Asymptotic Optimality of Antidictionary Codes

An antidictionary code is a lossless compression algorithm using an antidictionary which is a set of minimal words that do not occur as substrings in an input string. The code was proposed by Crochemore et al. in 2000, and its asymptotic optimality has been proved with respect to only a specific information source, called balanced binary source that is a binary Markov source in which a state transition occurs with probability 1/2 or 1. In this paper, we prove the optimality of both static and dynamic antidictionary codes with respect to a stationary ergodic Markov source on finite alphabet such that a state transition occurs with probability $p (0 < p \leq 1)$.Comment: 5 pages, to appear in the proceedings of 2010 IEEE International Symposium on Information Theory (ISIT2010

Two-Dimensional Source Coding by Means of Subblock Enumeration

A technique of lossless compression via substring enumeration (CSE) attains compression ratios as well as popular lossless compressors for one-dimensional (1D) sources. The CSE utilizes a probabilistic model built from the circular string of an input source for encoding the source.The CSE is applicable to two-dimensional (2D) sources such as images by dealing with a line of pixels of 2D source as a symbol of an extended alphabet. At the initial step of the CSE encoding process, we need to output the number of occurrences of all symbols of the extended alphabet, so that the time complexity increase exponentially when the size of source becomes large. To reduce the time complexity, we propose a new CSE which can encode a 2D source in block-by-block instead of line-by-line. The proposed CSE utilizes the flat torus of an input 2D source as a probabilistic model for encoding the source instead of the circular string of the source. Moreover, we analyze the limit of the average codeword length of the proposed CSE for general sources.Comment: 5 pages, Submitted to ISIT201

On the Structure of Bispecial Sturmian Words

A balanced word is one in which any two factors of the same length contain the same number of each letter of the alphabet up to one. Finite binary balanced words are called Sturmian words. A Sturmian word is bispecial if it can be extended to the left and to the right with both letters remaining a Sturmian word. There is a deep relation between bispecial Sturmian words and Christoffel words, that are the digital approximations of Euclidean segments in the plane. In 1997, J. Berstel and A. de Luca proved that \emph{palindromic} bispecial Sturmian words are precisely the maximal internal factors of \emph{primitive} Christoffel words. We extend this result by showing that bispecial Sturmian words are precisely the maximal internal factors of \emph{all} Christoffel words. Our characterization allows us to give an enumerative formula for bispecial Sturmian words. We also investigate the minimal forbidden words for the language of Sturmian words.Comment: arXiv admin note: substantial text overlap with arXiv:1204.167

A Universal Two-Dimensional Source Coding by Means of Subblock Enumeration

The technique of lossless compression via substring enumeration (CSE) is a kind of enumerative code and uses a probabilistic model built from the circular string of an input source for encoding a one-dimensional (1D) source. CSE is applicable to two-dimensional (2D) sources, such as images, by dealing with a line of pixels of a 2D source as a symbol of an extended alphabet. At the initial step of CSE encoding process, we need to output the number of occurrences of all symbols of the extended alphabet, so that the time complexity increases exponentially when the size of source becomes large. To reduce computational time, we can rearrange pixels of a 2D source into a 1D source string along a space-filling curve like a Hilbert curve. However, information on adjacent cells in a 2D source may be lost in the conversion. To reduce the time complexity and compress a 2D source without converting to a 1D source, we propose a new CSE which can encode a 2D source in a block-by-block fashion instead of in a line-by-line fashion. The proposed algorithm uses the flat torus of an input 2D source as a probabilistic model instead of the circular string of the source. Moreover, we prove the asymptotic optimality of the proposed algorithm for 2D general sources

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

Algorithm engineering : string processing

The string matching problem has attracted a lot of interest throughout the history of computer science, and is crucial to the computing industry. The theoretical community in Computer Science has a developed a rich literature in the design and analysis of string matching algorithms. To date, most of this work has been based on the asymptotic analysis of the algorithms. This analysis rarely tell us how the algorithm will perform in practice and considerable experimentation and fine-tuning is typically required to get the most out of a theoretical idea. In this thesis, promising string matching algorithms discovered by the theoretical community are implemented, tested and refined to the point where they can be usefully applied in practice. In the course of this work we have presented the following new algorithms. We prove that the time complexity of the new algorithms, for the average case is linear. We also compared the new algorithms with the existing algorithms by experimentation. " We implemented the existing one dimensional string matching algorithms for English texts. From the findings of the experimental results we identified the best two algorithms. We combined these two algorithms and introduce a new algorithm. " We developed a new two dimensional string matching algorithm. This algorithm uses the structure of the pattern to reduce the number of comparisons required to search for the pattern. " We described a method for efficiently storing text. Although this reduces the size of the storage space, it is not a compression method as in the literature. Our aim is to improve both space and time taken by a string matching algorithm. Our new algorithm searches for patterns in the efficiently stored text without decompressing the text. " We illustrated that by pre-processing the text we can improve the speed of the string matching algorithm when we search for a large number of patterns in a given text. " We proposed a hardware solution for searching in an efficiently stored DNA text