The like regular expression predicate has been part of the SQL standard since at least 1989. However, despite its popularity and wide usage, database vendors provide only limited indexing support for regular expression queries which almost always require a full table scan. In this paper we propose a rigorous and robust approach for providing indexing support for regular expression queries. Our approach consists of formulating the indexing problem as a combinatorial optimization problem. We begin with a database, abstracted as a collection of strings. From this data set we generate a query workload. The input to the optimization problem is the database and the workload. The output is a set of multigrams (substrings) which can be used as keys to records which satisfy the query workload. The multigrams can then be integrated with the data structure (like B+ trees) to provide indexing support for the queries. We provide a deterministic and a randomized approximation algorithm (with provable guarantees) to solve the optimization problem. Extensive experiments on synthetic data sets demonstrate that our approach is accurate and efficient. We also present a case study on PROSITE patterns - which are complex regular expression signatures for classes of proteins. Again, we are able to demonstrate the utility of our indexing approach in terms of accuracy and efficiency. Thus, perhaps for the first time, there is a robust and practical indexing mechanism for an important class of database queries.
The two most commonly indexes which have been currently using in both database systems are B+trees @cite_18 @cite_3 and bitmaps @cite_1 . Both of them are designed to support exact pattern matching rather than regular expression querying. Therefore, some database vendor tailor these indexes to support regular expression query, such as: full text indexing in PostgreSQL, and function-based index in Oracle. However, their application is criticized as quite restricted.
@cite_18 @cite_1 @cite_3
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NoSQL databases are increasingly used in big data applications, because they achieve fast write throughput and fast lookups on the primary key. Many of these applications also require queries on non-primary attributes. For that reason, several NoSQL databases have added support for secondary indexes. However, these works are fragmented, as each system generally supports one type of secondary index, and may be using different names or no name at all to refer to such indexes. As there is no single system that supports all types of secondary indexes, no experimental head-to-head comparison or performance analysis of the various secondary indexing techniques in terms of throughput and space exists. In this paper, we present a taxonomy of NoSQL secondary indexes, broadly split into two classes: Embedded Indexes (i.e. lightweight filters embedded inside the primary table) and Stand-Alone Indexes (i.e. separate data structures). To ensure the fairness of our comparative study, we built a system, LevelDB++, on top of Google's popular open-source LevelDB key-value store. There, we implemented two Embedded Indexes and three state-of-the-art Stand-Alone indexes, which cover most of the popular NoSQL databases. Our comprehensive experimental study and theoretical evaluation show that none of these indexing techniques dominate the others: the embedded indexes offer superior write throughput and are more space efficient, whereas the stand-alone secondary indexes achieve faster query response times. Thus, the optimal choice of secondary index depends on the application workload. This paper provides an empirical guideline for choosing secondary indexes In-memory tree structured index search is a fundamental database operation. Modern processors provide tremendous computing power by integrating multiple cores, each with wide vector units. There has been much work to exploit modern processor architectures for database primitives like scan, sort, join and aggregation. However, unlike other primitives, tree search presents significant challenges due to irregular and unpredictable data accesses in tree traversal. In this paper, we present FAST, an extremely fast architecture sensitive layout of the index tree. FAST is a binary tree logically organized to optimize for architecture features like page size, cache line size, and SIMD width of the underlying hardware. FAST eliminates impact of memory latency, and exploits thread-level and datalevel parallelism on both CPUs and GPUs to achieve 50 million (CPU) and 85 million (GPU) queries per second, 5X (CPU) and 1.7X (GPU) faster than the best previously reported performance on the same architectures. FAST supports efficient bulk updates by rebuilding index trees in less than 0.1 seconds for datasets as large as 64Mkeys and naturally integrates compression techniques, overcoming the memory bandwidth bottleneck and achieving a 6X performance improvement over uncompressed index search for large keys on CPUs. We introduce a new text-indexing data