Related papers: Note on the Greedy Parsing Optimality for Dictiona…
The Lempel-Ziv parsing of a string (LZ77 for short) is one of the most important and widely-used algorithmic tools in data compression and string processing. We show that the Lempel-Ziv parsing of a string of length $n$ on an alphabet of…
The unrestricted LZ78 universal data-compression algorithm (as well as the LZ77 and LZW versions) achieves asymptotically, as the block-length tends to infinity, the FS compressibility, namely the best compression-ratio that may be achieved…
The problem of storing a set of strings --- a string dictionary --- in compact form appears naturally in many cases. While classically it has represented a small part of the whole data to be processed (e.g., for Natural Language processing…
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 propose algorithms computing the semi-greedy Lempel-Ziv 78 (LZ78), the Lempel-Ziv Double (LZD), and the Lempel-Ziv-Miller-Wegman (LZMW) factorizations in linear time for integer alphabets. For LZD and LZMW, we additionally propose data…
We consider lossless compression based on statistical data modeling followed by prediction-based encoding, where an accurate statistical model for the input data leads to substantial improvements in compression. We propose DZip, a…
The rise of repetitive datasets has lately generated a lot of interest in compressed self-indexes based on dictionary compression, a rich and heterogeneous family that exploits text repetitions in different ways. For each such compression…
Text compression for large language model (LLM) systems is usually framed as token deletion, retrieval, summarization, or exact reconstruction. We study a more aggressive but explicitly lossy setting: compress text into compact codes that…
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…
We present a simple adaptation of the Lempel Ziv 78' (LZ78) compression scheme ({\em IEEE Transactions on Information Theory, 1978}) that supports efficient random access to the input string. Namely, given query access to the compressed…
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…
Boob et al. [1] described an iterative peeling algorithm called Greedy++ for the Densest Subgraph Problem (DSG) and conjectured that it converges to an optimum solution. Chekuri, Quanrud, and Torres [2] extended the algorithm to general…
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…
Re-Pair is an efficient grammar compressor that operates by recursively replacing high-frequency character pairs with new grammar symbols. The most space-efficient linear-time algorithm computing Re-Pair uses $(1+\epsilon)n+\sqrt n$ words…
Motivated by the recent submission to cond-mat archives by J. Goodman (cond-mat/0202383) whose results apparently discredit the approach we have proposed in a recent paper (Phys. Rev. Lett., 88, 048702 (2002), cond-mat/0108530), we report…
A well-known but rarely used approach to text categorization uses conditional entropy estimates computed using data compression tools. Text affinity scores derived from compressed sizes can be used for classification and ranking tasks, but…
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…
Past work has established scaling laws that predict the performance of a neural language model (LM) as a function of its parameter count and the number of tokens it's trained on, enabling optimal allocation of a fixed compute budget. Are…
We introduce a new approach to LZ77 factorization that uses O(n/d) words of working space and O(dn) time for any d >= 1 (for polylogarithmic alphabet sizes). We also describe carefully engineered implementations of alternative approaches to…
The goal of grammar compression is to construct a small sized context free grammar which uniquely generates the input text data. Among grammar compression methods, RePair is known for its good practical compression performance. MR-RePair…