Related papers: LZ-Compressed String Dictionaries
Given a string $S$, the \emph{compressed indexing problem} is to preprocess $S$ into a compressed representation that supports fast \emph{substring queries}. The goal is to use little space relative to the compressed size of $S$ while…
Advances in DNA sequencing mean databases of thousands of human genomes will soon be commonplace. In this paper we introduce a simple technique for reducing the size of conventional indexes on such highly repetitive texts. Given upper…
We present a new algorithm for computing the Lempel-Ziv Factorization (LZ77) of a given string of length $N$ in linear time, that utilizes only $N\log N + O(1)$ bits of working space, i.e., a single integer array, for constant size integer…
We investigate two closely related LZ78-based compression schemes: LZMW (an old scheme by Miller and Wegman) and LZD (a recent variant by Goto et al.). Both LZD and LZMW naturally produce a grammar for a string of length $n$; we show that…
While the language modeling objective has been shown to be deeply connected with compression, it is surprising that modern LLMs are not employed in practical text compression systems. In this paper, we provide an in-depth analysis of neural…
Physics concepts have often been borrowed and independently developed by other fields of science. In this perspective a significant example is that of entropy in Information Theory. The aim of this paper is to provide a short and…
The paper proposes an improved error-resilient Lempel-Ziv'77 (LZ'77) algorithm employing an adaptive amount of parity bits for error protection. It is a modified version of error resilient algorithm LZRS'77, proposed recently, which uses a…
Compression algorithms reduce the redundancy in data representation to decrease the storage required for that data. Data compression offers an attractive approach to reducing communication costs by using available bandwidth effectively.…
We derive upper and lower bounds on the overall compression ratio of the 1978 Lempel-Ziv (LZ78) algorithm, applied independently to $k$-blocks of a finite individual sequence. Both bounds are given in terms of normalized empirical entropies…
Traditional lossless text compression preserves every byte, but its gains on natural language are often modest in realistic operating regimes. We study \emph{lossy semantic text compression}, where the encoder strategically deletes parts of…
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…
The paper introduces a new lossless, highly robust compression algorithm that similar with LZW algorithm, yet the algorithm discards dictionary processing and uses irregular sequences with massive, random information instead. Then the paper…
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…
A family of Lempel-Ziv factorizations is a well-studied string structure. The LZ-End factorization is a member of the family that achieved faster extraction of any substrings (Kreft & Navarro, TCS 2013). One of the interests for LZ-End…
We study the sensitivity of the Lempel-Ziv 77 compression algorithm to edits, showing how modifying a string $w$ can deteriorate or improve its compression. Our first result is a tight upper bound for $k$ edits: $\forall w' \in B(w,k)$, we…
This paper investigates the size in bits of the LZ77 encoding, which is the most popular and efficient variant of the Lempel-Ziv encodings used in data compression. We prove that, for a wide natural class of variable-length encoders for…
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…
The sensitivity of a string compression algorithm $C$ asks how much the output size $C(T)$ for an input string $T$ can increase when a single character edit operation is performed on $T$. This notion enables one to measure the robustness of…
In this paper we compare the difference in performance of two of the Prediction by Partial Matching (PPM) family of compressors (PPM$^*$ and the original Bounded PPM algorithm) and the Lempel-Ziv 78 (LZ) algorithm. We construct an infinite…
The properties of maximum Lempel-Ziv complexity strings are studied for the binary case. A comparison between MLZs and random strings is carried out. The length profile of both type of sequences show different distribution functions. The…