17 Search Results for "Manzini, Giovanni"

Document
DOI: 10.4230/LIPIcs.SEA.2024.1
Move-r: Optimizing the r-index

Authors: Nico Bertram, Johannes Fischer, and Lukas Nalbach

Published in: LIPIcs, Volume 301, 22nd International Symposium on Experimental Algorithms (SEA 2024)

Abstract
We present a static text index called Move-r, which is a highly optimized version of the r-index ([Travis Gagie et al., 2020] Gagie et al., 2020) that encorporates recent theoretical developments of the move data structure ([Takaaki Nishimoto and Yasuo Tabei, 2021] Nishimoto and Tabei, 2021). The r-index is the method of choice for indexing highly repetitive texts, such as different versions of a text document or DNA from the same species, as it exploits the compressibilty of the underlying data. With Move-r, we can answer count- and locate queries 2-35 (typically 15) times as fast as with any other r-index supporting locate queries while being 0.8-2.5 (typically 2) times as large. A Move-r index can be constructed 0.9-2 (typically 2) times as fast while using 1/3-1 (typically 1/2) times as much space.
Cite as

Nico Bertram, Johannes Fischer, and Lukas Nalbach. Move-r: Optimizing the r-index. In 22nd International Symposium on Experimental Algorithms (SEA 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 301, pp. 1:1-1:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{bertram_et_al:LIPIcs.SEA.2024.1,
  author =	{Bertram, Nico and Fischer, Johannes and Nalbach, Lukas},
  title =	{{Move-r: Optimizing the r-index}},
  booktitle =	{22nd International Symposium on Experimental Algorithms (SEA 2024)},
  pages =	{1:1--1:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-325-6},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{301},
  editor =	{Liberti, Leo},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SEA.2024.1},
  URN =		{urn:nbn:de:0030-drops-203662},
  doi =		{10.4230/LIPIcs.SEA.2024.1},
  annote =	{Keywords: Compressed Text Index, Burrows-Wheeler Transform}
}
Document
DOI: 10.4230/LIPIcs.SEA.2024.2
Engineering Zuffix Arrays

Authors: Paolo Boldi, Stefano Marchini, and Sebastiano Vigna

Published in: LIPIcs, Volume 301, 22nd International Symposium on Experimental Algorithms (SEA 2024)

Abstract
Searching patterns in long strings is a classical algorithmic problem with countless practical applications. Suffix trees and suffix arrays (and their variants) are a long-established solution that yields linear-time search (in the size of the pattern). In [Paolo Boldi and Sebastiano Vigna, 2018] it is shown that a z-map gadget can be attached to (enhanced) suffix arrays to improve their theoretical query time, obtaining a data structure called zuffix array. The main contribution of this paper is to show that a carefully engineered implementation of the z-map gadget does provide significant speedups with respect to enhanced suffix arrays on real-world datasets, albeit doubling the required space. In particular, for large alphabets we observe a sevenfold improvement in query time with respect to enhanced suffix arrays; even in the worst case (small alphabets), the query time is almost halved. Thus, zuffix arrays provide a very interesting new point in the space-time tradeoff spectrum.
Cite as

Paolo Boldi, Stefano Marchini, and Sebastiano Vigna. Engineering Zuffix Arrays. In 22nd International Symposium on Experimental Algorithms (SEA 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 301, pp. 2:1-2:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{boldi_et_al:LIPIcs.SEA.2024.2,
  author =	{Boldi, Paolo and Marchini, Stefano and Vigna, Sebastiano},
  title =	{{Engineering Zuffix Arrays}},
  booktitle =	{22nd International Symposium on Experimental Algorithms (SEA 2024)},
  pages =	{2:1--2:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-325-6},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{301},
  editor =	{Liberti, Leo},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SEA.2024.2},
  URN =		{urn:nbn:de:0030-drops-203677},
  doi =		{10.4230/LIPIcs.SEA.2024.2},
  annote =	{Keywords: Suffix trees, suffix arrays, z-fast tries}
}
Document
DOI: 10.4230/LIPIcs.SEA.2024.10
Taxonomic Classification with Maximal Exact Matches in KATKA Kernels and Minimizer Digests

Authors: Dominika Draesslerová, Omar Ahmed, Travis Gagie, Jan Holub, Ben Langmead, Giovanni Manzini, and Gonzalo Navarro

Published in: LIPIcs, Volume 301, 22nd International Symposium on Experimental Algorithms (SEA 2024)

