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We raise the question of approximating the compressibility of a string with respect to a fixed compression scheme, in sublinear time. We study this question in detail for two popular lossless compression schemes: run-length encoding (RLE)…

Data Structures and Algorithms · Computer Science 2007-06-11 Sofya Raskhodnikova , Dana Ron , Ronitt Rubinfeld , Adam Smith

Motivated by mass-spectrometry protein sequencing, we consider a simply-stated problem of reconstructing a string from the multiset of its substring compositions. We show that all strings of length 7, one less than a prime, or one less than…

Discrete Mathematics · Computer Science 2014-03-12 Jayadev Acharya , Hirakendu Das , Olgica Milenkovic , Alon Orlitsky , Shengjun Pan

Described are two algorithms to find long approximate palindromes in a string, for example a DNA sequence. A simple algorithm requires O(n)-space and almost always runs in $O(k.n)$-time where n is the length of the string and k is the…

Data Structures and Algorithms · Computer Science 2007-05-23 L. Allison

A $\lambda$-cover of a string $S$ is a set of strings $\{C_i\}_1^\lambda$ such that every index in $S$ is contained in an occurrence of at least one string $C_i$. The existence of a $1$-cover defines a well-known class of quasi-periodic…

Data Structures and Algorithms · Computer Science 2024-05-21 Itai Boneh , Shay Golan , Arseny Shur

A popular approach to sentence compression is to formulate the task as a constrained optimization problem and solve it with integer linear programming (ILP) tools. Unfortunately, dependence on ILP may make the compressor prohibitively slow,…

Computation and Language · Computer Science 2015-10-29 Katja Filippova , Enrique Alfonseca

Consider an input text string T[1,N] drawn from an unbounded alphabet. We study partial computation in suffix-based problems for Data Compression and Text Indexing such as (I) retrieve any segment of K<=N consecutive symbols from the…

Data Structures and Algorithms · Computer Science 2011-10-18 Gianni Franceschini , Roberto Grossi , S. Muthukrishnan

Given a string $T$ of length $n$ over an alphabet $\Sigma\subset \{1,2,\ldots,n^{O(1)}\}$ of size $\sigma$, we are to preprocess $T$ so that given a range $[i,j]$, we can return a representation of a shortest string over $\Sigma$ that is…

Data Structures and Algorithms · Computer Science 2021-06-04 Golnaz Badkobeh , Panagiotis Charalampopoulos , Dmitry Kosolobov , Solon P. Pissis

Shannon's entropy is a definitive lower bound for statistical compression. Unfortunately, no such clear measure exists for the compressibility of repetitive strings. Thus, ad hoc measures are employed to estimate the repetitiveness of…

Data Structures and Algorithms · Computer Science 2023-11-16 Giulia Bernardini , Gabriele Fici , Paweł Gawrychowski , Solon P. Pissis

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…

Data Structures and Algorithms · Computer Science 2016-09-01 Shouhei Fukunaga , Yoshimasa Takabatake , I Tomohiro , Hiroshi Sakamoto

Cadences are structurally maximal arithmetic progressions of indices corresponding to equal characters in an underlying string. This paper provides a polynomial time detection algorithm for 3-cadences in grammar-compressed binary strings.…

Data Structures and Algorithms · Computer Science 2020-08-14 Julian Pape-Lange

Many researchers in artificial intelligence are beginning to explore the use of soft constraints to express a set of (possibly conflicting) problem requirements. A soft constraint is a function defined on a collection of variables which…

Artificial Intelligence · Computer Science 2011-07-04 D. Cohen , M. Cooper , P. Jeavons , A. Krokhin

We study the problem of minimizing a multivariate polynomial function over the unit hypercube. By representing the polynomial through a hypergraph and exploiting its sparsity structure, we establish a new sufficient condition under which…

Optimization and Control · Mathematics 2026-04-29 Aida Khajavirad

Sequence representations supporting queries $access$, $select$ and $rank$ are at the core of many data structures. There is a considerable gap between the various upper bounds and the few lower bounds known for such representations, and how…

Data Structures and Algorithms · Computer Science 2013-08-26 Djamal Belazzougui , Gonzalo Navarro

We consider the problem of computing a shortest solid cover of an indeterminate string. An indeterminate string may contain non-solid symbols, each of which specifies a subset of the alphabet that could be present at the corresponding…

Data Structures and Algorithms · Computer Science 2014-12-12 Maxime Crochemore , Costas S. Iliopoulos , Tomasz Kociumaka , Jakub Radoszewski , Wojciech Rytter , Tomasz Waleń

Let $\D = $$ \{d_1,d_2,...d_D\}$ be a given set of $D$ string documents of total length $n$, our task is to index $\D$, such that the $k$ most relevant documents for an online query pattern $P$ of length $p$ can be retrieved efficiently. We…

Data Structures and Algorithms · Computer Science 2012-04-03 Wing-Kai Hon , Rahul Shah , Sharma V. Thankachan

The problem of dictionary matching is a classical problem in string matching: given a set S of d strings of total length n characters over an (not necessarily constant) alphabet of size sigma, build a data structure so that we can match in…

Data Structures and Algorithms · Computer Science 2015-05-18 Djamal Belazzougui

We extend the concept of polynomial time approximation algorithms to apply to problems for hierarchically specified graphs, many of which are PSPACE-complete. Assuming P != PSPACE, the existence or nonexistence of such efficient…

Combinatorics · Mathematics 2016-09-06 Madhav V. Marathe , Harry B. Hunt , S. S. Ravi

Satisfiability of word equations is an important problem in the intersection of formal languages and algebra: Given two sequences consisting of letters and variables we are to decide whether there is a substitution for the variables that…

Formal Languages and Automata Theory · Computer Science 2020-10-19 Artur Jeż

Given an array A containing arbitrary (positive and negative) numbers, we consider the problem of supporting range maximum-sum segment queries on A: i.e., given an arbitrary range [i,j], return the subrange [i' ,j' ] \subseteq [i,j] such…

Data Structures and Algorithms · Computer Science 2015-06-12 Pawel Gawrychowski , Patrick K. Nicholson

Word Break is a prototypical factorization problem in string processing: Given a word $w$ of length $N$ and a dictionary $\mathcal{D} = \{d_1, d_2, \ldots, d_{K}\}$ of $K$ strings, determine whether we can partition $w$ into words from…

Data Structures and Algorithms · Computer Science 2025-06-19 Rajat De , Dominik Kempa