structure, the String B-Tree , that can be seen as a link between some traditional external-memory and string-matching data structures. In a short phrase, it is a combination of B-trees and Patricia tries for internal-node indices that is made more effective by adding extra pointers to speed up search and update operations. Consequently, the String B-Tree overcomes the theoretical limitations of inverted files, B-trees, prefix B-trees, suffix arrays, compacted tries and suffix trees. String B-trees have the same worst-case performance as B-trees but they manage unbounded-length strings and perform much more powerful search operations such as the ones supported by suffix trees. String B-trees are also effective in main memory (RAM model) because they improve the online suffix tree search on a dynamic set of strings. They also can be successfully applied to database indexing and software duplication. Main memory capacities have grown up to a point where most databases fit into RAM. For main-memory database systems, index structure performance is a critical bottleneck. Traditional in-memory data structures like balanced binary search trees are not efficient on modern hardware, because they do not optimally utilize on-CPU caches. Hash tables, also often used for main-memory indexes, are fast but only support point queries. To overcome these shortcomings, we present ART, an adaptive radix tree (trie) for efficient indexing in main memory. Its lookup performance surpasses highly tuned, read-only search trees, while supporting very efficient insertions and deletions as well. At the same time, ART is very space efficient and solves the problem of excessive worst-case space consumption, which plagues most radix trees, by adaptively choosing compact and efficient data structures for internal nodes. Even though ART's performance is comparable to hash tables, it maintains the data in sorted order, which enables additional operations like range scan and prefix lookup. Indexes are models: a B-Tree-Index can be seen as a model to map a key to the position of a record within a sorted array, a Hash-Index as a model to map a key to a position of a record within an unsorted array, and a BitMap-Index as a model to indicate if a data record exists or not. In this exploratory research paper, we start from this premise and posit that all existing index structures can be replaced with other types of models, including deep-learning models, which we term learned indexes. The key idea is that a model can learn the sort order or structure of lookup keys and use this signal to effectively predict the position or existence of records. We theoretically analyze under which conditions learned indexes outperform traditional index structures and describe the main challenges in designing learned index structures. Our initial results show, that by using neural nets we are able to outperform cache-optimized B-Trees by up to 70 in speed while saving an order-of-magnitude in memory over several real-world data sets. More importantly though, we believe that the idea of replacing core components of a data management system through learned models has far reaching implications for future systems designs and that this work just provides a glimpse of what might be possible. Bitmap indexes must be compressed to reduce input output costs and minimize CPU usage. To accelerate logical operations (AND, OR, XOR) over bitmaps, we use techniques based on run-length encoding (RLE), such as Word-Aligned Hybrid (WAH) compression. These techniques are sensitive to the order of the rows: a simple lexicographical sort can divide the index size by 9 and make indexes several times faster. We investigate row-reordering heuristics. Simply permuting the columns of the table can increase the sorting efficiency by 40 . Secondary contributions include efficient algorithms to construct and aggregate bitmaps. The effect of word length is also reviewed by constructing 16-bit, 32-bit and 64-bit indexes. Using 64-bit CPUs, we find that 64-bit indexes are slightly faster than 32-bit indexes despite being nearly twice as large. The performance of in-memory databases is significantly affected by the number of data blocks fetched from memory into the processor-resident cache. In recent years, various tree-based indexes have been proposed for main memory databases. A common assumption in the analysis of these indexes is that there is no data in the cache that can be reused between key lookups, i.e. the system has a cold cache for each lookup. In practice, though, the ?temperature? of the cache is strongly dependent on the application. For example, a warm cache is typical for OLTP applications that query the same index over and over with little computation in between lookups. In this paper, we present a comparative study of the cache behavior of various B+-tree-based indexes which shows that none of them performs best in all cases. Also, we propose a lightweight technique for improving the cache behavior of any B+-tree based index that performs best in all settings. Compressed