Abstract
For taxonomic classification, we are asked to index the genomes in a phylogenetic tree such that later, given a DNA read, we can quickly choose a small subtree likely to contain the genome from which that read was drawn. Although popular classifiers such as Kraken use k-mers, recent research indicates that using maximal exact matches (MEMs) can lead to better classifications. For example, we can - build an augmented FM-index over the the genomes in the tree concatenated in left-to-right order; - for each MEM in a read, find the interval in the suffix array containing the starting positions of that MEM’s occurrences in those genomes; - find the minimum and maximum values stored in that interval; - take the lowest common ancestor (LCA) of the genomes containing the characters at those positions. This solution is practical, however, only when the total size of the genomes in the tree is fairly small. In this paper we consider applying the same solution to three lossily compressed representations of the genomes' concatenation: - a KATKA kernel, which discards characters that are not in the first or last occurrence of any k_max-tuple, for a parameter k_max; - a minimizer digest; - a KATKA kernel of a minimizer digest. With a test dataset and these three representations of it, simulated reads and various parameter settings, we checked how many reads' longest MEMs occurred only in the sequences from which those reads were generated ("true positive" reads). For some parameter settings we achieved significant compression while only slightly decreasing the true-positive rate.
Cite as

Dominika Draesslerová, Omar Ahmed, Travis Gagie, Jan Holub, Ben Langmead, Giovanni Manzini, and Gonzalo Navarro. Taxonomic Classification with Maximal Exact Matches in KATKA Kernels and Minimizer Digests. In 22nd International Symposium on Experimental Algorithms (SEA 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 301, pp. 10:1-10:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{draesslerova_et_al:LIPIcs.SEA.2024.10,
  author =	{Draesslerov\'{a}, Dominika and Ahmed, Omar and Gagie, Travis and Holub, Jan and Langmead, Ben and Manzini, Giovanni and Navarro, Gonzalo},
  title =	{{Taxonomic Classification with Maximal Exact Matches in KATKA Kernels and Minimizer Digests}},
  booktitle =	{22nd International Symposium on Experimental Algorithms (SEA 2024)},
  pages =	{10:1--10:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-325-6},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{301},
  editor =	{Liberti, Leo},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SEA.2024.10},
  URN =		{urn:nbn:de:0030-drops-203756},
  doi =		{10.4230/LIPIcs.SEA.2024.10},
  annote =	{Keywords: Taxonomic classification, metagenomics, KATKA, maximal exact matches, string kernels, minimizer digests}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2024.89
Breaking a Barrier in Constructing Compact Indexes for Parameterized Pattern Matching

Authors: Kento Iseri, Tomohiro I, Diptarama Hendrian, Dominik Köppl, Ryo Yoshinaka, and Ayumi Shinohara

Published in: LIPIcs, Volume 297, 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)

Abstract
A parameterized string (p-string) is a string over an alphabet (Σ_s ∪ Σ_p), where Σ_s and Σ_p are disjoint alphabets for static symbols (s-symbols) and for parameter symbols (p-symbols), respectively. Two p-strings x and y are said to parameterized match (p-match) if and only if x can be transformed into y by applying a bijection on Σ_p to every occurrence of p-symbols in x. The indexing problem for p-matching is to preprocess a p-string T of length n so that we can efficiently find the occurrences of substrings of T that p-match with a given pattern. Let σ_s and respectively σ_p be the numbers of distinct s-symbols and p-symbols that appear in T and σ = σ_s + σ_p. Extending the Burrows-Wheeler Transform (BWT) based index for exact string pattern matching, Ganguly et al. [SODA 2017] proposed parameterized BWTs (pBWTs) to design the first compact index for p-matching, and posed an open problem on how to construct the pBWT-based index in compact space, i.e., in O(n lg |Σ_s ∪ Σ_p|) bits of space. Hashimoto et al. [SPIRE 2022] showed how to construct the pBWT for T, under the assumption that Σ_s ∪ Σ_p = [0..O(σ)], in O(n lg σ) bits of space and O(n (σ_p lg n)/(lg lg n)) time in an online manner while reading the symbols of T from right to left. In this paper, we refine Hashimoto et al.’s algorithm to work in O(n lg σ) bits of space and O(n (lg σ_p lg n)/(lg lg n)) time in a more general assumption that Σ_s ∪ Σ_p = [0..n^{O(1)}]. Our result has an immediate application to constructing parameterized suffix arrays in O(n (lg σ_p lg n)/(lg lg n)) time and O(n lg σ) bits of working space. We also show that our data structure can support backward search, a core procedure of BWT-based indexes, at any stage of the online construction, making it the first compact index for p-matching that can be constructed in compact space and even in an online manner.
Cite as

Kento Iseri, Tomohiro I, Diptarama Hendrian, Dominik Köppl, Ryo Yoshinaka, and Ayumi Shinohara. Breaking a Barrier in Constructing Compact Indexes for Parameterized Pattern Matching. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 89:1-89:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{iseri_et_al:LIPIcs.ICALP.2024.89,
  author =	{Iseri, Kento and I, Tomohiro and Hendrian, Diptarama and K\"{o}ppl, Dominik and Yoshinaka, Ryo and Shinohara, Ayumi},
  title =	{{Breaking a Barrier in Constructing Compact Indexes for Parameterized Pattern Matching}},
  booktitle =	{51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)},
  pages =	{89:1--89:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-322-5},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{297},
  editor =	{Bringmann, Karl and Grohe, Martin and Puppis, Gabriele and Svensson, Ola},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2024.89},
  URN =		{urn:nbn:de:0030-drops-202324},
  doi =		{10.4230/LIPIcs.ICALP.2024.89},
  annote =	{Keywords: Index for parameterized pattern matching, Parameterized Burrows-Wheeler Transform, Online construction}
}
Document
DOI: 10.4230/LIPIcs.CPM.2024.1
Computing the LCP Array of a Labeled Graph

