Tying up the loose ends in fully LZW-compressed pattern matching

We consider a natural generalization of the classical pattern matching problem: given compressed representations of a pattern p[1..M] and a text t[1..N] of sizes m and n, respectively, does p occur in t? We develop an optimal linear time solution for the case when p and t are compressed using the LZW method. This improves the previously known O((n+m)log(n+m)) time solution of Gasieniec and Rytter, and essentially closes the line of research devoted to tudying LZW-compressed exact pattern matching

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

Re-Use Dynamic Programming for Sequence Alignment: An Algorithmic Toolkit

International audienceThe problem of comparing two sequences S and T to determine their similarity is one of the fundamental problems in pattern matching. In this manuscript we will be primarily concerned with sequences as our objects and with various string comparison metrics. Our goal is to survey a methodology for utilizing repetitions in sequences in order to speed up the comparison process. Within this framework we consider various methods of parsing the sequences in order to frame their repetitions, and present a toolkit of various solutions whose time complexity depends both on the chosen parsing method as well as on the string-comparison metric used for the alignment

A Space-Optimal Grammar Compression

A grammar compression is a context-free grammar (CFG) deriving a single string deterministically. For an input string of length N over an alphabet of size sigma, the smallest CFG is O(log N)-approximable in the offline setting and O(log N log^* N)-approximable in the online setting. In addition, an information-theoretic lower bound for representing a CFG in Chomsky normal form of n variables is log (n!/n^sigma) + n + o(n) bits. Although there is an online grammar compression algorithm that directly computes the succinct encoding of its output CFG with O(log N log^* N) approximation guarantee, the problem of optimizing its working space has remained open. We propose a fully-online algorithm that requires the fewest bits of working space asymptotically equal to the lower bound in O(N log log n) compression time. In addition we propose several techniques to boost grammar compression and show their efficiency by computational experiments

ON THE COMPRESSION OF DIGITAL HOLOGRAMS

This thesis investigates the compression of computer-generated transmission holograms through lossless schemes such as the Burrows-Wheeler compression scheme (BWCS). Ever since Gabor’s discovery of holography, much research have been done to improve the record­ ing and viewing of holograms into more convenient uses such as video viewing. However, the compression of holograms where recording is performed from virtual scenes has not received much attention. Phase-shift digital holograms, on the other hand, have received more attention due to their practical application in object recognition, imaging, and video sequencing of phys­ ical objects. This study is performed for virtually recorded computer-generated holograms in order to understand compression factors in virtually recorded holograms. We also investigate application of lossless compression schemes to holograms with reduced precision for the in­ tensity and phase values. The overall objective is to explore the factors that affect effective compression of virtual holograms. As a result, this work can be used to assist in the design­ ing of better compression algorithms for applications such as virtual object simulations, video gaming application, and holographic video viewing