New Algorithms for δγ-Order Preserving Matching

Context: Order-preserving matching regards the relative order of strings. However, its application areas require more flexibility in the matching paradigm. We advance in this direction in this paper that extends our previous work [27]. Method: We define γ -order preserving matching as an approximate variant of order-preserving matching. We devise two solutions for it based on segment and Fenwick trees: segtreeBA and bitBA. Results: We experimentally show the efficiency of our algorithms compared to the ones presented in [26] (naiveA and updateBA). Also, we present applications of our approach in music retrieval and stock market analysis. Conclusions: Even though the worst-case time complexity of the proposed algorithms (namely, O(nm log m)) is higher than the Ѳ(nm)-time complexity of updateBA, their Ω (n log n) lower bound makes them more efficient in practice. On the other hand, we show that our approach is useful to identify similarity in music melodies and stock price trends through real application examples

Nuevos Algoritmos para Búsqueda de Orden δγ

Context: Order-preserving matching regards the relative order of strings. However, its application areas require more flexibility in the matching paradigm. We advance in this direction in this paper that extends our previous work [27].Method: We define γ -order preserving matching as an approximate variant of order-preserving matching. We devise two solutions for it based on segment and Fenwick trees: segtreeBA and bitBA.Results: We experimentally show the efficiency of our algorithms compared to the ones presented in [26] (naiveA and updateBA). Also, we present applications of our approach in music retrieval and stock market analysis.Conclusions: Even though the worst-case time complexity of the proposed algorithms (namely, O(nm log m)) is higher than the Ѳ(nm)-time complexity of updateBA, their Ω (n log n) lower bound makes them more efficient in practice. On the other hand, we show that our approach is useful to identify similarity in music melodies and stock price trends through real application examples.Contexto: El emparejamiento de cadenas según el orden compara la estructura de las cadenas de texto. Sin embargo, sus áreas de aplicación requieren mayor flexibilidad en el criterio de comparación. Este artículo avanza en esta dirección al extender [27]. Método: Se define la búsqueda de orden – γ como una variante aproximada del problema de emparejamiento de cadenas según orden. Se proponen dos soluciones basadas en árboles de segmentos y árboles Fenwick: segtree BA and bit BA.Resultados: La eficiencia de los algoritmos propuestos se muestra experimentalmente comparándolos con los algoritmos presentados en [26] (naive A y update BA). Además, se presentan aplicaciones.Conclusiones: A pesar de que la complejidad en tiempo de peor-caso de los algoritmos propuestos (a decir, O (nm log m)) es mayor que la complejidad de update BA (Ѳ (nm)), su cota baja Ω(n log n) los hace más eficientes en la práctica. También se muestran aplicaciones del enfoque propuesto en recuperación de música y análisis del mercado de acciones con ejemplos reales

Definition and solution of a new approximate variant of the order preserving matching problem

En esta tesis se combinan dos problemas de búsqueda de cadenas: la búsqueda aproximada de cadenas bajo parámetros δγ, y el emparejamiento con preservación de orden. Uno permite un nivel de error en la búsqueda, mientras que el otro considera la estructura interna de las cadenas en lugar de sus valores absolutos. Se define formalmente el Emparejamiento con preservación de orden bajo distancias δγ. Se diseñaron e implementaron en C++ cuatro algoritmos que resuelven el problema, y una configuración experimental para compararlos. El algoritmo más simple, tiene complejidad O(nm lg m). El segundo tiene una complejidad de O(nm). El tercero y el cuarto se basan en estructuras de datos: árbol de segmentos y árbol de fenwick respectivamente. Ambos tienen complejidad O(nm lg n). Los resultados experimentales muestran que los algoritmos basados en estructuras de datos tiene un mejor rendimiento en muchos casos. El de mejor rendimiento experimental es del basado en el árbol Fenwick, seguido por el basado en árboles de segmentos. Estos resultados se pueden explicar debido a su complejidad Ω(n lg n). Se muestran aplicaciones en música y finanzas.Abstract: In this thesis we combine two string searching related problems: the approximate string matching under parameters δ and γ, and the order preserving matching problem. Orderpreserving matching regards the internal structure of the strings rather than their absolute values while matching under δ and γ distances permit a level of error. We formally define the δγ–order-preserving matching problem. We designed and implement in C++ four algorithms that solve the proposed problem and an experimental setup to compare them. The first algorithm is the naive algorithm with complexity Θ(nm lg m) time. The second has a complexity of Θ(nm) time. The third and four algorithms are based on the segment tree and Fenwick tree data structures, respectively, and both have O(nm log n) time complexities. The data structure based algorithms show better experimental performance due to their better lower bound of Ω(n lg n) complexity. We show applications in music and finance.Maestrí

