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We discuss inequalities holding between the vocabulary size, i.e., the number of distinct nonterminal symbols in a grammar-based compression for a string, and the excess length of the respective universal code, i.e., the code-based analog…
In this paper, we analyze the information theoretic lower bound on the necessary number of samples needed for recovering a sparse signal under different compressed sensing settings. We focus on the weighted graph model, a model-based…
We present a highly parallelizable text compression algorithm that scales efficiently to terabyte-sized datasets. Our method builds on locally consistent grammars, a lightweight form of compression, combined with simple recompression…
We present an algorithm for computing the Lyndon factorization of a string that is given in grammar compressed form, namely, a Straight Line Program (SLP). The algorithm runs in $O(n^4 + mn^3h)$ time and $O(n^2)$ space, where $m$ is the…
In the problem of $\texttt{Generalised Pattern Matching}\ (\texttt{GPM})$ [STOC'94, Muthukrishnan and Palem], we are given a text $T$ of length $n$ over an alphabet $\Sigma_T$, a pattern $P$ of length $m$ over an alphabet $\Sigma_P$, and a…
We present OnPair, a dictionary-based compression algorithm designed to meet the needs of in-memory database systems that require both high compression and fast random access. Existing methods either achieve strong compression ratios at…
In this paper we consider word equations with one variable (and arbitrary many appearances of it). A recent technique of recompression, which is applicable to general word equations, is shown to be suitable also in this case. While in…
The suffix array and the suffix tree are the two most fundamental data structures for string processing. For a length-$n$ text, however, they use $\Theta(n \log n)$ bits of space, which is often too costly. To address this, Grossi and…
Chain-of-thought reasoning in large language models can trigger an "overthinking trap": longer rollouts raise cost and latency yet often yield unreliable accuracy gains. Existing methods use global, static controls that may suppress needed…
Most of the attention in statistical compression is given to the space used by the compressed sequence, a problem completely solved with optimal prefix codes. However, in many applications, the storage space used to represent the prefix…
This paper describes substantial advances in the analysis (parsing) of diagrams using constraint grammars. The addition of set types to the grammar and spatial indexing of the data make it possible to efficiently parse real diagrams of…
We consider a standard distributed optimisation setting where $N$ machines, each holding a $d$-dimensional function $f_i$, aim to jointly minimise the sum of the functions $\sum_{i = 1}^N f_i (x)$. This problem arises naturally in…
Lempel-Ziv (LZ77) factorization is a fundamental problem in string processing: Greedily partition a given string $T$ from left to right into blocks (called phrases) so that each phrase is either the leftmost occurrence of a letter or the…
In memory-constrained algorithms we have read-only access to the input, and the number of additional variables is limited. In this paper we introduce the compressed stack technique, a method that allows to transform algorithms whose space…
Two strings are considered to have parameterized matching when there exists a bijection of the parameterized alphabet onto itself such that it transforms one string to another. Parameterized matching has application in software duplication…
With the wide adoption of language models for IR -- and specifically RAG systems -- the latency of the underlying LLM becomes a crucial bottleneck, since the long contexts of retrieved passages lead large prompts and therefore, compute…
We study semantic compression for text where meanings contained in the text are conveyed to a source decoder, e.g., for classification. The main motivator to move to such an approach of recovering the meaning without requiring exact…
We analyze the grammar generation algorithm of the RePair compression algorithm and show the relation between a grammar generated by RePair and maximal repeats. We reveal that RePair replaces step by step the most frequent pairs within the…
Unlike in statistical compression, where Shannon's entropy is a definitive lower bound, no such clear measure exists for the compressibility of repetitive sequences. Since statistical entropy does not capture repetitiveness, ad-hoc measures…
Long-context large language models remain computationally expensive to run and often fail to reliably process very long inputs, which makes context compression an important component of many systems. Existing compression approaches…