Fast Searching in Packed Strings

Given strings $P$ and $Q$ the (exact) string matching problem is to find all positions of substrings in $Q$ matching $P$. The classical Knuth-Morris-Pratt algorithm [SIAM J. Comput., 1977] solves the string matching problem in linear time which is optimal if we can only read one character at the time. However, most strings are stored in a computer in a packed representation with several characters in a single word, giving us the opportunity to read multiple characters simultaneously. In this paper we study the worst-case complexity of string matching on strings given in packed representation. Let $m \leq n$ be the lengths $P$ and $Q$, respectively, and let $\sigma$ denote the size of the alphabet. On a standard unit-cost word-RAM with logarithmic word size we present an algorithm using time O\left(\frac{n}{\log_\sigma n} + m + \occ\right). Here \occ is the number of occurrences of $P$ in $Q$. For $m = o(n)$ this improves the $O(n)$ bound of the Knuth-Morris-Pratt algorithm. Furthermore, if $m = O(n/\log_\sigma n)$ our algorithm is optimal since any algorithm must spend at least \Omega(\frac{(n+m)\log \sigma}{\log n} + \occ) = \Omega(\frac{n}{\log_\sigma n} + \occ) time to read the input and report all occurrences. The result is obtained by a novel automaton construction based on the Knuth-Morris-Pratt algorithm combined with a new compact representation of subautomata allowing an optimal tabulation-based simulation.Comment: To appear in Journal of Discrete Algorithms. Special Issue on CPM 200

Universal Indexes for Highly Repetitive Document Collections

Indexing highly repetitive collections has become a relevant problem with the emergence of large repositories of versioned documents, among other applications. These collections may reach huge sizes, but are formed mostly of documents that are near-copies of others. Traditional techniques for indexing these collections fail to properly exploit their regularities in order to reduce space. We introduce new techniques for compressing inverted indexes that exploit this near-copy regularity. They are based on run-length, Lempel-Ziv, or grammar compression of the differential inverted lists, instead of the usual practice of gap-encoding them. We show that, in this highly repetitive setting, our compression methods significantly reduce the space obtained with classical techniques, at the price of moderate slowdowns. Moreover, our best methods are universal, that is, they do not need to know the versioning structure of the collection, nor that a clear versioning structure even exists. We also introduce compressed self-indexes in the comparison. These are designed for general strings (not only natural language texts) and represent the text collection plus the index structure (not an inverted index) in integrated form. We show that these techniques can compress much further, using a small fraction of the space required by our new inverted indexes. Yet, they are orders of magnitude slower.Comment: This research has received funding from the European Union's Horizon 2020 research and innovation programme under the Marie Sk{\l}odowska-Curie Actions H2020-MSCA-RISE-2015 BIRDS GA No. 69094

Compressed Representations of Permutations, and Applications

We explore various techniques to compress a permutation $\pi$ over n integers, taking advantage of ordered subsequences in $\pi$, while supporting its application $\pi$(i) and the application of its inverse $\pi^{-1}(i)$ in small time. Our compression schemes yield several interesting byproducts, in many cases matching, improving or extending the best existing results on applications such as the encoding of a permutation in order to support iterated applications $\pi^k(i)$ of it, of integer functions, and of inverted lists and suffix arrays

A new word-based compression model allowing compressed pattern matching

In this study a new semistatic data compression model that has a fast coding process and that allows compressed pattern matching is introduced. The name of the proposed model is chosen as tagged word-based compression algorithm (TWBCA) since it has a word-based coding and word-based compressed matching algorithm. The model has two phases. In the first phase a dictionary is constructed by adding a phrase, paying attention to word boundaries, and in the second phase compression is done by using codewords of phrases in this dictionary. The first byte of the codeword determines whether the word is compressed or not. By paying attention to this rule, the CPM process can be conducted as word based. In addition, the proposed method makes it possible to also search for the group of consecutively compressed words. Any of the previous pattern matching algorithms can be chosen to use in compressed pattern matching as a black box. The duration of the CPM process is always less than the duration of the same process on the texts coded by Gzip tool. While matching longer patterns, compressed pattern matching takes more time on the texts coded by compress and end-tagged dense code (ETDC). However, searching shorter patterns takes less time on texts coded by our approach than the texts compressed with compress. Besides this, the compression ratio of our algorithm has a better performance against ETDC only on a file that has been written in Turkish. The compression performance of TWBCA is stable and does not vary over 6% on different text files