Regular Languages meet Prefix Sorting

Indexing strings via prefix (or suffix) sorting is, arguably, one of the most successful algorithmic techniques developed in the last decades. Can indexing be extended to languages? The main contribution of this paper is to initiate the study of the sub-class of regular languages accepted by an automaton whose states can be prefix-sorted. Starting from the recent notion of Wheeler graph [Gagie et al., TCS 2017]-which extends naturally the concept of prefix sorting to labeled graphs-we investigate the properties of Wheeler languages, that is, regular languages admitting an accepting Wheeler finite automaton. Interestingly, we characterize this family as the natural extension of regular languages endowed with the co-lexicographic ordering: when sorted, the strings belonging to a Wheeler language are partitioned into a finite number of co-lexicographic intervals, each formed by elements from a single Myhill-Nerode equivalence class. Moreover: (i) We show that every Wheeler NFA (WNFA) with $n$ states admits an equivalent Wheeler DFA (WDFA) with at most $2n-1-|\Sigma|$ states that can be computed in $O(n^3)$ time. This is in sharp contrast with general NFAs. (ii) We describe a quadratic algorithm to prefix-sort a proper superset of the WDFAs, a $O(n\log n)$-time online algorithm to sort acyclic WDFAs, and an optimal linear-time offline algorithm to sort general WDFAs. By contribution (i), our algorithms can also be used to index any WNFA at the moderate price of doubling the automaton's size. (iii) We provide a minimization theorem that characterizes the smallest WDFA recognizing the same language of any input WDFA. The corresponding constructive algorithm runs in optimal linear time in the acyclic case, and in $O(n\log n)$ time in the general case. (iv) We show how to compute the smallest WDFA equivalent to any acyclic DFA in nearly-optimal time.Comment: added minimization theorems; uploaded submitted version; New version with new results (W-MH theorem, linear determinization), added author: Giovanna D'Agostin

Transform Based And Search Aware Text Compression Schemes And Compressed Domain Text Retrieval

