25 Search Results for "Restivo, Antonio"

Document
DOI: 10.4230/LIPIcs.ESA.2025.60
Fast and Memory-Efficient BWT Construction of Repetitive Texts Using Lyndon Grammars

Authors: Jannik Olbrich

Published in: LIPIcs, Volume 351, 33rd Annual European Symposium on Algorithms (ESA 2025)

Abstract
The Burrows-Wheeler Transform (BWT) serves as the basis for many important sequence indexes. On very large datasets (e.g. genomic databases), classical BWT construction algorithms are often infeasible because they usually need to have the entire dataset in main memory. Fortunately, such large datasets are often highly repetitive. It can thus be beneficial to compute the BWT from a compressed representation. We propose an algorithm for computing the BWT via the Lyndon straight-line program, a grammar based on the standard factorization of Lyndon words. Our algorithm can also be used to compute the extended BWT (eBWT) of a multiset of sequences. We empirically evaluate our implementation and find that we can compute the BWT and eBWT of very large datasets faster and/or with less memory than competing methods.
Cite as

Jannik Olbrich. Fast and Memory-Efficient BWT Construction of Repetitive Texts Using Lyndon Grammars. In 33rd Annual European Symposium on Algorithms (ESA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 351, pp. 60:1-60:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{olbrich:LIPIcs.ESA.2025.60,
  author =	{Olbrich, Jannik},
  title =	{{Fast and Memory-Efficient BWT Construction of Repetitive Texts Using Lyndon Grammars}},
  booktitle =	{33rd Annual European Symposium on Algorithms (ESA 2025)},
  pages =	{60:1--60:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-395-9},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{351},
  editor =	{Benoit, Anne and Kaplan, Haim and Wild, Sebastian and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2025.60},
  URN =		{urn:nbn:de:0030-drops-245286},
  doi =		{10.4230/LIPIcs.ESA.2025.60},
  annote =	{Keywords: Burrows-Wheeler Transform, Grammar compression}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2025.48
Generalized De Bruijn Words, Invertible Necklaces, and the Burrows-Wheeler Transform

Authors: Gabriele Fici and Estéban Gabory

Published in: LIPIcs, Volume 345, 50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025)

Abstract
We define generalized de Bruijn words as those words having a Burrows-Wheeler transform that is a concatenation of permutations of the alphabet. We show that generalized de Bruijn words are in 1-to-1 correspondence with Hamiltonian cycles in the generalized de Bruijn graphs, introduced in the early '80s in the context of network design. When the size of the alphabet is a prime p, we define invertible necklaces as those whose BWT-matrix is non-singular. We show that invertible necklaces of length n correspond to normal bases of the finite field 𝔽_{pⁿ}, and that they form an Abelian group isomorphic to the Reutenauer group RG_pⁿ. Using known results in abstract algebra, we can make a bridge between generalized de Bruijn words and invertible necklaces. In particular, we highlight a correspondence between binary de Bruijn words of order d+1, binary necklaces of length 2^{d} having an odd number of 1’s, invertible BWT matrices of size 2^{d}× 2^{d}, and normal bases of the finite field 𝔽_{2^{2^{d}}}.
Cite as

Gabriele Fici and Estéban Gabory. Generalized De Bruijn Words, Invertible Necklaces, and the Burrows-Wheeler Transform. In 50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 345, pp. 48:1-48:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{fici_et_al:LIPIcs.MFCS.2025.48,
  author =	{Fici, Gabriele and Gabory, Est\'{e}ban},
  title =	{{Generalized De Bruijn Words, Invertible Necklaces, and the Burrows-Wheeler Transform}},
  booktitle =	{50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025)},
  pages =	{48:1--48:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-388-1},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{345},
  editor =	{Gawrychowski, Pawe{\l} and Mazowiecki, Filip and Skrzypczak, Micha{\l}},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2025.48},
  URN =		{urn:nbn:de:0030-drops-241555},
  doi =		{10.4230/LIPIcs.MFCS.2025.48},
  annote =	{Keywords: Burrows-Wheeler Transform, Generalized de Bruijn Word, Generalized de Bruijn Graph, Circulant Matrix, Invertible Necklace, Sandpile Group, Reutenauer Group}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2025.49
Morphisms and BWT-Run Sensitivity