bitmap indexes are used to speed up simple aggregate queries in databases. Indeed, set operations like intersections, unions and complements can be represented as logical operations AND, OR and NOT that are ideally suited for bitmaps. However, it is less obvious how to apply bitmaps to more advanced queries. For example, we might seek products in a store that meet some, but maybe not all, criteria. Such threshold queries generalize intersections and unions; they are often used in information-retrieval and data-mining applications. We introduce new algorithms that are sometimes three orders of magnitude faster than a naive approach. Our work shows that bitmap indexes are more broadly applicable than is commonly believed. Copyright © 2014 John Wiley & Sons, Ltd. In this paper; we describe the design, architecture, and lessons learned from the implementation of a fast regular-expression indexing engine FREE. FREE uses a prebuilt index to identify the text data units which may contain a matching string and only examines these further. In this way, FREE shows orders of magnitude performance improvement in certain cases over standard regular expression matching systems, such as lex, awk and grep. Bitmap indices are widely used for large read-only repositories in data warehouses and scientific databases. Their binary representation allows for the use of bitwise operations and specialized run-length compression techniques. Due to a trade-off between compression and query efficiency, bitmap compression schemes are aligned using a fixed encoding length size (typically the word length) to avoid explicit decompression during query time. In general, smaller encoding lengths provide better compression, but require more decoding during query execution. However, when the difference in size is considerable, it is possible for smaller encodings to also provide better execution time. We posit that a tailored encoding length for each bit vector will provide better performance than a one-size-fits-all approach. We present a framework that optimizes compression and query efficiency by allowing bitmaps to be compressed using variable encoding lengths while still maintaining alignment to avoid explicit decompression. Efficient algorithms are introduced to process queries over bitmaps compressed using different encoding lengths. An input parameter controls the aggressiveness of the compression providing the user with the ability to tune the tradeoff between space and query time. Our empirical study shows this approach achieves significant improvements in terms of both query time and compression ratio for synthetic and real data sets. Compared to 32-bit WAH, VAL-WAH produces up to 1.8× smaller bitmaps and achieves query times that are 30 faster. B+-Trees have been traditionally optimized for I O performance with disk pages as tree nodes. Recently, researchers have proposed new types of B+-Trees optimized for CPU cache performance in main memory environments, where the tree node sizes are one or a few cache lines. Unfortunately, due primarily to this large discrepancy in optimal node sizes, existing disk-optimized B+-Trees suffer from poor cache performance while cache-optimized B+-Trees exhibit poor disk performance. In this paper, we propose fractal prefetching B+-Trees (fpB+-Trees), which embed "cache-optimized" trees within "disk-optimized" trees, in order to optimize both cache and I O performance. We design and evaluate two approaches to breaking disk pages into cache-optimized nodes: disk-first and cache-first. These approaches are somewhat biased in favor of maximizing disk and cache performance, respectively, as demonstrated by our results. Both implementations of fpB+-Trees achieve dramatically better cache performance than disk-optimized B+-Trees: a factor of 1.1-1.8 improvement for search, up to a factor of 4.2 improvement for range scans, and up to a 20-fold improvement for updates, all without significant degradation of I O performance. In addition, fpB+-Trees accelerate I O performance for range scans by using jump-pointer arrays to prefetch leaf pages, thereby achieving a speed-up of 2.5-5 on IBM's DB2 Universal Database. Compressed bitmap indexes are used in systems such as Git or Oracle to accelerate queries. They represent sets and often support operations such as unions, intersections, differences, and symmetric differences. Several important systems such as Elasticsearch, Apache Spark, Netflix's Atlas, LinkedIn's Pivot, Metamarkets' Druid, Pilosa, Apache Hive, Apache Tez, Microsoft Visual Studio Team Services and Apache Kylin rely on a specific type of compressed bitmap index called Roaring. We present an optimized software library written in C implementing Roaring bitmaps: CRoaring. It benefits from several algorithms designed for the single-instruction-multiple-data (SIMD) instructions available on commodity processors. In particular, we present vectorized algorithms to compute the intersection, union, difference and symmetric difference between arrays. We benchmark the library against a wide