A New Algorithm for “the LCS problem” with Application in Compressing Genome Resequencing Data

Background: The longest common subsequence (LCS) problem is a classical problem in computer science, and forms the basis of the current best-performing reference-based compression schemes for genome resequencing data. Methods: First, we present a new algorithm for the LCS problem. Using the generalized suffix tree, we identify the common substrings shared between the two input sequences. Using the maximal common substrings, we construct a directed acyclic graph (DAG), based on which we determine the LCS as the longest path in the DAG. Then, we introduce an LCS-motivated reference-based compression scheme using the components of the LCS, rather than the LCS itself. Results: Our basic scheme compressed the Homo sapiens genome (with an original size of 3,080,436,051 bytes) to 15,460,478 bytes. An improvement on the basic method further reduced this to 8,556,708 bytes, or an overall compression ratio of 360. This can be compared to the previous state-of-the-art compression ratios of 157 (Wang and Zhang, 2011) and 171 (Pinho, Pratas, and Garcia, 2011). Conclusion: We propose a new algorithm to address the longest common subsequence problem. Motivated by our LCS algorithm, we introduce a new reference-based compression scheme for genome resequencing data. Comparative results against state-of-the-art reference-based compression algorithms demonstrate the performance of the proposed method

The Longest Common Subsequence via Generalized Suffix Trees

Given two strings S1 and S 2, finding the longest common subsequence (LCS) is a classical problem in computer science. Many algorithms have been proposed to find the longest common subsequence between two strings. The most common and widely used method is the dynamic programming approach, which runs in quadratic time and takes quadratic space. Other algorithms have been introduced later to solve the LCS problem in less time and space. In this work, we present a new algorithm to find the longest common subsequence using the generalized suffix tree and directed acyclic graph.;The Generalized suffix tree (GST) is the combined suffix tree for a set of strings {lcub}S1, S 2, ..., Sn{rcub}. Both the suffix tree and the generalized suffix tree can be calculated in linear time and linear space. One application for generalized suffix tree is to find the longest common substring between two strings. But finding the longest common subsequence is not straight forward using the generalized suffix tree. Here we describe how we can use the GST to find the common substrings between two strings and introduce a new approach to calculate the longest common subsequence (LCS) from the common substrings. This method takes a different view at the LCS problem, shading more light at novel applications of the LCS. We also show how this method can motivate the development of new compression techniques for genome resequencing data

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