Authors: Gabriele Fici, Giuseppe Romana, Marinella Sciortino, and Cristian Urbina

Published in: LIPIcs, Volume 345, 50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025)

Abstract
We study how the application of morphisms affects the number r of equal-letter runs in the Burrows–Wheeler Transform (BWT). This parameter has emerged as a key repetitiveness measure in compressed indexing. We focus on the notion of BWT-run sensitivity after application of morphisms. For binary alphabets, we characterize the class of injective morphisms that preserve the number of BWT-runs up to a bounded additive increase by showing that it coincides with the known class of primitivity-preserving morphisms, which are those that map primitive words to primitive words. We further prove that deciding whether a given binary morphism has bounded BWT-run sensitivity is possible in polynomial time with respect to the total length of the images of the two letters. Additionally, we explore new structural and combinatorial properties of synchronizing and recognizable morphisms. These results establish new connections between BWT-based compressibility, code theory, and symbolic dynamics.
Cite as

Gabriele Fici, Giuseppe Romana, Marinella Sciortino, and Cristian Urbina. Morphisms and BWT-Run Sensitivity. In 50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 345, pp. 49:1-49:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{fici_et_al:LIPIcs.MFCS.2025.49,
  author =	{Fici, Gabriele and Romana, Giuseppe and Sciortino, Marinella and Urbina, Cristian},
  title =	{{Morphisms and BWT-Run Sensitivity}},
  booktitle =	{50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025)},
  pages =	{49:1--49:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-388-1},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{345},
  editor =	{Gawrychowski, Pawe{\l} and Mazowiecki, Filip and Skrzypczak, Micha{\l}},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2025.49},
  URN =		{urn:nbn:de:0030-drops-241567},
  doi =		{10.4230/LIPIcs.MFCS.2025.49},
  annote =	{Keywords: Burrows-Wheeler transform, BWT-runs, morphism, pure code, repetitiveness}
}
Document
DOI: 10.4230/LIPIcs.CONCUR.2025.5
Characterizations of Fragments of Temporal Logic over Mazurkiewicz Traces

Authors: Bharat Adsul, Paul Gastin, and Shantanu Kulkarni

Published in: LIPIcs, Volume 348, 36th International Conference on Concurrency Theory (CONCUR 2025)

Abstract
We study fragments of temporal logics over Mazurkiewicz traces which are well known and established partial-order models of concurrent behaviours. We focus on concurrent versions of "strict past" and "strict future" modalities. Over words, the corresponding fragments have been shown to coincide with natural algebraic conditions on the recognizing monoids. We provide non-trivial generalizations of these classical results to traces. We exploit the local nature of the temporal modalities and obtain modular translations of specifications into asynchronous automata. More specifically, we provide novel characterizations of these fragments via local cascade products of a very simple two-state asynchronous automaton operating on a single process.
Cite as

Bharat Adsul, Paul Gastin, and Shantanu Kulkarni. Characterizations of Fragments of Temporal Logic over Mazurkiewicz Traces. In 36th International Conference on Concurrency Theory (CONCUR 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 348, pp. 5:1-5:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{adsul_et_al:LIPIcs.CONCUR.2025.5,
  author =	{Adsul, Bharat and Gastin, Paul and Kulkarni, Shantanu},
  title =	{{Characterizations of Fragments of Temporal Logic over Mazurkiewicz Traces}},
  booktitle =	{36th International Conference on Concurrency Theory (CONCUR 2025)},
  pages =	{5:1--5:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-389-8},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{348},
  editor =	{Bouyer, Patricia and van de Pol, Jaco},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CONCUR.2025.5},
  URN =		{urn:nbn:de:0030-drops-239551},
  doi =		{10.4230/LIPIcs.CONCUR.2025.5},
  annote =	{Keywords: Mazurkiewicz traces, temporal logics, asynchronous automata, cascade product, Green’s relations, algebraic automata theory}
}
Document
DOI: 10.4230/LIPIcs.WABI.2025.9
Dolphyin: A Combinatorial Algorithm for Identifying 1-Dollo Phylogenies in Cancer

