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The longest common prefix (LCP) array is a versatile auxiliary data structure in indexed string matching. It can be used to speed up searching using the suffix array (SA) and provides an implicit representation of the topology of an…

Data Structures and Algorithms · Computer Science 2016-03-09 German Tischler

The random access problem for compressed strings is to build a data structure that efficiently supports accessing the character in position $i$ of a string given in compressed form. Given a grammar of size $n$ compressing a string of size…

Data Structures and Algorithms · Computer Science 2015-01-27 Patrick Hagge Cording

In this paper we define a new problem, motivated by computational biology, $LCSk$ aiming at finding the maximal number of $k$ length $substrings$, matching in both input strings while preserving their order of appearance. The traditional…

Data Structures and Algorithms · Computer Science 2014-02-11 Gary Benson , Avivit Levy , Riva Shalom

A classical measure of string comparison is given by the longest common subsequence (LCS) problem on a pair of strings. We consider its generalisation, called the semi-local LCS problem, which arises naturally in many string-related…

Data Structures and Algorithms · Computer Science 2015-03-13 Alexander Tiskin

We consider the problem of indexing a string $t$ of length $n$ to report the occurrences of a query pattern $p$ containing $m$ characters and $j$ wildcards. Let $occ$ be the number of occurrences of $p$ in $t$, and $\sigma$ the size of the…

Data Structures and Algorithms · Computer Science 2012-09-07 Philip Bille , Inge Li Goertz , Hjalte Wedel Vildhøj , Søren Vind

A longest repeat query on a string, motivated by its applications in many subfields including computational biology, asks for the longest repetitive substring(s) covering a particular string position (point query). In this paper, we extend…

Data Structures and Algorithms · Computer Science 2015-11-10 Bojian Xu

In this paper, we consider a generalized longest common subsequence problem, in which a constraining sequence of length $s$ must be included as a substring and the other constraining sequence of length $t$ must be excluded as a subsequence…

Data Structures and Algorithms · Computer Science 2015-06-02 Daxin Zhu , Lei Wang , Yingjie Wu , Xiaodong Wang

We consider the Consensus Patterns problem, where, given a set of input strings, one is asked to extract a long-enough pattern which appears (with some errors) in all strings. We prove that this problem is W[1]-hard when parameterized by…

Computational Complexity · Computer Science 2017-02-28 Laurent Bulteau

For a partial word $w$ the longest common compatible prefix of two positions $i,j$, denoted $lccp(i,j)$, is the largest $k$ such that $w[i,i+k-1]\uparrow w[j,j+k-1]$, where $\uparrow$ is the compatibility relation of partial words (it is…

We consider the longest common subsequence problem in the context of subsequences with gap constraints. In particular, following Day et al. 2022, we consider the setting when the distance (i. e., the gap) between two consecutive symbols of…

Data Structures and Algorithms · Computer Science 2023-06-05 Duncan Adamson , Maria Kosche , Tore Koß , Florin Manea , Stefan Siemer

We consider the following problem: Given a set S of at most n elements from a universe of size m, represent it in memory as a bit string so that membership queries of the form "Is x in S?" can be answered by making at most t probes into the…

Data Structures and Algorithms · Computer Science 2022-01-03 Shyam Dhamapurkar , Shubham Vivek Pawar , Jaikumar Radhakrishnan

We develop a new technique for proving cell-probe lower bounds for static data structures. Previous lower bounds used a reduction to communication games, which was known not to be tight by counting arguments. We give the first lower bound…

Computational Complexity · Computer Science 2007-05-23 Mihai Patrascu , Mikkel Thorup

In binary jumbled pattern matching we wish to preprocess a binary string $S$ in order to answer queries $(i,j)$ which ask for a substring of $S$ that is of size $i$ and has exactly $j$ 1-bits. The problem naturally generalizes to…

Data Structures and Algorithms · Computer Science 2014-07-01 Danny Hermelin , Gad M. Landau , Yuri Rabinovich , Oren Weimann

Given a pattern $P$ and a text $T$, both strings over a binary alphabet, the binary jumbled string matching problem consists in telling whether any permutation of $P$ occurs in $T$. The indexed version of this problem, i.e., preprocessing a…

Data Structures and Algorithms · Computer Science 2013-05-09 Emanuele Giaquinta , Szymon Grabowski

We present a compressed representation of tries based on top tree compression [ICALP 2013] that works on a standard, comparison-based, pointer machine model of computation and supports efficient prefix search queries. Namely, we show how to…

Data Structures and Algorithms · Computer Science 2019-09-23 Philip Bille , Inge Li Gørtz , Paweł Gawrychowski , Gad M. Landau , Oren Weimann

Let $S$ be a string of length $n$ over an alphabet $\Sigma$ and let $Q$ be a subset of $\Sigma$ of size $q \geq 2$. The 'co-occurrence problem' is to construct a compact data structure that supports the following query: given an integer $w$…

Data Structures and Algorithms · Computer Science 2022-11-11 Philip Bille , Inge Li Gørtz , Tord Stordalen

Much research in stringology focuses on structures that can, in a way, ``grasp'' repeats (substrings that occur multiple times) as, for example, the so-called runs, a.k.a. maximal repetitions, compactly describe all tandem repeats. In this…

Data Structures and Algorithms · Computer Science 2024-10-02 Dmitry Kosolobov

The Shortest Superstring Problem (SSP) consists, for a set of strings S = {s_1,...,s_n}, to find a minimum length string that contains all s_i, 1 <= i <= k, as substrings. This problem is proved to be NP-Complete and APX-hard. Guaranteed…

Discrete Mathematics · Computer Science 2016-05-19 Tristan Braquelaire , Marie Gasparoux , Mathieu Raffinot , Raluca Uricaru

String consensus problems aim at finding a string that minimizes some given distance with respect to an input set of strings. In particular, in the Closest string problem, we are given a set of strings of equal length and a radius $d$. The…

Data Structures and Algorithms · Computer Science 2025-07-29 Estéban Gabory , Laurent Bulteau , Gabriele Fici , Hilde Verbeek

Let $X=(X_i)_{i\ge 1}$ and $Y=(Y_i)_{i\ge 1}$ be two sequences of independent and identically distributed (iid) random variables taking their values, uniformly, in a common totally ordered finite alphabet. Let LCI$_n$ be the length of the…

Probability · Mathematics 2018-08-27 Jean-Christophe Breton , Christian Houdré