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Given a string of length $n$ that is composed of $r$ runs of letters from the alphabet $\{0,1,\ldots,\sigma{-}1\}$ such that $2 \le \sigma \le r$, we describe a data structure that, provided $r \le n / \log^{\omega(1)} n$, stores the string…

Data Structures and Algorithms · Computer Science 2018-02-27 José Fuentes-Sepúlveda , Juha Kärkkäinen , Dmitry Kosolobov , Simon J. Puglisi

Suppose an oracle knows a string $S$ that is unknown to us and that we want to determine. The oracle can answer queries of the form "Is $s$ a substring of $S$?". In 1995, Skiena and Sundaram showed that, in the worst case, any algorithm…

Data Structures and Algorithms · Computer Science 2021-10-20 Gabriele Fici , Nicola Prezza , Rossano Venturini

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…

Data Structures and Algorithms · Computer Science 2013-04-29 Tomohiro I , Yuto Nakashima , Shunsuke Inenaga , Hideo Bannai , Masayuki Takeda

In the last decades, the necessity to process massive amounts of textual data fueled the development of compressed text indexes: data structures efficiently answering queries on a given text while occupying space proportional to the…

Data Structures and Algorithms · Computer Science 2024-09-24 Dominik Kempa , Tomasz Kociumaka

We consider the problem of storing a dynamic string $S$ over an alphabet $\Sigma=\{\,1,\ldots,\sigma\,\}$ in compressed form. Our representation supports insertions and deletions of symbols and answers three fundamental queries:…

Data Structures and Algorithms · Computer Science 2015-07-27 J. Ian Munro , Yakov Nekrich

We continue the investigation of polynomial-time sparsification for NP-complete Boolean Constraint Satisfaction Problems (CSPs). The goal in sparsification is to reduce the number of constraints in a problem instance without changing the…

Computational Complexity · Computer Science 2018-09-18 Hubie Chen , Bart M. P. Jansen , Astrid Pieterse

We consider the problem of encoding a string of length $n$ from an integer alphabet of size $\sigma$ so that access and substring equality queries (that is, determining the equality of any two substrings) can be answered efficiently. Any…

Data Structures and Algorithms · Computer Science 2020-05-12 Nicola Prezza

A binary string of length $2^k$ induces the Boolean function of $k$ variables whose Shannon expansion is the given binary string. This Boolean function then is representable via a unique reduced ordered binary decision diagram (ROBDD). The…

Information Theory · Computer Science 2011-11-08 J. Kieffer , P. Flajolet , E. -h. Yang

We present a new algorithm for subsequence matching in grammar compressed strings. Given a grammar of size $n$ compressing a string of size $N$ and a pattern string of size $m$ over an alphabet of size $\sigma$, our algorithm uses…

Data Structures and Algorithms · Computer Science 2014-06-06 Philip Bille , Patrick Hagge Cording , Inge Li Gørtz

Consider the case where consecutive blocks of N letters of a semi-infinite individual sequence X over a finite-alphabet are being compressed into binary sequences by some one-to-one mapping. No a-priori information about X is available at…

Information Theory · Computer Science 2013-01-25 Jacob Ziv

Abelian string matching problems are becoming an object of considerable interest in last years. Very recently, Alatabbi et al. \cite{AILR2015} presented the first solution for the longest common Abelian factor problem for a pair of strings,…

Data Structures and Algorithms · Computer Science 2015-03-12 Szymon Grabowski

Byte-Pair Encoding (BPE) is a widely used method for subword tokenization, with origins in grammar-based text compression. It is employed in a variety of language processing tasks such as machine translation or large language model (LLM)…

Data Structures and Algorithms · Computer Science 2024-11-14 László Kozma , Johannes Voderholzer

We show that the number of distinct squares in a packed string of length $n$ over an alphabet of size $\sigma$ can be computed in $O(n/\log_\sigma n)$ time in the word-RAM model. This paper is the first to introduce a sublinear-time…

Data Structures and Algorithms · Computer Science 2025-09-03 Panagiotis Charalampopoulos , Manal Mohamed , Jakub Radoszewski , Wojciech Rytter , Tomasz Waleń , Wiktor Zuba

The notions of synchronizing and partitioning sets are recently introduced variants of locally consistent parsings with great potential in problem-solving. In this paper we propose a deterministic algorithm that constructs for a given…

Data Structures and Algorithms · Computer Science 2024-04-23 Dmitry Kosolobov , Nikita Sivukhin

Let $s$ be a string of length $n$ over an alphabet of constant size $\sigma$ and let $c$ and $\epsilon$ be constants with (1 \geq c \geq 0) and (\epsilon > 0). Using (O (n)) time, (O (n^c)) bits of memory and one pass we can always encode…

Information Theory · Computer Science 2007-08-15 Travis Gagie

A key principle in string processing is local consistency: using short contexts to handle matching fragments of a string consistently. String synchronizing sets [Kempa, Kociumaka; STOC 2019] are an influential instantiation of this…

Data Structures and Algorithms · Computer Science 2026-02-13 Jonas Ellert , Tomasz Kociumaka

We consider string matching with variable length gaps. Given a string $T$ and a pattern $P$ consisting of strings separated by variable length gaps (arbitrary strings of length in a specified range), the problem is to find all ending…

Data Structures and Algorithms · Computer Science 2011-10-14 Philip Bille , Inge Li Goertz , Hjalte Wedel Vildhøj , David Kofoed Wind

We consider the problem of decompressing the Lempel--Ziv 77 representation of a string $S$ of length $n$ using a working space as close as possible to the size $z$ of the input. The folklore solution for the problem runs in $O(n)$ time but…

Data Structures and Algorithms · Computer Science 2019-11-05 Philip Bille , Mikko Berggren Ettienne , Travis Gagie , Inge Li Gørtz , Nicola Prezza

Sentence Compression is the task of generating a shorter, yet grammatical version of a given sentence, preserving the essence of the original sentence. This paper proposes a Black-Box Optimizer for Compression (B-BOC): given a black-box…

Computation and Language · Computer Science 2021-01-26 Yotam Shichel , Meir Kalech , Oren Tsur

This paper is motivated by a conjecture that BPP can be characterized in terms of polynomial-time nonadaptive reductions to the set of Kolmogorov-random strings. In this paper we show that an approach laid out in [Allender et al] to settle…

Computational Complexity · Computer Science 2015-07-01 Eric Allender , Harry Buhrman , Luke Friedman , Bruno Loff