Authors: Daniel W. Feng and Mohammed El-Kebir

Published in: LIPIcs, Volume 344, 25th International Conference on Algorithms for Bioinformatics (WABI 2025)

Abstract
Several recent cancer phylogeny inference methods have used the k-Dollo evolutionary model for single-nucleotide variants. Specifically, in this problem one is given an m × n binary matrix B and seeks a rooted tree T with m leaves that correspond to the m rows of B, and each node of T is labeled by a binary state for each of the n characters subject to the restriction that each character is gained at most once (0-to-1 transition) and subsequently lost at most k times (1-to-0 transitions). The 1-Dollo variant, also known as the persistent perfect phylogeny where one is restricted to at most k = 1 losses per character, has been studied extensively, but its hardness remains an open question. Here, we prove that the 1-Dollo Linear Phylogeny (1DLP) problem, where we additionally require the resulting 1-Dollo phylogeny T to be linear, is equivalent to verifying whether the input matrix B adheres to the Consecutive Ones Property (C1P), which can be solved in polynomial time. Due to the equivalence, several known NP-hardness results for relevant variants of C1P carry over to 1DLP, including the minimization of false negatives (0-to-1 modifications to the input matrix B) or the allowance of 2 gains and 2 losses. We furthermore show how we can recursively decompose any, not necessarily linear, 1-Dollo phylogeny T into several 1-Dollo linear phylogenies, connected by matching branching points. We extend this characterization to matrices B that admit 1-Dollo phylogenies, giving necessary and sufficient conditions for the existence of a novel decomposition of B into several submatrices and corresponding branching points. This decomposition forms the basis of Dolphyin, a new exponential-time algorithm for inferring 1-Dollo phylogenies that efficiently leverages the determination of linear 1-Dollo phylogenies as a subroutine. Dolphyin can also be applied to input matrices B with false negatives. We demonstrate that Dolphyin is runtime-competitive with a previous integer linear programming based algorithm SPhyR on simulated datasets. We additionally analyze simulated datasets with false negative errors and find that in the median case, Dolphyin infers 1-Dollo phylogenies with inferred error rates at or below the ground truth rate. Finally, we apply Dolphyin to 99 acute myeloid leukemia single-cell sequencing datasets, finding that the majority of the cancers can be explained by 1-Dollo phylogenies with false negative error rates in line with the used sequencing technology. Availability. Dolphyin is available at: https://github.com/elkebir-group/Dolphyin.
Cite as

Daniel W. Feng and Mohammed El-Kebir. Dolphyin: A Combinatorial Algorithm for Identifying 1-Dollo Phylogenies in Cancer. In 25th International Conference on Algorithms for Bioinformatics (WABI 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 344, pp. 9:1-9:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{feng_et_al:LIPIcs.WABI.2025.9,
  author =	{Feng, Daniel W. and El-Kebir, Mohammed},
  title =	{{Dolphyin: A Combinatorial Algorithm for Identifying 1-Dollo Phylogenies in Cancer}},
  booktitle =	{25th International Conference on Algorithms for Bioinformatics (WABI 2025)},
  pages =	{9:1--9:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-386-7},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{344},
  editor =	{Brejov\'{a}, Bro\v{n}a and Patro, Rob},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.WABI.2025.9},
  URN =		{urn:nbn:de:0030-drops-239356},
  doi =		{10.4230/LIPIcs.WABI.2025.9},
  annote =	{Keywords: Intra-tumor heterogeneity, persistent perfect phylogeny, consecutive ones property, combinatorics}
}
Document
Research
DOI: 10.4230/OASIcs.Grossi.14
Specific Patterns Against Reference Sequences

Authors: Marie-Pierre Béal and Maxime Crochemore

Published in: OASIcs, Volume 132, From Strings to Graphs, and Back Again: A Festschrift for Roberto Grossi's 60th Birthday (2025)

