Related papers: On Two LZ78-style Grammars: Compression Bounds and…
LZ77-based compression schemes compress the input text by replacing factors in the text with an encoded reference to a previous occurrence formed by the couple (length, offset). For a given factor, the smallest is the offset, the smallest…
We provide new estimates of an asymptotic upper bound on the entropy of English using the large language model LLaMA-7B as a predictor for the next token given a window of past tokens. This estimate is significantly smaller than currently…
Countless variants of the Lempel-Ziv compression are widely used in many real-life applications. This paper is concerned with a natural modification of the classical pattern matching problem inspired by the popularity of such compression…
We present a theoretical framework for the compression of automata, which are widely used in speech processing and other natural language processing tasks. The framework extends to graph compression. Similar to stationary ergodic processes,…
We present novel reductions from sample compression schemes in multiclass classification, regression, and adversarially robust learning settings to binary sample compression schemes. Assuming we have a compression scheme for binary classes…
A fundamental problem in shape matching and geometric similarity is computing the maximum area overlap between two polygons under translation. For general simple polygons, the best-known algorithm runs in $O((nm)^2 \log(nm))$ time [Mount,…
At the present scenario of the internet, there exist many optimization techniques to improve the Web speed but almost expensive in terms of bandwidth. So after a long investigation on different techniques to compress the data without any…
In a seminal paper, Kannan and Lov\'asz (1988) considered a quantity $\mu_{KL}(\Lambda,K)$ which denotes the best volume-based lower bound on the covering radius $\mu(\Lambda,K)$ of a convex body $K$ with respect to a lattice $\Lambda$.…
The aim of this note is to provide some reference facts for LZW---mostly from Thomas and Cover \cite{Cover:2006aa} and provide a reference for some metrics that can be derived from it. LZW is an algorithm to compute a Kolmogorov Complexity…
The circular dictionary matching problem is an extension of the classical dictionary matching problem where every string in the dictionary is interpreted as a circular string: after reading the last character of a string, we can move back…
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…
The majority of online content is written in languages other than English, and is most commonly encoded in UTF-8, the world's dominant Unicode character encoding. Traditional compression algorithms typically operate on individual bytes.…
The Lov\'{a}sz Local Lemma is a very powerful tool in probabilistic combinatorics, that is often used to prove existence of combinatorial objects satisfying certain constraints. Moser and Tardos have shown that the LLL gives more than just…
We present a new, simple, and efficient approach for computing the Lempel-Ziv (LZ77) factorization of a string in linear time, based on suffix arrays. Computational experiments on various data sets show that our approach constantly…
The compression-complexity trade-off of lossy compression algorithms that are based on a random codebook or a random database is examined. Motivated, in part, by recent results of Gupta-Verd\'{u}-Weissman (GVW) and their underlying…
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.…
Low Diameter Decompositions (LDDs) are invaluable tools in the design of combinatorial graph algorithms. While historically they have been applied mainly to undirected graphs, in the recent breakthrough for the negative-length Single Source…
We describe how, given a text $T [1..n]$ and a positive constant $\epsilon$, we can build a simple $O (z \log n)$-space index, where $z$ is the number of phrases in the LZ77 parse of $T$, such that later, given a pattern $P [1..m]$, in $O…
Given a regular language L over an ordered alphabet $\Sigma$, the set of lexicographically smallest (resp., largest) words of each length is itself regular. Moreover, there exists an unambiguous finite-state transducer that, on a given word…
The ``state-of-the-art'' in Length Limited Huffman Coding algorithms is the $\Theta(ND)$-time, $\Theta(N)$-space one of Hirschberg and Larmore, where $D\le N$ is the length restriction on the code. This is a very clever, very problem…