Related papers: At the Roots of Dictionary Compression: String Att…
In this paper, we propose a novel tensor learning and coding model for third-order data completion. Our model is to learn a data-adaptive dictionary from the given observations, and determine the coding coefficients of third-order tensor…
The quadratic complexity of self-attention constrains Large Language Models (LLMs) in processing long contexts, a capability essential for many advanced applications. Context compression aims to alleviate this computational bottleneck while…
Short spanning trees subject to additional constraints are important building blocks in various approximation algorithms. Especially in the context of the Traveling Salesman Problem (TSP), new techniques for finding spanning trees with…
Real-world data typically contain repeated and periodic patterns. This suggests that they can be effectively represented and compressed using only a few coefficients of an appropriate basis (e.g., Fourier, Wavelets, etc.). However, distance…
We propose algorithms that, given the input string of length $n$ over integer alphabet of size $\sigma$, construct the Burrows-Wheeler transform (BWT), the permuted longest-common-prefix (PLCP) array, and the LZ77 parsing in…
The idea that many important classes of signals can be well-represented by linear combinations of a small set of atoms selected from a given dictionary has had dramatic impact on the theory and practice of signal processing. For practical…
Compressing integer keys is a fundamental operation among multiple communities, such as database management (DB), information retrieval (IR), and high-performance computing (HPC). Recent advances in \emph{learned indexes} have inspired the…
This paper is concerned with practical implementations of approximate string dictionaries that allow edit errors. In this problem, we have as input a dictionary $D$ of $d$ strings of total length $n$ over an alphabet of size $\sigma$. Given…
The field of compressed sensing has shown that a sparse but otherwise arbitrary vector can be recovered exactly from a small number of randomly constructed linear projections (or samples). The question addressed in this paper is whether an…
We present a new data structure called the \emph{Compressed Random Access Memory} (CRAM) that can store a dynamic string $T$ of characters, e.g., representing the memory of a computer, in compressed form while achieving asymptotically…
The Kolmogorov complexity of x, denoted C(x), is the length of the shortest program that generates x. For such a simple definition, Kolmogorov complexity has a rich and deep theory, as well as applications to a wide variety of topics…
Vector databases typically rely on approximate nearest neighbor (ANN) search to retrieve the top-k closest vectors to a query in embedding space. While effective, this approach often yields semantically redundant results, missing the…
The suffix tree is arguably the most fundamental data structure on strings: introduced by Weiner (SWAT 1973) and McCreight (JACM 1976), it allows solving a myriad of computational problems on strings in linear time. Motivated by its large…
Given a string $S$ of length $N$ on a fixed alphabet of $\sigma$ symbols, a grammar compressor produces a context-free grammar $G$ of size $n$ that generates $S$ and only $S$. In this paper we describe data structures to support the…
The classic string indexing problem is to preprocess a string $S$ into a compact data structure that supports efficient subsequent pattern matching queries, that is, given a pattern string $P$, report all occurrences of $P$ within $S$. In…
We initiate a systematic study of utilizing predictions to improve over approximation guarantees of classic algorithms, without increasing the running time. We propose a systematic method for a wide class of optimization problems that ask…
We introduce the first self-index based on the Lempel-Ziv 1977 compression format (LZ77). It is particularly competitive for highly repetitive text collections such as sequence databases of genomes of related species, software repositories,…
Transformer-based Large Language Models (LLMs) often impose limitations on the length of the text input to ensure the generation of fluent and relevant responses. This constraint restricts their applicability in scenarios involving long…
This paper addresses the online exact string matching problem which consists in finding all occurrences of a given pattern p in a text t. It is an extensively studied problem in computer science, mainly due to its direct applications to…
Large-alphabet strings are common in scenarios such as information retrieval and natural-language processing. The efficient storage and processing of such strings usually introduces several challenges that are not witnessed in…