Authors: Jarno N. Alanko, Davide Cenzato, Nicola Cotumaccio, Sung-Hwan Kim, Giovanni Manzini, and Nicola Prezza

Published in: LIPIcs, Volume 296, 35th Annual Symposium on Combinatorial Pattern Matching (CPM 2024)

Abstract
The LCP array is an important tool in stringology, allowing to speed up pattern matching algorithms and enabling compact representations of the suffix tree. Recently, Conte et al. [DCC 2023] and Cotumaccio et al. [SPIRE 2023] extended the definition of this array to Wheeler DFAs and, ultimately, to arbitrary labeled graphs, proving that it can be used to efficiently solve matching statistics queries on the graph’s paths. In this paper, we provide the first efficient algorithm building the LCP array of a directed labeled graph with n nodes and m edges labeled over an alphabet of size σ. The first step is to transform the input graph G into a deterministic Wheeler pseudoforest G_{is} with O(n) edges encoding the lexicographically- smallest and largest strings entering in each node of the original graph. Using state-of-the-art algorithms, this step runs in O(min{mlog n, m+n²}) time on arbitrary labeled graphs, and in O(m) time on Wheeler DFAs. The LCP array of G stores the longest common prefixes between those strings, i.e. it can easily be derived from the LCP array of G_{is}. After arguing that the natural generalization of a compact-space LCP-construction algorithm by Beller et al. [J. Discrete Algorithms 2013] runs in time Ω(nσ) on pseudoforests, we present a new algorithm based on dynamic range stabbing building the LCP array of G_{is} in O(nlog σ) time and O(nlogσ) bits of working space. Combined with our reduction, we obtain the first efficient algorithm to build the LCP array of an arbitrary labeled graph. An implementation of our algorithm is publicly available at https://github.com/regindex/Labeled-Graph-LCP.
Cite as

Jarno N. Alanko, Davide Cenzato, Nicola Cotumaccio, Sung-Hwan Kim, Giovanni Manzini, and Nicola Prezza. Computing the LCP Array of a Labeled Graph. In 35th Annual Symposium on Combinatorial Pattern Matching (CPM 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 296, pp. 1:1-1:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{alanko_et_al:LIPIcs.CPM.2024.1,
  author =	{Alanko, Jarno N. and Cenzato, Davide and Cotumaccio, Nicola and Kim, Sung-Hwan and Manzini, Giovanni and Prezza, Nicola},
  title =	{{Computing the LCP Array of a Labeled Graph}},
  booktitle =	{35th Annual Symposium on Combinatorial Pattern Matching (CPM 2024)},
  pages =	{1:1--1:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-326-3},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{296},
  editor =	{Inenaga, Shunsuke and Puglisi, Simon J.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CPM.2024.1},
  URN =		{urn:nbn:de:0030-drops-201113},
  doi =		{10.4230/LIPIcs.CPM.2024.1},
  annote =	{Keywords: LCP array, Wheeler automata, prefix sorting, pattern matching, sorting}
}
Document
DOI: 10.4230/LIPIcs.CPM.2024.23
The Rational Construction of a Wheeler DFA

Authors: Giovanni Manzini, Alberto Policriti, Nicola Prezza, and Brian Riccardi

Published in: LIPIcs, Volume 296, 35th Annual Symposium on Combinatorial Pattern Matching (CPM 2024)

Abstract
Deterministic Finite Wheeler Automata are a natural generalisation to regular languages of the theory of compressed data structures originated by the introduction of the Burrows-Wheeler transform. Indeed, if we can find a Wheeler automaton recognizing a given language L, such automaton can be used to design time and space efficient algorithms for representing and searching L. In this paper we introduce an alternative representation of Deterministic Wheeler Automata by showing that a natural map between strings and rational numbers in ℚ [0,1) can be extended to represent the automaton’s states as intervals in ℚ [0,1). Using this representation it emerges a natural relationship between automata properties and some properties of real numbers. In addition, such representation enables us to formulate problems related to automata in a numerical setting. Although at the moment the numerical approach does not lead to time efficient algorithms, we believe this new perspective deserves further consideration. As a further demonstration of the convenience of this new representation, we use it to provide a simple proof of an unexpected result on regular languages. More precisely, we compare the size of the smallest Wheeler automaton recognizing a given language L with respect to the size of the smallest automaton, possibly non-Wheeler, recognizing the same language. We show settings in which there can be an exponential gap between the two sizes, and we discuss the implications of this result on the problem of representing regular languages.
Cite as