Abstract
We design alignment-free techniques for comparing a set of sequences or just a word, called a target, against another set of words, called a reference. This is done with the detection of factor patterns that distinguish the target from the reference. A target-specific factor of a target T against a reference R is then a factor w of a word in T that is not a factor of a word in R but whose proper factors of w are factors of a word in R. The strategy is based on the notion of minimal absent/forbidden words. We first address the computation of the set of target-specific factors of a target T against a reference R, where T and R are finite sets of sequences. The result is the construction of an automaton accepting the set of all considered target-specific factors. The construction algorithm runs in linear time according to the size of T ∪ R. The second result is the design of an algorithm to compute all the occurrences in a single sequence T of its target-specific factors against a reference R. The algorithm runs in real-time on the target sequence, independently of the number of occurrences of target-specific factors.
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Marie-Pierre Béal and Maxime Crochemore. Specific Patterns Against Reference Sequences. In From Strings to Graphs, and Back Again: A Festschrift for Roberto Grossi's 60th Birthday. Open Access Series in Informatics (OASIcs), Volume 132, pp. 14:1-14:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{beal_et_al:OASIcs.Grossi.14,
  author =	{B\'{e}al, Marie-Pierre and Crochemore, Maxime},
  title =	{{Specific Patterns Against Reference Sequences}},
  booktitle =	{From Strings to Graphs, and Back Again: A Festschrift for Roberto Grossi's 60th Birthday},
  pages =	{14:1--14:12},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-95977-391-1},
  ISSN =	{2190-6807},
  year =	{2025},
  volume =	{132},
  editor =	{Conte, Alessio and Marino, Andrea and Rosone, Giovanna and Vitter, Jeffrey Scott},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.Grossi.14},
  URN =		{urn:nbn:de:0030-drops-238130},
  doi =		{10.4230/OASIcs.Grossi.14},
  annote =	{Keywords: Specific pattern, Minimal absent word, Minimal forbidden word, Directed Acyclic Word Graph (DAWG), Suffix automaton}
}
Document
DOI: 10.4230/OASIcs.Manzini.3
BWT for String Collections

Authors: Davide Cenzato, Zsuzsanna Lipták, Nadia Pisanti, Giovanna Rosone, and Marinella Sciortino

Published in: OASIcs, Volume 131, The Expanding World of Compressed Data: A Festschrift for Giovanni Manzini's 60th Birthday (2025)

Abstract
We survey the different methods used for extending the BWT to collections of strings, following largely [Cenzato and Lipták, CPM 2022, Bioinformatics 2024]. We analyze the specific aspects and combinatorial properties of the resulting BWT variants and give a categorization of publicly available tools for computing the BWT of string collections. We show how the specific method used impacts on the resulting transform, including the number of runs, and on the dynamicity of the transform with respect to adding or removing strings from the collection. We then focus on the number of runs of these BWT variants and present the optimal BWT introduced in [Cenzato et al., DCC 2023], which implements an algorithm originally proposed by [Bentley et al., ESA 2020] to minimize the number of BWT-runs. We also discuss several recent heuristics and study their impact on the compression of biological sequences. We conclude with an overview of the applications and the impact of the BWT of string collections in bioinformatics.
Cite as

Davide Cenzato, Zsuzsanna Lipták, Nadia Pisanti, Giovanna Rosone, and Marinella Sciortino. BWT for String Collections. In The Expanding World of Compressed Data: A Festschrift for Giovanni Manzini's 60th Birthday. Open Access Series in Informatics (OASIcs), Volume 131, pp. 3:1-3:29, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{cenzato_et_al:OASIcs.Manzini.3,
  author =	{Cenzato, Davide and Lipt\'{a}k, Zsuzsanna and Pisanti, Nadia and Rosone, Giovanna and Sciortino, Marinella},
  title =	{{BWT for String Collections}},
  booktitle =	{The Expanding World of Compressed Data: A Festschrift for Giovanni Manzini's 60th Birthday},
  pages =	{3:1--3:29},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-95977-390-4},
  ISSN =	{2190-6807},
  year =	{2025},
  volume =	{131},
  editor =	{Ferragina, Paolo and Gagie, Travis and Navarro, Gonzalo},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.Manzini.3},
  URN =		{urn:nbn:de:0030-drops-239113},
  doi =		{10.4230/OASIcs.Manzini.3},
  annote =	{Keywords: Burrows-Wheeler transform, Extended Burrows-Wheeler transform, compressed text indexes, text compression, string collections, bioinformatics}
}
Document
DOI: 10.4230/OASIcs.Manzini.1
BWT and Combinatorics on Words

