Related papers: Approximation of grammar-based compression via rec…
Multiple algorithms are known for efficiently calculating the prefix probability of a string under a probabilistic context-free grammar (PCFG). Good algorithms for the problem have a runtime cubic in the length of the input string. However,…
We present a novel parsing algorithm for all context-free languages, based on computing the relation between configurations and reaching transitions in a recursive transition network. Parsing complexity w.r.t. input length matches the state…
Internal Pattern Matching (IPM) queries on a text $T$, given two fragments $X$ and $Y$ of $T$ such that $|Y|<2|X|$, ask to compute all exact occurrences of $X$ within $Y$. IPM queries have been introduced by Kociumaka, Radoszewski, Rytter,…
In the era of big data, learning from categorical features with very large vocabularies (e.g., 28 million for the Criteo click prediction dataset) has become a practical challenge for machine learning researchers and practitioners. We…
We propose a systematic method for constructing a sparse data reconstruction algorithm in compressed sensing at a relatively low computational cost for general observation matrix. It is known that the cost of l1-norm minimization using a…
Here we study the complexity of string problems as a function of the size of a program that generates input. We consider straight-line programs (SLP), since all algorithms on SLP-generated strings could be applied to processing…
The $k$-mappability problem has two integers parameters $m$ and $k$. For every subword of size $m$ in a text $S$, we wish to report the number of indices in $S$ in which the word occurs with at most $k$ mismatches. The problem was lately…
In-context learning has established itself as an important learning paradigm for Large Language Models (LLMs). In this paper, we demonstrate that LLMs can learn encoding keys in-context and perform analysis directly on encoded…
In this paper, we consider the problem of efficiently representing a set $S$ of $n$ items out of a universe $U=\{0,...,u-1\}$ while supporting a number of operations on it. Let $G=g_1...g_n$ be the gap stream associated with $S$, $gap$ its…
Mauer et al. [A Lempel-Ziv-style Compression Method for Repetitive Texts, PSC 2017] proposed a hybrid text compression method called LZ-LFS which has both features of Lempel-Ziv 77 factorization and longest first substitution. They showed…
We present the first linear time algorithm to construct the $2n$-bit version of the Lyndon array for a string of length $n$ using only $o(n)$ bits of working space. A simpler variant of this algorithm computes the plain ($n\lg n$-bit)…
In this paper we study the adaptive prefix coding problem in cases where the size of the input alphabet is large. We present an online prefix coding algorithm that uses $O(\sigma^{1 / \lambda + \epsilon}) $ bits of space for any constants…
We describe a compression-aware method to compute all-vs-all maximal exact matches (MEM) among strings of a repetitive collection $\mathcal{T}$. The key concept in our work is the construction of a fully-balanced grammar $\mathcal{G}$ from…
In this paper, we show that the LZ77 factorization of a text T {\in\Sigma^n} can be computed in O(R log n) bits of working space and O(n log R) time, R being the number of runs in the Burrows-Wheeler transform of T reversed. For extremely…
Grammar-based compression is a loss-less data compression scheme that represents a given string $w$ by a context-free grammar that generates only $w$. While computing the smallest grammar which generates a given string $w$ is NP-hard in…
An LZ-like factorization of a string divides it into factors, each being either a single character or a copy of a preceding substring. While grammar-based compression schemes support efficient random access with space linear in the…
Given a set of strings, the shortest common superstring problem is to find the shortest possible string that contains all the input strings. The problem is NP-hard, but a lot of work has gone into designing approximation algorithms for…
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…
We consider document listing on string collections, that is, finding in which strings a given pattern appears. In particular, we focus on repetitive collections: a collection of size $N$ over alphabet $[1,\sigma]$ is composed of $D$ copies…
We study the classical approximate string matching problem, that is, given strings $P$ and $Q$ and an error threshold $k$, find all ending positions of substrings of $Q$ whose edit distance to $P$ is at most $k$. Let $P$ and $Q$ have…