Giovanni Manzini, Alberto Policriti, Nicola Prezza, and Brian Riccardi. The Rational Construction of a Wheeler DFA. In 35th Annual Symposium on Combinatorial Pattern Matching (CPM 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 296, pp. 23:1-23:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{manzini_et_al:LIPIcs.CPM.2024.23,
  author =	{Manzini, Giovanni and Policriti, Alberto and Prezza, Nicola and Riccardi, Brian},
  title =	{{The Rational Construction of a Wheeler DFA}},
  booktitle =	{35th Annual Symposium on Combinatorial Pattern Matching (CPM 2024)},
  pages =	{23:1--23:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-326-3},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{296},
  editor =	{Inenaga, Shunsuke and Puglisi, Simon J.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CPM.2024.23},
  URN =		{urn:nbn:de:0030-drops-201336},
  doi =		{10.4230/LIPIcs.CPM.2024.23},
  annote =	{Keywords: String Matching, Deterministic Finite Automata, Wheeler languages, Graph Indexing, Co-lexicographical Sorting}
}
Document
Invited Talk
DOI: 10.4230/LIPIcs.CPM.2022.3
Compact Text Indexing for Advanced Pattern Matching Problems: Parameterized, Order-Isomorphic, 2D, etc. (Invited Talk)

Authors: Sharma V. Thankachan

Published in: LIPIcs, Volume 223, 33rd Annual Symposium on Combinatorial Pattern Matching (CPM 2022)

Abstract
In the past two decades, we have witnessed the design of various compact data structures for pattern matching over an indexed text [Navarro, 2016]. Popular indexes like the FM-index [Paolo Ferragina and Giovanni Manzini, 2005], compressed suffix arrays/trees [Roberto Grossi and Jeffrey Scott Vitter, 2005; Kunihiko Sadakane, 2007], the recent r-index [Travis Gagie et al., 2020; Takaaki Nishimoto and Yasuo Tabei, 2021], etc., capture the key functionalities of classic suffix arrays/trees [Udi Manber and Eugene W. Myers, 1993; Peter Weiner, 1973] in compact space. Mostly, they rely on the Burrows-Wheeler Transform (BWT) and its associated operations [Burrows and Wheeler, 1994]. However, compactly encoding some advanced suffix tree (ST) variants, like parameterized ST [Brenda S. Baker, 1993; S. Rao Kosaraju, 1995; Juan Mendivelso et al., 2020], order-isomorphic/preserving ST [Maxime Crochemore et al., 2016], two-dimensional ST [Raffaele Giancarlo, 1995; Dong Kyue Kim et al., 1998], etc. [Sung Gwan Park et al., 2019; Tetsuo Shibuya, 2000]- collectively known as suffix trees with missing suffix links [Richard Cole and Ramesh Hariharan, 2003], has been challenging. The previous techniques are not easily extendable because these variants do not hold some structural properties of the standard ST that enable compression. However, some limited progress has been made in these directions recently [Arnab Ganguly et al., 2017; Travis Gagie et al., 2017; Gianni Decaroli et al., 2017; Dhrumil Patel and Rahul Shah, 2021; Arnab Ganguly et al., 2021; Sung{-}Hwan Kim and Hwan{-}Gue Cho, 2021; Sung{-}Hwan Kim and Hwan{-}Gue Cho, 2021; Arnab Ganguly et al., 2017; Arnab Ganguly et al., 2022; Arnab Ganguly et al., 2021]. This talk will briefly survey them and highlight some interesting open problems.
Cite as

Sharma V. Thankachan. Compact Text Indexing for Advanced Pattern Matching Problems: Parameterized, Order-Isomorphic, 2D, etc. (Invited Talk). In 33rd Annual Symposium on Combinatorial Pattern Matching (CPM 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 223, pp. 3:1-3:3, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{thankachan:LIPIcs.CPM.2022.3,
  author =	{Thankachan, Sharma V.},
  title =	{{Compact Text Indexing for Advanced Pattern Matching Problems: Parameterized, Order-Isomorphic, 2D, etc.}},
  booktitle =	{33rd Annual Symposium on Combinatorial Pattern Matching (CPM 2022)},
  pages =	{3:1--3:3},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-234-1},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{223},
  editor =	{Bannai, Hideo and Holub, Jan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CPM.2022.3},
  URN =		{urn:nbn:de:0030-drops-161300},
  doi =		{10.4230/LIPIcs.CPM.2022.3},
  annote =	{Keywords: Text Indexing, Suffix Trees, String Matching}
}
Document
DOI: 10.4230/LIPIcs.ISAAC.2021.60
Inverse Suffix Array Queries for 2-Dimensional Pattern Matching in Near-Compact Space

Authors: Dhrumil Patel and Rahul Shah

Published in: LIPIcs, Volume 212, 32nd International Symposium on Algorithms and Computation (ISAAC 2021)