In recent times, we have witnessed an unprecedented growth of textual information via the Internet, digital libraries and archival text in many applications. While a good fraction of this information is of transient interest, useful information of archival value will continue to accumulate. We need ways to manage, organize and transport this data from one point to the other on data communications links with limited bandwidth. We must also have means to speedily find the information we need from this huge mass of data. Sometimes, a single site may also contain large collections of data such as a library database, thereby requiring an efficient search mechanism even to search within the local data. To facilitate the information retrieval, an emerging ad hoc standard for uncompressed text is XML which preprocesses the text by putting additional user defined metadata such as DTD or hyperlinks to enable searching with better efficiency and effectiveness. This increases the file size considerably, underscoring the importance of applying text compression. On account of efficiency (in terms of both space and time), there is a need to keep the data in compressed form for as much as possible. Text compression is concerned with techniques for representing the digital text data in alternate representations that takes less space. Not only does it help conserve the storage space for archival and online data, it also helps system performance by requiring less number of secondary storage (disk or CD Rom) accesses and improves the network transmission bandwidth utilization by reducing the transmission time. Unlike static images or video, there is no international standard for text compression, although compressed formats like .zip, .gz, .Z files are increasingly being used. In general, data compression methods are classified as lossless or lossy. Lossless compression allows the original data to be recovered exactly. Although used primarily for text data, lossless compression algorithms are useful in special classes of images such as medical imaging, finger print data, astronomical images and data bases containing mostly vital numerical data, tables and text information. Many lossy algorithms use lossless methods at the final stage of the encoding stage underscoring the importance of lossless methods for both lossy and lossless compression applications. In order to be able to effectively utilize the full potential of compression techniques for the future retrieval systems, we need efficient information retrieval in the compressed domain. This means that techniques must be developed to search the compressed text without decompression or only with partial decompression independent of whether the search is done on the text or on some inversion table corresponding to a set of key words for the text. In this dissertation, we make the following contributions: (1) Star family compression algorithms: We have proposed an approach to develop a reversible transformation that can be applied to a source text that improves existing algorithm\u27s ability to compress. We use a static dictionary to convert the English words into predefined symbol sequences. These transformed sequences create additional context information that is superior to the original text. Thus we achieve some compression at the preprocessing stage. We have a series of transforms which improve the performance. Star transform requires a static dictionary for a certain size. To avoid the considerable complexity of conversion, we employ the ternary tree data structure that efficiently converts the words in the text to the words in the star dictionary in linear time. (2) Exact and approximate pattern matching in Burrows-Wheeler transformed (BWT) files: We proposed a method to extract the useful context information in linear time from the BWT transformed text. The auxiliary arrays obtained from BWT inverse transform brings logarithm search time. Meanwhile, approximate pattern matching can be performed based on the results of exact pattern matching to extract the possible candidate for the approximate pattern matching. Then fast verifying algorithm can be applied to those candidates which could be just small parts of the original text. We present algorithms for both k-mismatch and k-approximate pattern matching in BWT compressed text. A typical compression system based on BWT has Move-to-Front and Huffman coding stages after the transformation. We propose a novel approach to replace the Move-to-Front stage in order to extend compressed domain search capability all the way to the entropy coding stage. A modification to the Move-to-Front makes it possible to randomly access any part of the compressed text without referring to the part before the access point. (3) Modified LZW algorithm that allows random access and partial decoding for the compressed text retrieval: Although many compression algorithms provide good compression ratio and/or time complexity, LZW is the first one studied for the compressed pattern matching because of its simplicity and efficiency. Modifications on LZW algorithm provide the extra advantage for fast random access and partial decoding ability that is especially useful for text retrieval systems. Based on this algorithm, we can provide a dynamic hierarchical semantic structure for the text, so that the text search can be performed on the expected level of granularity. For example, user can choose to retrieve a single line, a paragraph, or a file, etc. that contains the keywords. More importantly, we will show that parallel encoding and decoding algorithm is trivial with the modified LZW. Both encoding and decoding can be performed with multiple processors easily and encoding and decoding process are independent with respect to the number of processors

Bridging the gap between algorithmic and learned index structures

Index structures such as B-trees and bloom filters are the well-established petrol engines of database systems. However, these structures do not fully exploit patterns in data distribution. To address this, researchers have suggested using machine learning models as electric engines that can entirely replace index structures. Such a paradigm shift in data system design, however, opens many unsolved design challenges. More research is needed to understand the theoretical guarantees and design efficient support for insertion and deletion. In this thesis, we adopt a different position: index algorithms are good enough, and instead of going back to the drawing board to fit data systems with learned models, we should develop lightweight hybrid engines that build on the benefits of both algorithmic and learned index structures. The indexes that we suggest provide the theoretical performance guarantees and updatability of algorithmic indexes while using position prediction models to leverage the data distributions and thereby improve the performance of the index structure. We investigate the potential for minimal modifications to algorithmic indexes such that they can leverage data distribution similar to how learned indexes work. In this regard, we propose and explore the use of helping models that boost classical index performance using techniques from machine learning. Our suggested approach inherits performance guarantees from its algorithmic baseline index, but at the same time it considers the data distribution to improve performance considerably. We study single-dimensional range indexes, spatial indexes, and stream indexing, and show that the suggested approach results in range indexes that outperform the algorithmic indexes and have comparable performance to the read-only, fully learned indexes and hence can be reliably used as a default index structure in a database engine. Besides, we consider the updatability of the indexes and suggest solutions for updating the index, notably when the data distribution drastically changes over time (e.g., for indexing data streams). In particular, we propose a specific learning-augmented index for indexing a sliding window with timestamps in a data stream. Additionally, we highlight the limitations of learned indexes for low-latency lookup on real- world data distributions. To tackle this issue, we suggest adding an algorithmic enhancement layer to a learned model to correct the prediction error with a small memory latency. This approach enables efficient modelling of the data distribution and resolves the local biases of a learned model at the cost of roughly one memory lookup.Open Acces

