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We introduce the first index that can be built in $o(n)$ time for a text of length $n$, and can also be queried in $o(q)$ time for a pattern of length $q$. On an alphabet of size $\sigma$, our index uses $O(n\sqrt{\log n\log\sigma})$ bits,…

Data Structures and Algorithms · Computer Science 2019-07-16 J. Ian Munro , Gonzalo Navarro , Yakov Nekrich

Let $A$ be a static array storing $n$ elements from a totally ordered set. We present a data structure of optimal size at most $n\log_2(3+2\sqrt{2})+o(n)$ bits that allows us to answer the following queries on $A$ in constant time, without…

Data Structures and Algorithms · Computer Science 2011-02-03 Johannes Fischer

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

Matching statistics were introduced to solve the approximate string matching problem, which is a recurrent subroutine in bioinformatics applications. In 2010, Ohlebusch et al. [SPIRE 2010] proposed a time and space efficient algorithm for…

Data Structures and Algorithms · Computer Science 2023-01-16 Alessio Conte , Nicola Cotumaccio , Travis Gagie , Giovanni Manzini , Nicola Prezza , Marinella Sciortino

Re-Pair is an effective grammar-based compression scheme achieving strong compression rates in practice. Let $n$, $\sigma$, and $d$ be the text length, alphabet size, and dictionary size of the final grammar, respectively. In their original…

Data Structures and Algorithms · Computer Science 2016-11-07 Philip Bille , Inge Li Gørtz , Nicola Prezza

In this paper we study the number $r_{bwt}$ of equal-letter runs produced by the Burrows-Wheeler transform ($BWT$) when it is applied to purely morphic finite words, which are words generated by iterating prolongable morphisms. Such a…

Formal Languages and Automata Theory · Computer Science 2022-02-08 Andrea Frosini , Ilaria Mancini , Simone Rinaldi , Giuseppe Romana , Marinella Sciortino

The $r$-index (Gagie et al., JACM 2020) represented a breakthrough in compressed indexing of repetitive text collections, outperforming its alternatives by orders of magnitude. Its space usage, $\mathcal{O}(r)$ where $r$ is the number of…

Data Structures and Algorithms · Computer Science 2021-03-30 Dustin Cobas , Travis Gagie , Gonzalo Navarro

The rise of repetitive datasets has lately generated a lot of interest in compressed self-indexes based on dictionary compression, a rich and heterogeneous family that exploits text repetitions in different ways. For each such compression…

Data Structures and Algorithms · Computer Science 2020-12-17 Gonzalo Navarro , Nicola Prezza

We characterize those strings whose suffix arrays are based on arithmetic progressions, in particular, arithmetically progressed permutations where all pairs of successive entries of the permutation have the same difference modulo the…

Combinatorics · Mathematics 2021-07-07 Jacqueline W. Daykin , Dominik Köppl , David Kübel , Florian Stober

We consider the problem of finding, given two documents of total length $n$, a longest string occurring as a substring of both documents. This problem, known as the Longest Common Substring (LCS) problem, has a classic $O(n)$-time solution…

Data Structures and Algorithms · Computer Science 2020-04-29 Stav Ben-Nun , Shay Golan , Tomasz Kociumaka , Matan Kraus

This paper shows that a simple algorithm produces the {\em all-prefixes-LCSs-graph} in $O(mn)$ time for two input sequences of size $m$ and $n$. Given any prefix $p$ of the first input sequence and any prefix $q$ of the second input…

Data Structures and Algorithms · Computer Science 2011-03-09 Ronald I. Greenberg

Efficient optimal prefix coding has long been accomplished via the Huffman algorithm. However, there is still room for improvement and exploration regarding variants of the Huffman problem. Length-limited Huffman coding, useful for many…

Information Theory · Computer Science 2007-07-13 Michael B. Baer

In this paper we develop a theory describing how the extended Burrows-Wheeler Transform (eBWT) of a collection of DNA fragments tends to cluster together the copies of nucleotides sequenced from a genome G. Our theory accurately predicts…

Data Structures and Algorithms · Computer Science 2018-05-11 Nicola Prezza , Nadia Pisanti , Marinella Sciortino , Giovanna Rosone

Mauer et al. [A Lempel-Ziv-style Compression Method for Repetitive Texts, PSC 2017] proposed a hybrid text compression method called LZ-LFS which has both features of Lempel-Ziv 77 factorization and longest first substitution. They showed…

Data Structures and Algorithms · Computer Science 2018-06-14 Akihiro Nishi , Yuto Nakashima , Shunsuke Inenaga , Hideo Bannai , Masayuki Takeda

While short read aligners, which predominantly use the FM-index, are able to easily index one or a few human genomes, they do not scale well to indexing databases containing thousands of genomes. To understand why, it helps to examine the…

Data Structures and Algorithms · Computer Science 2018-11-19 Alan Kuhnle , Taher Mun , Christina Boucher , Travis Gagie , Ben Langmead , Giovanni Manzini

Let $\mathcal{D}$ be a collection of $D$ documents, which are strings over an alphabet of size $\sigma$, of total length $n$. We describe a data structure that uses linear space and and reports $k$ most relevant documents that contain a…

Data Structures and Algorithms · Computer Science 2013-08-02 Gonzalo Navarro , Yakov Nekrich

We show how to represent sets in a linear space data structure such that expressions involving unions and intersections of sets can be computed in a worst-case efficient way. This problem has applications in e.g. information retrieval and…

Data Structures and Algorithms · Computer Science 2007-08-27 Philip Bille , Anna Pagh , Rasmus Pagh

In this paper we describe algorithms for computing the BWT and for building (compressed) indexes in external memory. The innovative feature of our algorithms is that they are lightweight in the sense that, for an input of size $n$, they use…

Data Structures and Algorithms · Computer Science 2009-09-25 Paolo Ferragina , Travis Gagie , Giovanni Manzini

Canonical Huffman code is an optimal prefix-free compression code whose codewords enumerated in the lexicographical order form a list of binary words in non-decreasing lengths. Gagie et al. (2015) gave a representation of this coding…

Data Structures and Algorithms · Computer Science 2021-08-19 Szymon Grabowski , Dominik Köppl

In highly repetitive strings, like collections of genomes from the same species, distinct measures of repetition all grow sublinearly in the length of the text, and indexes targeted to such strings typically depend only on one of these…

Data Structures and Algorithms · Computer Science 2015-02-24 Djamal Belazzougui , Fabio Cunial , Travis Gagie , Nicola Prezza , Mathieu Raffinot