Abstract
In a 2-dimensional (2D) pattern matching problem, the text is arranged as a matrix 𝖬[1..n, 1..n] and consists of N = n × n symbols drawn from alphabet set Σ of size σ. The query consists of a m × m square matrix 𝖯[1..m, 1..m] drawn from the same alphabet set Σ and the task is to find all the locations in 𝖬 where 𝖯 appears as a (contiguous) submatrix. The patterns can be of any size, but as long as they are square in shape data structures like suffix trees and suffix array exist [Raffaele Giancarlo, 1995; Dong Kyue Kim et al., 1998] for the task of efficient pattern matching. These are essentially 2D counterparts of classic suffix trees and arrays known for traditional 1-dimensional (1D) pattern matching. They work based on linearization of 2D suffixes which would preserve the prefix match property (i.e., every pattern match is a prefix of some suffix). The main limitation of the suffix trees and the suffix arrays (in 1D) was their space utilization of O(N log N) bits, where N is the size of the text. This was suboptimal compared to Nlog σ bits of space, which is information theoretic optimal for the text. With the advent of the field of succinct/compressed data structures, it was possible to develop compressed variants of suffix trees and array based on Burrows-Wheeler Tansform and LF-mapping (or Φ function) [Roberto Grossi and Jeffrey Scott Vitter, 2005; Paolo Ferragina and Giovanni Manzini, 2005; Kunihiko Sadakane, 2007]. These data structures indeed achieve O(N log σ) bits of space or better. This gives rise to the question: analogous to 1D case, can we design a succinct or compressed index for 2D pattern matching? Can there be a 2D compressed suffix tree? Are there analogues of Burrows-Wheeler Transform or LF-mapping? The problem has been acknowledged for over a decade now and there have been a few attempts at applying Φ function [Ankur Gupta, 2004] and achieving entropy based compression [Veli Mäkinen and Gonzalo Navarro, 2008]. However, achieving the complexity breakthrough akin to 1D case has yet to be found. In this paper, we still do not know how to answer suffix array queries in O(N log σ) bits of space - which would have led to efficient pattern matching. However, for the first time, we show an interesting result that it is indeed possible to compute inverse suffix array (ISA) queries in near compact space in O(polylog n) time. Our 2D succinct text index design is based on two 1D compressed suffix trees and it takes O(N log log N + N logσ) bits of space which is much smaller than its naive design that takes O(N log N) bits. Although the main problem is still evasive, this index gives a hope on the existence of a full 2D succinct index with all functionalities similar to that of 1D case.
Cite as

Dhrumil Patel and Rahul Shah. Inverse Suffix Array Queries for 2-Dimensional Pattern Matching in Near-Compact Space. In 32nd International Symposium on Algorithms and Computation (ISAAC 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 212, pp. 60:1-60:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{patel_et_al:LIPIcs.ISAAC.2021.60,
  author =	{Patel, Dhrumil and Shah, Rahul},
  title =	{{Inverse Suffix Array Queries for 2-Dimensional Pattern Matching in Near-Compact Space}},
  booktitle =	{32nd International Symposium on Algorithms and Computation (ISAAC 2021)},
  pages =	{60:1--60:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-214-3},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{212},
  editor =	{Ahn, Hee-Kap and Sadakane, Kunihiko},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2021.60},
  URN =		{urn:nbn:de:0030-drops-154932},
  doi =		{10.4230/LIPIcs.ISAAC.2021.60},
  annote =	{Keywords: Pattern Matching, Succinct Data Structures}
}
Document
DOI: 10.4230/LIPIcs.ISAAC.2021.64
Repetition- and Linearity-Aware Rank/Select Dictionaries

Authors: Paolo Ferragina, Giovanni Manzini, and Giorgio Vinciguerra

Published in: LIPIcs, Volume 212, 32nd International Symposium on Algorithms and Computation (ISAAC 2021)

Abstract
We revisit the fundamental problem of compressing an integer dictionary that supports efficient rank and select operations by exploiting two kinds of regularities arising in real data: repetitiveness and approximate linearity. Our first contribution is a Lempel-Ziv parsing properly enriched to also capture approximate linearity in the data and still be compressed to the kth order entropy. Our second contribution is a variant of the block tree structure whose space complexity takes advantage of both repetitiveness and approximate linearity, and results highly competitive in time too. Our third and final contribution is an implementation and experimentation of this last data structure, which achieves new space-time trade-offs compared to known data structures that exploit only one of the two regularities.
Cite as

Paolo Ferragina, Giovanni Manzini, and Giorgio Vinciguerra. Repetition- and Linearity-Aware Rank/Select Dictionaries. In 32nd International Symposium on Algorithms and Computation (ISAAC 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 212, pp. 64:1-64:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{ferragina_et_al:LIPIcs.ISAAC.2021.64,
  author =	{Ferragina, Paolo and Manzini, Giovanni and Vinciguerra, Giorgio},
  title =	{{Repetition- and Linearity-Aware Rank/Select Dictionaries}},
  booktitle =	{32nd International Symposium on Algorithms and Computation (ISAAC 2021)},
  pages =	{64:1--64:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-214-3},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{212},
  editor =	{Ahn, Hee-Kap and Sadakane, Kunihiko},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2021.64},
  URN =		{urn:nbn:de:0030-drops-154974},
  doi =		{10.4230/LIPIcs.ISAAC.2021.64},
  annote =	{Keywords: Data compression, Compressed data structures, Entropy}
}
Document
DOI: 10.4230/LIPIcs.WABI.2021.13
Compressing and Indexing Aligned Readsets

