On optimally partitioning a text to improve its compression

In this paper we investigate the problem of partitioning an input string T in such a way that compressing individually its parts via a base-compressor C gets a compressed output that is shorter than applying C over the entire T at once. This problem was introduced in the context of table compression, and then further elaborated and extended to strings and trees. Unfortunately, the literature offers poor solutions: namely, we know either a cubic-time algorithm for computing the optimal partition based on dynamic programming, or few heuristics that do not guarantee any bounds on the efficacy of their computed partition, or algorithms that are efficient but work in some specific scenarios (such as the Burrows-Wheeler Transform) and achieve compression performance that might be worse than the optimal-partitioning by a $\Omega(\sqrt{\log n})$ factor. Therefore, computing efficiently the optimal solution is still open. In this paper we provide the first algorithm which is guaranteed to compute in O(n \log_{1+\eps}n) time a partition of T whose compressed output is guaranteed to be no more than $(1+\epsilon)$-worse the optimal one, where $\epsilon$ may be any positive constant

When a Dollar Makes a BWT

TheBurrows-Wheeler-Transform(BWT)isareversiblestring transformation which plays a central role in text compression and is fun- damental in many modern bioinformatics applications. The BWT is a permutation of the characters, which is in general better compressible and allows to answer several different query types more efficiently than the original string. It is easy to see that not every string is a BWT image, and exact charac- terizations of BWT images are known. We investigate a related combi- natorial question. In many applications, a sentinel character $is added to mark the end of the string, and thus the BWT of a string ending with$ contains exactly one $character. We ask, given a string w, in which positions, if any, can the$-character be inserted to turn w into the BWT image of a word ending with the sentinel character. We show that this depends only on the standard permutation of w and give a combinatorial characterization of such positions via this permutation. We then develop an O(n log n)-time algorithm for identifying all such positions, improving on the naive quadratic time algorithm

New Algorithms and Lower Bounds for Sequential-Access Data Compression

This thesis concerns sequential-access data compression, i.e., by algorithms that read the input one or more times from beginning to end. In one chapter we consider adaptive prefix coding, for which we must read the input character by character, outputting each character's self-delimiting codeword before reading the next one. We show how to encode and decode each character in constant worst-case time while producing an encoding whose length is worst-case optimal. In another chapter we consider one-pass compression with memory bounded in terms of the alphabet size and context length, and prove a nearly tight tradeoff between the amount of memory we can use and the quality of the compression we can achieve. In a third chapter we consider compression in the read/write streams model, which allows us passes and memory both polylogarithmic in the size of the input. We first show how to achieve universal compression using only one pass over one stream. We then show that one stream is not sufficient for achieving good grammar-based compression. Finally, we show that two streams are necessary and sufficient for achieving entropy-only bounds.Comment: draft of PhD thesi

Scalable succinct indexing for large text collections

Self-indexes save space by emulating operations of traditional data structures using basic operations on bitvectors. Succinct text indexes provide full-text search functionality which is traditionally provided by suffix trees and suffix arrays for a given text, while using space equivalent to the compressed representation of the text. Succinct text indexes can therefore provide full-text search functionality over inputs much larger than what is viable using traditional uncompressed suffix-based data structures. Fields such as Information Retrieval involve the processing of massive text collections. However, the in-memory space requirements of succinct text indexes during construction have hampered their adoption for large text collections. One promising approach to support larger data sets is to avoid constructing the full suffix array by using alternative indexing representations. This thesis focuses on several aspects related to the scalability of text indexes to larger data sets. We identify practical improvements in the core building blocks of all succinct text indexing algorithms, and subsequently improve the index performance on large data sets. We evaluate our findings using several standard text collections and demonstrate: (1) the practical applications of our improved indexing techniques; and (2) that succinct text indexes are a practical alternative to inverted indexes for a variety of top-k ranked document retrieval problems