Authors: Gabriele Fici, Sabrina Mantaci, Antonio Restivo, Giuseppe Romana, Giovanna Rosone, and Marinella Sciortino

Published in: OASIcs, Volume 131, The Expanding World of Compressed Data: A Festschrift for Giovanni Manzini's 60th Birthday (2025)

Abstract
The Burrows-Wheeler Transform (BWT) is a reversible transformation on words (strings) introduced in 1994 in the context of data compression, which is a permutation of the characters in the word. Its clustering effect, i.e., the remarkable property of grouping identical characters (BWT runs) when they share common contexts, has made it a powerful tool for boosting compression performances and enabling efficient pattern searching in highly repetitive string collections. In this chapter, we analyze the Burrows-Wheeler transform under the combinatorial point of view, and we survey known properties and connections with different aspects of combinatorics on words. In particular, we focus on the properties of words in relation to the number of their BWT runs. The value r, which counts the number of BWT runs, impacts both compression performance and indexing efficiency, and is considered a measure to evaluate the above-mentioned clustering effect and, consequently, the repetitiveness of a word. We give an overview of the results relating r to other combinatorial repetitiveness measures related to the factor complexity. The chapter also explores extremal cases of the clustering effect. Finally, some results on the sensitivity of the measure r are considered, where the effects of combinatorial operations are studied, such as reversal, edits, and the application of morphisms.
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Gabriele Fici, Sabrina Mantaci, Antonio Restivo, Giuseppe Romana, Giovanna Rosone, and Marinella Sciortino. BWT and Combinatorics on Words. In The Expanding World of Compressed Data: A Festschrift for Giovanni Manzini's 60th Birthday. Open Access Series in Informatics (OASIcs), Volume 131, pp. 1:1-1:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{fici_et_al:OASIcs.Manzini.1,
  author =	{Fici, Gabriele and Mantaci, Sabrina and Restivo, Antonio and Romana, Giuseppe and Rosone, Giovanna and Sciortino, Marinella},
  title =	{{BWT and Combinatorics on Words}},
  booktitle =	{The Expanding World of Compressed Data: A Festschrift for Giovanni Manzini's 60th Birthday},
  pages =	{1:1--1:23},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-95977-390-4},
  ISSN =	{2190-6807},
  year =	{2025},
  volume =	{131},
  editor =	{Ferragina, Paolo and Gagie, Travis and Navarro, Gonzalo},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.Manzini.1},
  URN =		{urn:nbn:de:0030-drops-239090},
  doi =		{10.4230/OASIcs.Manzini.1},
  annote =	{Keywords: Burrows-Wheeler Transform, Combinatorics on Words, Clustering Effect, BWT Runs}
}
Document
DOI: 10.4230/OASIcs.Manzini.2
A Survey of the Bijective Burrows-Wheeler Transform

Authors: Hideo Bannai, Dominik Köppl, and Zsuzsanna Lipták

Published in: OASIcs, Volume 131, The Expanding World of Compressed Data: A Festschrift for Giovanni Manzini's 60th Birthday (2025)

