Related papers: Computing the LZ-End parsing: Easy to implement an…
We consider iterative (`turbo') algorithms for compressed sensing. First, a unified exposition of the different approaches available in the literature is given, thereby enlightening the general principles and main differences. In particular…
We describe a universal information compression scheme that compresses any pure quantum i.i.d. source asymptotically to its von Neumann entropy, with no prior knowledge of the structure of the source. We introduce a diagonalisation…
We consider a natural generalization of the classical pattern matching problem: given compressed representations of a pattern p[1..M] and a text t[1..N] of sizes m and n, respectively, does p occur in t? We develop an optimal linear time…
In this paper, we present an efficient, functional, and formally verified parsing algorithm for LL(1) context-free expressions based on the concept of derivatives of formal languages. Parsing with derivatives is an elegant parsing…
Random sequences attain the highest entropy rate. The estimation of entropy rate for an ergodic source can be done using the Lempel Ziv complexity measure yet, the exact entropy rate value is only reached in the infinite limit. We prove…
Various grammar compression algorithms have been proposed in the last decade. A grammar compression is a restricted CFG deriving the string deterministically. An efficient grammar compression develops a smaller CFG by finding duplicated…
We study the complexity of constructing an optimal parsing $\varphi$ of a string ${\bf s} = s_1 \dots s_n$ under the constraint that given a position $p$ in the original text, and the LZ76-like (Lempel Ziv 76) encoding of $T$ based on…
We present a new algorithm for finding a near optimal low-rank approximation of a matrix $A$ in $O(nnz(A))$ time. Our method is based on a recursive sampling scheme for computing a representative subset of $A$'s columns, which is then used…
In this paper we present a 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 string.…
We present simple and efficient algorithms for calculating $q$-gram frequencies on strings represented in compressed form, namely, as a straight line program (SLP). Given an SLP of size $n$ that represents string $T$, we present an $O(qn)$…
As nowadays Machine Learning (ML) techniques are generating huge data collections, the problem of how to efficiently engineer their storage and operations is becoming of paramount importance. In this article we propose a new lossless…
In this paper, we present the following results: (1) We propose a new \emph{dynamic compressed index} of $O(w)$ space, that supports searching for a pattern $P$ in the current text in $O(|P| f(M,w) + \log w \log |P| \log^* M (\log N + \log…
We present a framework facilitating the implementation and comparison of text compression algorithms. We evaluate its features by a case study on two novel compression algorithms based on the Lempel-Ziv compression schemes that perform well…
Kernel methods are powerful tools in machine learning. They have to be computationally efficient. In this paper, we present a novel Geometric-based approach to compute efficiently the string subsequence kernel (SSK). Our main idea is that…
Existing work on prompt compression for Large Language Models (LLM) focuses on lossy methods that try to maximize the retention of semantic information that is relevant to downstream tasks while significantly reducing the sequence length.…
A canonical approach to approximating the partition function of a Gibbs distribution via sampling is simulated annealing. This method has led to efficient reductions from counting to sampling, including: $\bullet$ classic non-adaptive…
We describe a data structure that stores a string $S$ in space similar to that of its Lempel-Ziv encoding and efficiently supports access, rank and select queries. These queries are fundamental for implementing succinct and compressed data…
We introduce Lexico, a novel KV cache compression method that leverages sparse coding with a universal dictionary. Our key finding is that key-value cache in modern LLMs can be accurately approximated using sparse linear combination from a…
Grammar based compression, where one replaces a long string by a small context-free grammar that generates the string, is a simple and powerful paradigm that captures many popular compression schemes. In this paper, we present a novel…
This paper gives new results for synchronization strings, a powerful combinatorial object that allows to efficiently deal with insertions and deletions in various communication settings: $\bullet$ We give a deterministic, linear time…