The analysis of enumerative source codes and their use in Burrows‑Wheeler compression algorithms

In the late 20th century the reliable and efficient transmission, reception and storage of information proved to be central to the most successful economies all over the world. The Internet, once a classified project accessible to a selected few, is now part of the everyday lives of a large part of the human population, and as such the efficient storage of information is an important part of the information economy. The improvement of the information storage density of optical and electronic media has been remarkable, but the elimination of redundancy in stored data and the reliable reconstruction of the original data is still a desired goal. The field of source coding is concerned with the compression of redundant data and its reliable decompression. The arithmetic source code, which was independently proposed by J. J. Rissanen and R. Pasco in 1976, revolutionized the field of source coding. Compression algorithms that use an arithmetic code to encode redundant data are typically more effective and computationally more efficient than compression algorithms that use earlier source codes such as extended Huffman codes. The arithmetic source code is also more flexible than earlier source codes, and is frequently used in adaptive compression algorithms. The arithmetic code remains the source code of choice, despite having been introduced more than 30 years ago. The problem of effectively encoding data from sources with known statistics (i.e. where the probability distribution of the source data is known) was solved with the introduction of the arithmetic code. The probability distribution of practical data is seldomly available to the source encoder, however. The source coding of data from sources with unknown statistics is a more challenging problem, and remains an active research topic. Enumerative source codes were introduced by T. J. Lynch and L. D. Davisson in the 1960s. These lossless source codes have the remarkable property that they may be used to effectively encode source sequences from certain sources without requiring any prior knowledge of the source statistics. One drawback of these source codes is the computationally complex nature of their implementations. Several years after the introduction of enumerative source codes, J. G. Cleary and I. H. Witten proved that approximate enumerative source codes may be realized by using an arithmetic code. Approximate enumerative source codes are significantly less complex than the original enumerative source codes, but are less effective than the original codes. Researchers have become more interested in arithmetic source codes than enumerative source codes since the publication of the work by Cleary and Witten. This thesis concerns the original enumerative source codes and their use in Burrows–Wheeler compression algorithms. A novel implementation of the original enumerative source code is proposed. This implementation has a significantly lower computational complexity than the direct implementation of the original enumerative source code. Several novel enumerative source codes are introduced in this thesis. These codes include optimal fixed–to–fixed length source codes with manageable computational complexity. A generalization of the original enumerative source code, which includes more complex data sources, is proposed in this thesis. The generalized source code uses the Burrows–Wheeler transform, which is a low–complexity algorithm for converting the redundancy of sequences from complex data sources to a more accessible form. The generalized source code effectively encodes the transformed sequences using the original enumerative source code. It is demonstrated and proved mathematically that this source code is universal (i.e. the code has an asymptotic normalized average redundancy of zero bits). AFRIKAANS : Die betroubare en doeltreffende versending, ontvangs en berging van inligting vorm teen die einde van die twintigste eeu die kern van die mees suksesvolle ekonomie¨e in die wˆereld. Die Internet, eens op ’n tyd ’n geheime projek en toeganklik vir slegs ’n klein groep verbruikers, is vandag deel van die alledaagse lewe van ’n groot persentasie van die mensdom, en derhalwe is die doeltreffende berging van inligting ’n belangrike deel van die inligtingsekonomie. Die verbetering van die bergingsdigteid van optiese en elektroniese media is merkwaardig, maar die uitwissing van oortolligheid in gebergde data, asook die betroubare herwinning van oorspronklike data, bly ’n doel om na te streef. Bronkodering is gemoeid met die kompressie van