Related papers: Random Access to Grammar Compressed Strings
The convolution between a text string $S$ of length $N$ and a pattern string $P$ of length $m$ can be computed in $O(N \log m)$ time by FFT. It is known that various types of approximate string matching problems are reducible to…
We consider the problem of decompressing the Lempel--Ziv 77 representation of a string $S$ of length $n$ using a working space as close as possible to the size $z$ of the input. The folklore solution for the problem runs in $O(n)$ time but…
Neural networks using numerous text data have been successfully applied to a variety of tasks. While massive text data is usually compressed using techniques such as grammar compression, almost all of the previous machine learning methods…
In this work we introduce a new linear time compression algorithm, called "Re-pair for Trees", which compresses ranked ordered trees using linear straight-line context-free tree grammars. Such grammars generalize straight-line context-free…
We consider the problem of computing the q-gram profile of a string \str of size $N$ compressed by a context-free grammar with $n$ production rules. We present an algorithm that runs in $O(N-\alpha)$ expected time and uses $O(n+q+\kq)$…
Motivated by the imminent growth of massive, highly redundant genomic databases, we study the problem of compressing a string database while simultaneously supporting fast random access, substring extraction and pattern matching to the…
In this paper we present a really simple linear-time algorithm constructing a context-free grammar of size O(g log (N/g)) for the input string, where N is the size of the input string and g the size of the optimal grammar generating this…
In past work (Onokpasa, Wild, Wong, DCC 2023), we showed that (a) for joint compression of RNA sequence and structure, stochastic context-free grammars are the best known compressors and (b) that grammars which have better compression…
We show that, given a string $s$ of length $n$, with constant memory and logarithmic passes over a constant number of streams we can build a context-free grammar that generates $s$ and only $s$ and whose size is within an $\Oh{\min (g \log…
We show how to generate random derangements efficiently by two different techniques: random restricted transpositions and sequential importance sampling. The algorithm employing restricted transpositions can also be used to generate random…
Relative compression, where a set of similar strings are compressed with respect to a reference string, is a very effective method of compressing DNA datasets containing multiple similar sequences. Relative compression is fast to perform…
This paper deals with the two fundamental problems concerning the handling of large n-gram language models: indexing, that is compressing the n-gram strings and associated satellite data without compromising their retrieval speed; and…
We continue our study of ordered context-free grammars, a grammar formalism that places an order on the parse trees produced by the corresponding context-free grammar. In particular, we simplify our previous definition of a derivation of a…
It is shown that every tree of size $n$ over a fixed set of $\sigma$ different ranked symbols can be decomposed (in linear time as well as in logspace) into $O\big(\frac{n}{\log_\sigma n}\big) = O\big(\frac{n \log \sigma}{\log n}\big)$ many…
We propose a new type of representation learning method that models words, phrases and sentences seamlessly. Our method does not depend on word segmentation and any human-annotated resources (e.g., word dictionaries), yet it is very…
Given a string $S$ of length $n$, the classic string indexing problem is to preprocess $S$ into a compact data structure that supports efficient subsequent pattern queries. In the \emph{deterministic} variant the goal is to solve the string…
A lot of work has been done in the field of image compression via machine learning, but not much attention has been given to the compression of natural language. Compressing text into lossless representations while making features easily…
We address the non-redundant random generation of $k$ words of length $n$ in a context-free language. Additionally, we want to avoid a predefined set of words. We study a rejection-based approach, whose worst-case time complexity is shown…
We address the non-redundant random generation of k words of length n from a context-free language. Additionally, we want to avoid a predefined set of words. We study the limits of a rejection-based approach, whose time complexity is shown…
We present OnPair, a dictionary-based compression algorithm designed to meet the needs of in-memory database systems that require both high compression and fast random access. Existing methods either achieve strong compression ratios at…