Authors: Travis Gagie, Garance Gourdel, and Giovanni Manzini

Published in: LIPIcs, Volume 201, 21st International Workshop on Algorithms in Bioinformatics (WABI 2021)

Abstract
Compressed full-text indexes are one of the main success stories of bioinformatics data structures but even they struggle to handle some DNA readsets. This may seem surprising since, at least when dealing with short reads from the same individual, the readset will be highly repetitive and, thus, highly compressible. If we are not careful, however, this advantage can be more than offset by two disadvantages: first, since most base pairs are included in at least tens reads each, the uncompressed readset is likely to be at least an order of magnitude larger than the individual’s uncompressed genome; second, these indexes usually pay some space overhead for each string they store, and the total overhead can be substantial when dealing with millions of reads. The most successful compressed full-text indexes for readsets so far are based on the Extended Burrows-Wheeler Transform (EBWT) and use a sorting heuristic to try to reduce the space overhead per read, but they still treat the reads as separate strings and thus may not take full advantage of the readset’s structure. For example, if we have already assembled an individual’s genome from the readset, then we can usually use it to compress the readset well: e.g., we store the gap-coded list of reads' starting positions; we store the list of their lengths, which is often highly compressible; and we store information about the sequencing errors, which are rare with short reads. There is nowhere, however, where we can plug an assembled genome into the EBWT. In this paper we show how to use one or more assembled or partially assembled genome as the basis for a compressed full-text index of its readset. Specifically, we build a labelled tree by taking the assembled genome as a trunk and grafting onto it the reads that align to it, at the starting positions of their alignments. Next, we compute the eXtended Burrows-Wheeler Transform (XBWT) of the resulting labelled tree and build a compressed full-text index on that. Although this index can occasionally return false positives, it is usually much more compact than the alternatives. Following the established practice for datasets with many repetitions, we compare different full-text indices by looking at the number of runs in the transformed strings. For a human Chr19 readset our preliminary experiments show that eliminating separators characters from the EBWT reduces the number of runs by 19%, from 220 million to 178 million, and using the XBWT reduces it by a further 15%, to 150 million.
Cite as

Travis Gagie, Garance Gourdel, and Giovanni Manzini. Compressing and Indexing Aligned Readsets. In 21st International Workshop on Algorithms in Bioinformatics (WABI 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 201, pp. 13:1-13:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{gagie_et_al:LIPIcs.WABI.2021.13,
  author =	{Gagie, Travis and Gourdel, Garance and Manzini, Giovanni},
  title =	{{Compressing and Indexing Aligned Readsets}},
  booktitle =	{21st International Workshop on Algorithms in Bioinformatics (WABI 2021)},
  pages =	{13:1--13:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-200-6},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{201},
  editor =	{Carbone, Alessandra and El-Kebir, Mohammed},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.WABI.2021.13},
  URN =		{urn:nbn:de:0030-drops-143660},
  doi =		{10.4230/LIPIcs.WABI.2021.13},
  annote =	{Keywords: data compression, compact data structures, FM-index, Burrows-Wheeler Transform, EBWT, XBWT, DNA reads}
}
Document
DOI: 10.4230/DagRep.9.6.55
25 Years of the Burrows-Wheeler Transform (Dagstuhl Seminar 19241)

Authors: Travis Gagie, Giovanni Manzini, Gonzalo Navarro, and Jens Stoye

Published in: Dagstuhl Reports, Volume 9, Issue 6 (2020)

Abstract
Dagstuhl Seminar 19241 ("25 Years of the Burrows-Wheeler Transform") took place from June 10th to 14th, 2019, and was attended by 45 people from 13 countries and the three fields of Algorithms and Data Structures, Bioinformatics, and Combinatorics on Words. There were four talks and a panel session for each field. Feedback was generally positive and we are confident the seminar fostered interdisciplinary connections and will eventually result in noteworthy joint publications.
Cite as

Travis Gagie, Giovanni Manzini, Gonzalo Navarro, and Jens Stoye. 25 Years of the Burrows-Wheeler Transform (Dagstuhl Seminar 19241). In Dagstuhl Reports, Volume 9, Issue 6, pp. 55-68, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@Article{gagie_et_al:DagRep.9.6.55,
  author =	{Gagie, Travis and Manzini, Giovanni and Navarro, Gonzalo and Stoye, Jens},
  title =	{{25 Years of the Burrows-Wheeler Transform (Dagstuhl Seminar 19241)}},
  pages =	{55--68},
  journal =	{Dagstuhl Reports},
  ISSN =	{2192-5283},
  year =	{2019},
  volume =	{9},
  number =	{6},
  editor =	{Gagie, Travis and Manzini, Giovanni and Navarro, Gonzalo and Stoye, Jens},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagRep.9.6.55},
  URN =		{urn:nbn:de:0030-drops-114874},
  doi =		{10.4230/DagRep.9.6.55},
  annote =	{Keywords: Bioinformatics, Burrows-Wheeler Transform, Combinatorics on Words, Data Compression, Data Structures, Indexing, Sequence Alignment}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2019.68
Additive Cellular Automata Over Finite Abelian Groups: Topological and Measure Theoretic Properties

