Related papers: LZRR: LZ77 Parsing with Right Reference
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…
This paper presents conditional versions of Lempel-Ziv (LZ) algorithm for settings where compressor and decompressor have access to the same side information. We propose a fixed-length-parsing LZ algorithm with side information, motivated…
We present RCT, a new compact data structure to represent trajectories of objects. It is based on a relative compression technique called Relative Lempel-Ziv (RLZ), which compresses sequences by applying an LZ77 encoding with respect to an…
Data compression continues to evolve, with traditional information theory methods being widely used for compressing text, images, and videos. Recently, there has been growing interest in leveraging Generative AI for predictive compression…
Shannon's entropy is a clear lower bound for statistical compression. The situation is not so well understood for dictionary-based compression. A plausible lower bound is $b$, the least number of phrases of a general bidirectional parse of…
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…
Lempel-Ziv is an easy-to-compute member of a wide family of so-called macro schemes; it restricts pointers to go in one direction only. Optimal bidirectional macro schemes are NP-complete to find, but they may provide much better…
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…
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…
Modern data compression methods are slowly reaching their limits after 80 years of research, millions of papers, and wide range of applications. Yet, the extravagant 6G communication speed requirement raises a major open question for…
We present an algorithm that constructs the LZ-End parsing (a variation of LZ77) of a given string of length $n$ in $O(n\log\ell)$ expected time and $O(z + \ell)$ space, where $z$ is the number of phrases in the parsing and $\ell$ is the…
Despite consistently yielding the best compression on repetitive text collections, the Lempel-Ziv parsing has resisted all attempts at offering relevant guarantees on the cost to access an arbitrary symbol. This makes it less attractive for…
The LZ-End parsing [Kreft & Navarro, 2011] of an input string yields compression competitive with the popular Lempel-Ziv 77 scheme, but also allows for efficient random access. Kempa and Kosolobov showed that the parsing can be computed in…
We propose a novel, lightweight supervised dictionary learning framework for text classification based on data compression and representation. This two-phase algorithm initially employs the Lempel-Ziv-Welch (LZW) algorithm to construct a…
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.…
Much research has been devoted to optimizing algorithms of the Lempel-Ziv (LZ) 77 family, both in terms of speed and memory requirements. Binary search trees and suffix trees (ST) are data structures that have been often used for this…
Today there are many universal compression algorithms, but in most cases is for specific data better using specific algorithm - JPEG for images, MPEG for movies, etc. For textual documents there are special methods based on PPM algorithm or…
Random access to highly compressed strings -- represented by straight-line programs or Lempel-Ziv parses, for example -- is a well-studied topic. Random access to such strings in strongly sublogarithmic time is impossible in the worst case,…
We consider the communication complexity of the Hamming distance of two strings. Bille et al. [SPIRE 2018] considered the communication complexity of the longest common prefix (LCP) problem in the setting where the two parties have their…
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…