range of competitive alternatives, identifying weaknesses and strengths in our software. Our work is available under a liberal open-source license. We study indexing techniques for main memory, including hash indexes, binary search trees, T-trees, B+-trees, interpolation search, and binary search on arrays. In a decision-support context, our primary concerns are the lookup time, and the space occupied by the index structure. Our goal is to provide faster lookup times than binary search by paying attention to reference locality and cache behavior, without using substantial extra space. We propose a new indexing technique called -Sensitive Search Trees" (CSS-trees). Our technique stores a directory structure on top of a sorted array. Nodes in this directory have size matching the cache-line size of the machine. We store the directory in an array and do not store internal-node pointers; child nodes can be found by performing arithmetic on array osets. We compare the algorithms based on their time and space requirements. We have implemented all of the techniques, and present a performance study on two popular modern machines. We demonstrate that with This research was supported by a David and Lucile Packard Foundation Fellowship in Science and Engineering, by an NSF Young Investigator Award, by NSF grant number IIS-98-12014, and by NSF CISE award CDA-9625374. Given a set @math of @math strings of total length @math , our task is to report the "most relevant"strings for a given query pattern @math . This involves somewhat more advanced query functionality than the usual pattern matching, as some notion of "most relevant" is involved. In information retrieval literature, this task is best achieved by using inverted indexes. However, inverted indexes work only for some predefined set of patterns. In the pattern matching community, the most popular pattern-matching data structures are suffix trees and suffix arrays. However, a typical suffix tree search involves going through all the occurrences of the pattern over the entire string collection, which might be a lot more than the required relevant documents. The first formal framework to study such kind of retrieval problems was given by [Muthukrishnan, 2002]. He considered two metrics for relevance: frequency and proximity. He took a threshold-based approach on these metrics and gave data structures taking @math words of space. We study this problem in a slightly different framework of reporting the top @math most relevant documents (in sorted order) under similar and more general relevance metrics. Our framework gives linear space data structure with optimal query times for arbitrary score functions. As a corollary, it improves the space utilization for the problems in [Muthukrishnan, 2002] while maintaining optimal query performance. We also develop compressed variants of these data structures for several specific relevance metrics. Data management workloads are increasingly write-intensive and subject to strict latency SLAs. This presents a dilemma: Update in place systems have unmatched latency but poor write throughput. In contrast, existing log structured techniques improve write throughput but sacrifice read performance and exhibit unacceptable latency spikes. We begin by presenting a new performance metric: read fanout, and argue that, with read and write amplification, it better characterizes real-world indexes than approaches such as asymptotic analysis and price performance. We then present bLSM, a Log Structured Merge (LSM) tree with the advantages of B-Trees and log structured approaches: (1) Unlike existing log structured trees, bLSM has near-optimal read and scan performance, and (2) its new "spring and gear" merge scheduler bounds write latency without impacting throughput or allowing merges to block writes for extended periods of time. It does this by ensuring merges at each level of the tree make steady progress without resorting to techniques that degrade read performance. We use Bloom filters to improve index performance, and find a number of subtleties arise. First, we ensure reads can stop after finding one version of a record. Otherwise, frequently written items would incur multiple B-Tree lookups. Second, many applications check for existing values at insert. Avoiding the seek performed by the check is crucial. In this paper, we propose a novel image indexing and retrieval algorithm using local tetra patterns (LTrPs) for content-based image retrieval (CBIR). The standard local binary pattern (LBP) and local ternary pattern (LTP) encode the relationship between the referenced pixel and its surrounding neighbors by computing gray-level difference. The proposed method encodes the relationship between the referenced pixel and its neighbors, based on the directions that are calculated using the first-order derivatives in vertical and horizontal directions. In addition, we propose a generic strategy to compute nth-order LTrP using (n - 1)th-order horizontal and vertical derivatives for efficient CBIR and analyze the effectiveness