Abstract
The Bijective BWT (BBWT), conceived by Scott in 2007, later summarized in a preprint by Gil and Scott in 2009 (arXiv 2012), is a variant of the Burrows-Wheeler Transform which is bijective: every string is the BBWT of some string. Indeed, the BBWT of a string is the extended BWT [Mantaci et al., 2007] of the factors of its Lyndon factorization. The BBWT has been receiving increasing interest in recent years. In this paper, we survey existing research on the BBWT, starting with its history and motivation. We then present algorithmic topics including construction algorithms with various complexities and an index on top of the BBWT for pattern matching. We subsequently address some properties of the BBWT as a compressor, discussing robustness to operations such as reversal, edits, rotation, as well as compression power. We close with listing other bijective variants of the BWT and open problems concerning the BBWT.
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Hideo Bannai, Dominik Köppl, and Zsuzsanna Lipták. A Survey of the Bijective Burrows-Wheeler Transform. In The Expanding World of Compressed Data: A Festschrift for Giovanni Manzini's 60th Birthday. Open Access Series in Informatics (OASIcs), Volume 131, pp. 2:1-2:26, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{bannai_et_al:OASIcs.Manzini.2,
  author =	{Bannai, Hideo and K\"{o}ppl, Dominik and Lipt\'{a}k, Zsuzsanna},
  title =	{{A Survey of the Bijective Burrows-Wheeler Transform}},
  booktitle =	{The Expanding World of Compressed Data: A Festschrift for Giovanni Manzini's 60th Birthday},
  pages =	{2:1--2:26},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-95977-390-4},
  ISSN =	{2190-6807},
  year =	{2025},
  volume =	{131},
  editor =	{Ferragina, Paolo and Gagie, Travis and Navarro, Gonzalo},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.Manzini.2},
  URN =		{urn:nbn:de:0030-drops-239100},
  doi =		{10.4230/OASIcs.Manzini.2},
  annote =	{Keywords: Burrows-Wheeler Transform, compression, text indexing, repetitiveness measure, Lyndon words, index construction algorithms, bijective string transformation}
}
Document
DOI: 10.4230/OASIcs.Manzini.5
FM-Adaptive: A Practical Data-Aware FM-Index

Authors: Hongwei Huo, Zongtao He, Pengfei Liu, and Jeffrey Scott Vitter

Published in: OASIcs, Volume 131, The Expanding World of Compressed Data: A Festschrift for Giovanni Manzini's 60th Birthday (2025)

Abstract
The FM-index provides an important solution for efficient retrieval and search in textual big data. Its variants have been widely used in many fields including information retrieval, genome analysis, and web searching. In this paper, we propose improvements via a new compressed representation of the wavelet tree of the Burrows-Wheeler transform of the input text, which incorporates the gap γ-encoding. Our theoretical analysis shows that the new index, called FM-Adaptive, achieves asymptotic space optimality within a factor of 2 in the leading term, but it has a better compression and faster retrieval in practice than the competitive optimal compression boosting used in previous FM-indexes. We present a practical improved locate algorithm that provides substantially faster locating time based upon memoization, which takes advantage of the overlapping subproblems property. We design the lookup table for accelerated decoding to support fast pattern matching in a text. Extensive experiments demonstrate that FM-Adaptive provides faster query performance, often by a considerable amount, and/or comparable or better compression than other state-of-the-art FM-index methods.
Cite as

Hongwei Huo, Zongtao He, Pengfei Liu, and Jeffrey Scott Vitter. FM-Adaptive: A Practical Data-Aware FM-Index. In The Expanding World of Compressed Data: A Festschrift for Giovanni Manzini's 60th Birthday. Open Access Series in Informatics (OASIcs), Volume 131, pp. 5:1-5:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{huo_et_al:OASIcs.Manzini.5,
  author =	{Huo, Hongwei and He, Zongtao and Liu, Pengfei and Vitter, Jeffrey Scott},
  title =	{{FM-Adaptive: A Practical Data-Aware FM-Index}},
  booktitle =	{The Expanding World of Compressed Data: A Festschrift for Giovanni Manzini's 60th Birthday},
  pages =	{5:1--5:23},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-95977-390-4},
  ISSN =	{2190-6807},
  year =	{2025},
  volume =	{131},
  editor =	{Ferragina, Paolo and Gagie, Travis and Navarro, Gonzalo},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.Manzini.5},
  URN =		{urn:nbn:de:0030-drops-239139},
  doi =		{10.4230/OASIcs.Manzini.5},
  annote =	{Keywords: Text indexing, Burrows-Wheeler transform, Compressed wavelet trees, Entropy-compressed, Compressed data structures}
}
Document
DOI: 10.4230/OASIcs.Manzini.11
Circular Dictionary Matching Using Extended BWT

