have been used in a wide variety of computing systems from handheld devices to mainframes and server farms. Over the years, many techniques have been added to the basic design in order to improve efficiency or to add functionality. Examples include separation of updates to structure or contents, utility operations such as non-logged yet transactional index creation, and robust query processing such as graceful degradation during index-to-index navigation. This survey reviews the basics of B-trees and of B-tree indexes in databases, transactional techniques and query processing techniques related to B-trees, B-tree utilities essential for database operations, and many optimizations and improvements. It is intended both as a survey and as a reference, enabling researchers to compare index innovations with advanced B-tree techniques and enabling professionals to select features, functions, and tradeoffs most appropriate for their data management challenges.

The purpose of this paper is to discuss the preference of B+ tree over B tree or any other indexing technique. Most of the modern commercial RDBMS are using B+ trees as their default indexing structure reason being the efficiency of B+ tree and the performance attribute of it. The cache hit is better for B+ trees. Various indexing techniques are discussed with their pros and cons.

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 present I/O-efficient fully persistent B-Trees that support range searches at any version in O(logBn + t/B) I/Os and updates at any version in O(logBn + log2B) amortized I/Os, using space O(m/B) disk blocks. By n we denote the number of elements in the accessed version, by m the total number of updates, by t the size of the query's output, and by B the disk block size. The result improves the previous fully persistent B-Trees of Lanka and Mays by a factor of O(logBm) for the range query complexity and O(logBn) for the update complexity. To achieve the result, we first present a new B-Tree implementation that supports searches and updates in O(logBn) I/Os, using O(n/B) blocks of space. Moreover, every update makes in the worst case a constant number of modifications to the data structure. We make these B-Trees fully persistent using an I/O-efficient method for full persistence that is inspired by the node-splitting method of Driscoll et al. The method we present is interesting...

Being popular for managing data dynamically in today's storage systems, fast data insertion, deletion and searching are also concerned with the system's performance. Those criteria are heavily dependent on the way to handle the attributes of the algorithm used because it can determine how large as well as how much the system can hold data and throughput. B+ tree-based indexing algorithm is capable of scaling data logarithmically and so widely used in distributed file system. However, the level of the system's scalability is solely associated with the order and height of the tree. The proposed system modifies the traditional B+ Tree in the form power of 2-based for data expansion and it is designed on object-based file system.

2017

The B+-tree is the most popular index structure that has been used in the disk-based DBMSs. The fast key-search times and the efficiency of storage usage are major causes of its popularity during the past time. When we adopt the B+-tree as a primary indexing scheme of databases stored in flash storage, however, its advantages above may diminish because of distinctive I/O features of flash memory. Differently from the hard disk drive, flash memory suffers from considerable performance asymmetry between the speeds of page reading and page updating. Therefore, it is crucial to reduce the amount of page updates in the case of flash-based databases. Since the random updates can severely degrade the storage performance, the efficiency for updating leaf nodes is very important for the B+tree stored in flash storage. In this context, we propose a new way for updating B+-tree leaf nodes at cheap costs. To this end, we devised some new algorithms for tree reconstruction that is performed in t...

Information Processing Letters, 1981

BIT, 1981

Computers & Electrical Engineering, 2012

We present two solutions for achieving a partially persistent B-tree with a worst case constant update time, in the case that the position of the update is given. The motivation for this work came from the observation that a known, general approach, which reduces the update cost of partially persistent data structures to a constant, has an inherent weakness concerning partially persistent B-trees, because it creates big nodes that cannot be retrieved from secondary memory in a constant time. Due to this, the I/O complexity of the resulting partially persistent B-tree is affected. Thus, we attack this specific problem, i.e. we do not develop a general approach for all partially persistent data structures. For our objectives, we add partial persistence to an ephemeral B-tree with constant worst case update time, by applying two known general methods, the fat-node and the node-copying method, that transform an ephemeral data structure into a partially persistent. The solution based on node-copying is asymptotically optimal.