Authors: Alberto Dennunzio, Enrico Formenti, Darij Grinberg, and Luciano Margara

Published in: LIPIcs, Volume 138, 44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019)

Abstract
We study the dynamical behavior of D-dimensional (D >= 1) additive cellular automata where the alphabet is any finite abelian group. This class of discrete time dynamical systems is a generalization of the systems extensively studied by many authors among which one may list [Masanobu Ito et al., 1983; Giovanni Manzini and Luciano Margara, 1999; Giovanni Manzini and Luciano Margara, 1999; Jarkko Kari, 2000; Gianpiero Cattaneo et al., 2000; Gianpiero Cattaneo et al., 2004]. Our main contribution is the proof that topologically transitive additive cellular automata are ergodic. This result represents a solid bridge between the world of measure theory and that of topology theory and greatly extends previous results obtained in [Gianpiero Cattaneo et al., 2000; Giovanni Manzini and Luciano Margara, 1999] for linear CA over Z_m i.e. additive CA in which the alphabet is the cyclic group Z_m and the local rules are linear combinations with coefficients in Z_m. In our scenario, the alphabet is any finite abelian group and the global rule is any additive map. This class of CA strictly contains the class of linear CA over Z_m^n, i.e. , with the local rule defined by n x n matrices with elements in Z_m which, in turn, strictly contains the class of linear CA over Z_m. In order to further emphasize that finite abelian groups are more expressive than Z_m we prove that, contrary to what happens in Z_m, there exist additive CA over suitable finite abelian groups which are roots (with arbitrarily large indices) of the shift map. As a consequence of our results, we have that, for additive CA, ergodic mixing, weak ergodic mixing, ergodicity, topological mixing, weak topological mixing, topological total transitivity and topological transitivity are all equivalent properties. As a corollary, we have that invertible transitive additive CA are isomorphic to Bernoulli shifts. Finally, we provide a first characterization of strong transitivity for additive CA which we suspect it might be true also for the general case.
Cite as

Alberto Dennunzio, Enrico Formenti, Darij Grinberg, and Luciano Margara. Additive Cellular Automata Over Finite Abelian Groups: Topological and Measure Theoretic Properties. In 44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 138, pp. 68:1-68:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{dennunzio_et_al:LIPIcs.MFCS.2019.68,
  author =	{Dennunzio, Alberto and Formenti, Enrico and Grinberg, Darij and Margara, Luciano},
  title =	{{Additive Cellular Automata Over Finite Abelian Groups: Topological and Measure Theoretic Properties}},
  booktitle =	{44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019)},
  pages =	{68:1--68:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-117-7},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{138},
  editor =	{Rossmanith, Peter and Heggernes, Pinar and Katoen, Joost-Pieter},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2019.68},
  URN =		{urn:nbn:de:0030-drops-110126},
  doi =		{10.4230/LIPIcs.MFCS.2019.68},
  annote =	{Keywords: Cellular Automata, Symbolic Dynamics, Complex Systems}
}
Document
DOI: 10.4230/LIPIcs.CPM.2019.12
A New Class of Searchable and Provably Highly Compressible String Transformations

Authors: Raffaele Giancarlo, Giovanni Manzini, Giovanna Rosone, and Marinella Sciortino

Published in: LIPIcs, Volume 128, 30th Annual Symposium on Combinatorial Pattern Matching (CPM 2019)

Abstract
The Burrows-Wheeler Transform is a string transformation that plays a fundamental role for the design of self-indexing compressed data structures. Over the years, researchers have successfully extended this transformation outside the domains of strings. However, efforts to find non-trivial alternatives of the original, now 25 years old, Burrows-Wheeler string transformation have met limited success. In this paper we bring new lymph to this area by introducing a whole new family of transformations that have all the "myriad virtues" of the BWT: they can be computed and inverted in linear time, they produce provably highly compressible strings, and they support linear time pattern search directly on the transformed string. This new family is a special case of a more general class of transformations based on context adaptive alphabet orderings, a concept introduced here. This more general class includes also the Alternating BWT, another invertible string transforms recently introduced in connection with a generalization of Lyndon words.
Cite as

Raffaele Giancarlo, Giovanni Manzini, Giovanna Rosone, and Marinella Sciortino. A New Class of Searchable and Provably Highly Compressible String Transformations. In 30th Annual Symposium on Combinatorial Pattern Matching (CPM 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 128, pp. 12:1-12:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{giancarlo_et_al:LIPIcs.CPM.2019.12,
  author =	{Giancarlo, Raffaele and Manzini, Giovanni and Rosone, Giovanna and Sciortino, Marinella},
  title =	{{A New Class of Searchable and Provably Highly Compressible String Transformations}},
  booktitle =	{30th Annual Symposium on Combinatorial Pattern Matching (CPM 2019)},
  pages =	{12:1--12:12},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-103-0},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{128},
  editor =	{Pisanti, Nadia and P. Pissis, Solon},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CPM.2019.12},
  URN =		{urn:nbn:de:0030-drops-104833},
  doi =		{10.4230/LIPIcs.CPM.2019.12},
  annote =	{Keywords: Data Indexing and Compression, Burrows-Wheeler Transformation, Combinatorics on Words}
}
Document
DOI: 10.4230/LIPIcs.WABI.2018.2
Prefix-Free Parsing for Building Big BWTs

