Two Access Methods Using Compact Binary Trees

ACM SIGMOD Record, 1989

Traversal recursion is a class of recursive queries where the evaluation of the query involves traversal of a graph or a tree. This limited type of recursion arises in many applications. In this report we investigate a simple file structure that efficiently supports traversal recursion over large, acyclic graphs. The nodes of the graph are sorted in topological order and stored in a B-tree. Hence, traversal of the graph can be done in a single scan. Nodes and edges can also be inserted, deleted, and modified efficiently.

INTERNATIONAL JOURNAL OF COMPUTERS & TECHNOLOGY

In this paper, a new and novel data structure is proposed to dynamically insert and delete segments. Unlike the standard segment trees, the proposed data structure permits insertion of a segment with interval range beyond the interval range of the existing tree, which is the interval between minimum and maximum values of the end points of all the segments. Moreover, the number of nodes in the proposed tree is lesser as compared to the dynamic version of the standard segment trees, and is able to answer both stabbing and range queries practically much faster compared to the standard segment trees.

GeoInformatica, 2012

Tree index structures are crucial components in data management systems. Existing tree index structure are designed with the implicit assumption that the underlying external memory storage is the conventional magnetic hard disk drives. This assumption is going to be invalid soon, as flash memory storage is increasingly adopted as the main storage media in mobile devices, digital cameras, embedded sensors, and notebooks. Though it is direct and simple to port existing tree index structures on the flash memory storage, that direct approach does not consider the unique characteristics of flash memory, i.e., slow write operations, and erase-beforeupdate property, which would result in a sub optimal performance. In this paper, we introduce FAST (i.e., Flash-Aware Search Trees) as a generic framework for flashaware tree index structures. FAST distinguishes itself from all previous attempts of flash memory indexing in two aspects: (1) FAST is a generic framework that can be applied to a wide class of data partitioning tree structures including R-tree and its variants, and (2) FAST achieves both ef f iciency and durability of read and write flash operations through memory flushing and crash recovery techniques. Extensive experimental results, based on an actual implementation of FAST inside the GiST The research of M. Sarwat and M. F.

Proceedings of the 26th …, 2000

Temporal databases assume a single line of time evolution. In other words, they support timeevolving data. However there are applications which require the support of temporal data with branched time evolution. With new branches created as time proceeds, branched and temporal data tends to increase in size rapidly, making the need for e cient indexing crucial. We propose a new paginated access method for branched and temporal data: the BT-tree. The BT-tree is both storage e cient and access e cient. We h a ve implemented the BT-tree and performance results con rm these properties.

2006 IEEE International Symposium on Signal Processing and Information Technology, 2006

In this paper, we propose a new indexing method called compressed B +-tree. The traditional B +-tree is the most common dynamic index structures in database systems. However, in practical applications, its performance still remains considerable room for improvement. Compressed B +-tree outperforms traditional access methods in two respects. The first is more economic storage requirement in the indexing structure. The second is better performance in retrieval. In addition, a compressed B +-tree can be used for the implementation of linebased database indexes.

2015 IEEE 31st International Conference on Data Engineering, 2015

With prices of main memory constantly decreasing, people nowadays are more interested in performing their computations in main memory, and leave high I/O costs of traditional disk-based systems out of the equation. This change of paradigm, however, represents new challenges to the way data should be stored and indexed in main memory in order to be processed efficiently. Traditional data structures, like the venerable B-tree, were designed to work on disk-based systems, but they are no longer the way to go in main-memory systems, at least not in their original form, due to the poor cache utilization of the systems they run on. Because of this, in particular, during the last decade there has been a considerable amount of research on index data structures for main-memory systems. Among the most recent and most interesting data structures for main-memory systems there is the recently-proposed adaptive radix tree ARTful (ART for short). The authors of ART presented experiments that indicate that ART was clearly a better choice over other recent tree-based data structures like FAST and B +-trees. However, ART was not the first adaptive radix tree. To the best of our knowledge, the first was the Judy Array (Judy for short), and a comparison between ART and Judy was not shown. Moreover, the same set of experiments indicated that only a hash table was competitive to ART. The hash table used by the authors of ART in their study was a chained hash table, but this kind of hash tables can be suboptimal in terms of space and performance due to their potentially high use of pointers. In this paper we present a thorough experimental comparison between ART, Judy, two variants of hashing via quadratic probing, and three variants of Cuckoo hashing. These hashing schemes are known to be very efficient. For our study we consider whether the data structures are to be used as a non-covering index (relying on an additional store), or as a covering index (covering key-value pairs). We consider both OLAP and OLTP scenarios. Our experiments strongly indicate that neither ART nor Judy are competitive to the aforementioned hashing schemes in terms of performance, and, in the case of ART, sometimes not even in terms of space.