of our proposed algorithm by combining it with the Gabor transform. The performance of the proposed method is compared with the LBP, the local derivative patterns, and the LTP based on the results obtained using benchmark image databases viz., Corel 1000 database (DB1), Brodatz texture database (DB2), and MIT VisTex database (DB3). Performance analysis shows that the proposed method improves the retrieval result from 70.34 44.9 to 75.9 48.7 in terms of average precision average recall on database DB1, and from 79.97 to 85.30 and 82.23 to 90.02 in terms of average retrieval rate on databases DB2 and DB3, respectively, as compared with the standard LBP. SPARQL basic graph pattern (BGP) (a.k.a. SQL inner-join) query optimization is a well researched area. However, optimization of OPTIONAL pattern queries (a.k.a. SQL left-outer-joins) poses additional challenges, due to the restrictions on the reordering of left-outer-joins. The occurrence of such queries tends to be as high as 50 of the total queries (e.g., DBPedia query logs). In this paper, we present Left Bit Right (LBR), a technique for well-designed nested BGP and OPTIONAL pattern queries. Through LBR, we propose a novel method to represent such queries using a graph of supernodes, which is used to aggressively prune the RDF triples, with the help of compressed indexes. We also propose novel optimization strategies -- first of a kind, to the best of our knowledge -- that combine together the characteristics of acyclicity of queries, minimality, and nullification, best-match operators. In this paper, we focus on OPTIONAL patterns without UNIONs or FILTERs, but we also show how UNIONs and FILTERs can be handled with our technique using a query rewrite. Our evaluation on RDF graphs of up to and over one billion triples, on a commodity laptop with 8 GB memory, shows that LBR can process well-designed low-selectivity complex queries up to 11 times faster compared to the state-of-the-art RDF column-stores as Virtuoso and MonetDB, and for highly selective queries, LBR is at par with them. Key-value stores such as LevelDB and RocksDB offer excellent write throughput, but suffer high write amplification. The write amplification problem is due to the Log-Structured Merge Trees data structure that underlies these key-value stores. To remedy this problem, this paper presents a novel data structure that is inspired by Skip Lists, termed Fragmented Log-Structured Merge Trees (FLSM). FLSM introduces the notion of guards to organize logs, and avoids rewriting data in the same level. We build PebblesDB, a high-performance key-value store, by modifying HyperLevelDB to use the FLSM data structure. We evaluate PebblesDB using micro-benchmarks and show that for write-intensive workloads, PebblesDB reduces write amplification by 2.4-3x compared to RocksDB, while increasing write throughput by 6.7x. We modify two widely-used NoSQL stores, MongoDB and HyperDex, to use PebblesDB as their underlying storage engine. Evaluating these applications using the YCSB benchmark shows that throughput is increased by 18-105 when using PebblesDB (compared to their default storage engines) while write IO is decreased by 35-55 . We propose a compact and efficient index structure for massive data sets. Several indexing techniques are widely-used and well-known such as binary trees and B+trees. Unfortunately, we find that these techniques suffer major two shortcomings when applied to massive sets; first, their indices are so large they could overflow regular main memory, and, second, they suffer from a variety of penalties (e.g., conditional branches, low cache hits, and TLB misses), which restricts the number of instructions executed per processor cycle. Our state-of-the-art index structure, called VAST-Tree, classifies branch nodes into multiple layers. It applies existing techniques such as cache-conscious, aligned, and branch-free structures to the top layers of branch nodes in trees. Next, it applies the adaptive compression technique to save space and harness data parallelism with SIMD instructions to the middle and bottom layers of branch nodes. Moreover, a processor-friendly compression technique is applied to leaf nodes. The end result is that trees are much more compact and traversal efficiency is high. We implement a prototype and show its resulting index size and performance as compared to binary trees, and the hardware-conscious technique called FAST which currently offers the highest performance. Compared to current alternatives, VAST-Tree compacts the branch nodes by more than 95 , and the overall index size by 47-84 given that there are 230 keys. With 228 keys, it has roughly 6.0-times and 1.24-times throughput and saves the memory consumption by more than 94.7 and 40.5 as compared to binary trees and FAST, respectively. 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 mergetree (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 cost-performance 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 Sect. 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.