Authors: Christina Boucher, Travis Gagie, Alan Kuhnle, and Giovanni Manzini

Published in: LIPIcs, Volume 113, 18th International Workshop on Algorithms in Bioinformatics (WABI 2018)

Abstract
High-throughput sequencing technologies have led to explosive growth of genomic databases; one of which will soon reach hundreds of terabytes. For many applications we want to build and store indexes of these databases but constructing such indexes is a challenge. Fortunately, many of these genomic databases are highly-repetitive - a characteristic that can be exploited and enable the computation of the Burrows-Wheeler Transform (BWT), which underlies many popular indexes. In this paper, we introduce a preprocessing algorithm, referred to as prefix-free parsing, that takes a text T as input, and in one-pass generates a dictionary D and a parse P of T with the property that the BWT of T can be constructed from D and P using workspace proportional to their total size and O(|T|)-time. Our experiments show that D and P are significantly smaller than T in practice, and thus, can fit in a reasonable internal memory even when T is very large. Therefore, prefix-free parsing eases BWT construction, which is pertinent to many bioinformatics applications.
Cite as

Christina Boucher, Travis Gagie, Alan Kuhnle, and Giovanni Manzini. Prefix-Free Parsing for Building Big BWTs. In 18th International Workshop on Algorithms in Bioinformatics (WABI 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 113, pp. 2:1-2:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{boucher_et_al:LIPIcs.WABI.2018.2,
  author =	{Boucher, Christina and Gagie, Travis and Kuhnle, Alan and Manzini, Giovanni},
  title =	{{Prefix-Free Parsing for Building Big BWTs}},
  booktitle =	{18th International Workshop on Algorithms in Bioinformatics (WABI 2018)},
  pages =	{2:1--2:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-082-8},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{113},
  editor =	{Parida, Laxmi and Ukkonen, Esko},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.WABI.2018.2},
  URN =		{urn:nbn:de:0030-drops-93044},
  doi =		{10.4230/LIPIcs.WABI.2018.2},
  annote =	{Keywords: Burrows-Wheeler Transform, prefix-free parsing, compression-aware algorithms, genomic databases}
}
Document
DOI: 10.4230/LIPIcs.WABI.2018.10
External memory BWT and LCP computation for sequence collections with applications

Authors: Lavinia Egidi, Felipe A. Louza, Giovanni Manzini, and Guilherme P. Telles

Published in: LIPIcs, Volume 113, 18th International Workshop on Algorithms in Bioinformatics (WABI 2018)

Abstract
We propose an external memory algorithm for the computation of the BWT and LCP array for a collection of sequences. Our algorithm takes the amount of available memory as an input parameter, and tries to make the best use of it by splitting the input collection into subcollections sufficiently small that it can compute their BWT in RAM using an optimal linear time algorithm. Next, it merges the partial BWTs in external memory and in the process it also computes the LCP values. We show that our algorithm performs O(n maxlcp) sequential I/Os, where n is the total length of the collection and maxlcp is the maximum LCP value. The experimental results show that our algorithm outperforms the current best algorithm for collections of sequences with different lengths and when the average LCP of the collection is relatively small compared to the length of the sequences. In the second part of the paper, we show that our algorithm can be modified to output two additional arrays that, combined with the BWT and LCP arrays, provide simple, scan based, external memory algorithms for three well known problems in bioinformatics: the computation of the all pairs suffix-prefix overlaps, the computation of maximal repeats, and the construction of succinct de Bruijn graphs.
Cite as

Lavinia Egidi, Felipe A. Louza, Giovanni Manzini, and Guilherme P. Telles. External memory BWT and LCP computation for sequence collections with applications. In 18th International Workshop on Algorithms in Bioinformatics (WABI 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 113, pp. 10:1-10:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{egidi_et_al:LIPIcs.WABI.2018.10,
  author =	{Egidi, Lavinia and Louza, Felipe A. and Manzini, Giovanni and Telles, Guilherme P.},
  title =	{{External memory BWT and LCP computation for sequence collections with applications}},
  booktitle =	{18th International Workshop on Algorithms in Bioinformatics (WABI 2018)},
  pages =	{10:1--10:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-082-8},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{113},
  editor =	{Parida, Laxmi and Ukkonen, Esko},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.WABI.2018.10},
  URN =		{urn:nbn:de:0030-drops-93122},
  doi =		{10.4230/LIPIcs.WABI.2018.10},
  annote =	{Keywords: Burrows-Wheeler Transform, Longest Common Prefix Array, All pairs suffix-prefix overlaps, Succinct de Bruijn graph, Maximal repeats}
}
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