2005

We present the interpolation search tree (ISB-tree), a new cache-aware indexing scheme that supports update operations (insertions and deletions) in O(1) worst-case (w.c.) block transfers and search operations in O(logB log n) expected block transfers, where B represents the disk block size and n denotes the number of stored elements. The expected search bound holds with high probability for a large class of (unknown) input distributions. The w.c. search bound of our indexing scheme is O(logB n) block transfers. Our update and expected search bounds constitute a considerable improvement over the O(logB n) w.c. block transfer bounds for search and update operations achieved by the B-tree and its numerous variants. This is also suggested by a set of preliminary experiments we have carried out. Our indexing scheme is based on an externalization of a main memory data structure based on interpolation search.

Software: Practice and Experience, 1993

Much has been said in praise of self-adjusting data structures, particularly self-adjusting binary search trees. Self-adjusting trees are most suited to skewed key-access distributions as the techniques attempt to place the most commonly accessed keys near the root of the tree. Theoretical bounds on worst-case and amortized performance (i.e. performance over a sequence of operations) have been derived which compare well with those for optimal binary search trees. In this paper, we compare the performance of three different techniques for self-adjusting trees with that of AVL and random binary search trees. Comparisons are made for various tree sizes, levels of key-access-frequency skewness and ratios of insertions and deletions to searches. The results show that, because of the high cost of maintaining selfadjusting trees, in almost all cases the AVL tree outperforms all the self-adjusting trees and in many cases even a random binary search tree has better performance, in terms of CPU time, than any of the self-adjusting trees. Self-adjusting trees seem to perform best in a highly dynamic environment, contrary to intuition.

Acta Informatica, 1996

High-performance transaction system applications typically insert rows in a History table to provide an activity trace; at the same time the transaction system generates log records for purposes of system recovery. Both types of generated information can benefit from efficient indexing. An example in a well-known setting is the TPC-A benchmark application, modified to support efficient queries on the History for account activity for specific accounts. This requires an index by account-id on the fast-growing History table. Unfortunately, standard disk-based index structures such as the B-tree will effectively double the I/O cost of the transaction to maintain an index such as this in real time, increasing the total system cost up to fifty percent. Clearly a method for maintaining a real-time index at low cost is desirable. The Log-Structured Merge-tree (LSM-tree) is a disk-based data structure designed to provide low-cost indexing for a file experiencing a high rate of record inserts (and deletes) over an extended period. The LSM-tree uses an algorithm that defers and batches index changes, cascading the changes from a memory-based component through one or more disk components in an efficient manner reminiscent of merge sort. During this process all index values are continuously accessible to retrievals (aside from very short locking periods), either through the memory component or one of the disk components. The algorithm has greatly reduced disk arm movements compared to a traditional access methods such as B-trees, and will improve costperformance in domains where disk arm costs for inserts with traditional access methods overwhelm storage media costs. The LSM-tree approach also generalizes to operations other than insert and delete. However, indexed finds requiring immediate response will lose I/O efficiency in some cases, so the LSM-tree is most useful in applications where index inserts are more common than finds that retrieve the entries. This seems to be a common property for History tables and log files, for example. The conclusions of Section 6 compare the hybrid use of memory and disk components in the LSM-tree access method with the commonly understood advantage of the hybrid method to buffer disk pages in memory.

We consider two tree-based indexing schemes that are widely used in practical systems as the basis for both primary and secondary key indexing. We define B-tree and its features, advantages, disadvantages of B-tree. The difference between B+-tree and B-tree has also been discussed. We show the algorithm, examples and figures in the context of B+-tree.