oortollige data, asook die betroubare dekompressie van die data. Die rekenkundige bronkode, wat onafhanklik voorgestel is deur J. J. Rissanen en R. Pasco in 1976, het ’n revolusie veroorsaak in die bronkoderingsveld. Kompressiealgoritmes wat rekenkundige bronkodes gebruik vir die kodering van oortollige data is tipies meer doeltreffend en rekenkundig meer effektief as kompressiealgoritmes wat vroe¨ere bronkodes, soos verlengde Huffman kodes, gebruik. Rekenkundige bronkodes, wat gereeld in aanpasbare kompressiealgoritmes gebruik word, is ook meer buigbaar as vroe¨ere bronkodes. Die rekenkundige bronkode bly na 30 jaar steeds die bronkode van eerste keuse. Die probleem om data wat afkomstig is van bronne met bekende statistieke (d.w.s. waar die waarskynlikheidsverspreiding van die brondata bekend is) doeltreffend te enkodeer is opgelos deur die instelling van rekenkundige bronkodes. Die bronenkodeerder het egter selde toegang tot die waarskynlikheidsverspreiding van praktiese data. Die bronkodering van data wat afkomstig is van bronne met onbekende statistieke is ’n groter uitdaging, en bly steeds ’n aktiewe navorsingsveld. T. J. Lynch and L. D. Davisson het tel–bronkodes in die 1960s voorgestel. Tel– bronkodes het die merkwaardige eienskap dat bronsekwensies van sekere bronne effektief met hierdie foutlose kodes ge¨enkodeer kan word, sonder dat die bronenkodeerder enige vooraf kennis omtrent die statistieke van die bron hoef te besit. Een nadeel van tel–bronkodes is die ho¨e rekenkompleksiteit van hul implementasies. J. G. Cleary en I. H. Witten het verskeie jare na die instelling van tel–bronkodes bewys dat benaderde tel–bronkodes gerealiseer kan word deur die gebruik van rekenkundige bronkodes. Benaderde tel–bronkodes het ’n laer rekenkompleksiteit as tel–bronkodes, maar benaderde tel–bronkodes is minder doeltreffend as die oorspronklike tel–bronkodes. Navorsers het sedert die werk van Cleary en Witten meer belangstelling getoon in rekenkundige bronkodes as tel–bronkodes. Hierdie tesis is gemoeid met die oorspronklike tel–bronkodes en die gebruik daarvan in Burrows–Wheeler kompressiealgoritmes. ’n Nuwe implementasie van die oorspronklike tel–bronkode word voorgestel. Die voorgestelde implementasie het ’n beduidende laer rekenkompleksiteit as die direkte implementasie van die oorspronklike tel–bronkode. Verskeie nuwe tel–bronkodes, insluitende optimale vaste–tot–vaste lengte tel–bronkodes met beheerbare rekenkompleksiteit, word voorgestel. ’n Veralgemening van die oorspronklike tel–bronkode, wat meer komplekse databronne insluit as die oorspronklike tel–bronkode, word voorgestel in hierdie tesis. The veralgemeende tel–bronkode maak gebruik van die Burrows–Wheeler omskakeling. Die Burrows–Wheeler omskakeling is ’n lae–kompleksiteit algoritme wat die oortolligheid van bronsekwensies wat afkomstig is van komplekse databronne omskakel na ’n meer toeganklike vorm. Die veralgemeende bronkode enkodeer die omgeskakelde sekwensies effektief deur die oorspronklike tel–bronkode te gebruik. Die universele aard van hierdie bronkode word gedemonstreer en wiskundig bewys (d.w.s. dit word bewys dat die kode ’n asimptotiese genormaliseerde gemiddelde oortolligheid van nul bisse het). CopyrightDissertation (MEng)--University of Pretoria, 2010.Electrical, Electronic and Computer Engineeringunrestricte

Dendrochronology: A Status Report for the Eastern United States

Architectural historians and historic preservation practitioners have turned with increasing frequency to dendrochronology to determine dates of construction for houses and other timber structures for which the application of traditional dating techniques, chief among them historical documentation and stylistic analysis, failed. Since the advent of modern, statistically-driven tree-ring dating, analysis of the application of dendrochronology on the eastern region of the United States reveals that the use of this scientific technique has been unevenly applied and is most often used in New England and the Chesapeake. While the techniques used by American dendrochronologists are generally similar, practitioners have failed to adopt a consistent methodology. This study is an assessment of the current state of dendrochronology in the eastern United States and a recordation of available information on locations of dendrochronologically dated buildings. Analysis of dendrochronology reports for 475 buildings conducted by seven labs and consultants reveal expanding application that has produced greater clarity and precision in regional architectural histories

LIPIcs, Volume 274, ESA 2023, Complete Volume

LIPIcs, Volume 274, ESA 2023, Complete Volum