Authors: Wing-Kai Hon, Rahul Shah, and Sharma V. Thankachan

Published in: OASIcs, Volume 131, The Expanding World of Compressed Data: A Festschrift for Giovanni Manzini's 60th Birthday (2025)

Abstract
The dictionary matching problem involves preprocessing a set of strings (patterns) into a data structure that efficiently identifies all occurrences of these patterns within a query string (text). In this work, we investigate a variation of this problem, termed circular dictionary matching, where the patterns are circular, meaning their cyclic shifts are also considered valid patterns. Such patterns naturally occur in areas such as bioinformatics and computational geometry. Based on the extended Burrows-Wheeler Transformation (eBWT), we design a space-efficient solution for this problem. Specifically, we show that a dictionary of d circular patterns of total length n can be indexed in nlog σ + O(n+dlog n+σ log n) bits of space and support circular dictionary matching on a query text T in O((|T|+occ)log n) time, where σ represents the size of the underlying alphabet and occ represents the output size.
Cite as

Wing-Kai Hon, Rahul Shah, and Sharma V. Thankachan. Circular Dictionary Matching Using Extended BWT. In The Expanding World of Compressed Data: A Festschrift for Giovanni Manzini's 60th Birthday. Open Access Series in Informatics (OASIcs), Volume 131, pp. 11:1-11:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{hon_et_al:OASIcs.Manzini.11,
  author =	{Hon, Wing-Kai and Shah, Rahul and Thankachan, Sharma V.},
  title =	{{Circular Dictionary Matching Using Extended BWT}},
  booktitle =	{The Expanding World of Compressed Data: A Festschrift for Giovanni Manzini's 60th Birthday},
  pages =	{11:1--11:14},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-95977-390-4},
  ISSN =	{2190-6807},
  year =	{2025},
  volume =	{131},
  editor =	{Ferragina, Paolo and Gagie, Travis and Navarro, Gonzalo},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.Manzini.11},
  URN =		{urn:nbn:de:0030-drops-239195},
  doi =		{10.4230/OASIcs.Manzini.11},
  annote =	{Keywords: String algorithms, Burrows-Wheeler transformation, suffix trees, succinct data structures}
}
Document
DOI: 10.4230/OASIcs.Manzini.7
Algorithms for Computing Very Large BWTs: a Short Survey

Authors: Diego Díaz-Domínguez, Lavinia Egidi, Veronica Guerrini, Felipe A. Louza, and Giovanna Rosone

Published in: OASIcs, Volume 131, The Expanding World of Compressed Data: A Festschrift for Giovanni Manzini's 60th Birthday (2025)

Abstract
The Burrows-Wheeler Transform (BWT) is a fundamental string transformation that, although initially introduced for data compression, has been extensively utilized across various domains, including text indexing and pattern matching within large datasets. Although the BWT construction is linear, the constants make the task impractical for large datasets, and as highlighted by Ferragina et al. [Paolo Ferragina et al., 2012], "to use it, one must first build it!". Thus, the construction of the BWT remains a significant challenge. For these reasons, during the past three decades there has been a succession of new algorithms for its construction using techniques that work in external memory or that use text compression. In this survey, we revise some of the most important advancements and tools presented in the past years for computing large BWTs exploiting external memory or text compression approaches without using additional information about the data.
Cite as

Diego Díaz-Domínguez, Lavinia Egidi, Veronica Guerrini, Felipe A. Louza, and Giovanna Rosone. Algorithms for Computing Very Large BWTs: a Short Survey. In The Expanding World of Compressed Data: A Festschrift for Giovanni Manzini's 60th Birthday. Open Access Series in Informatics (OASIcs), Volume 131, pp. 7:1-7:28, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{diazdominguez_et_al:OASIcs.Manzini.7,
  author =	{D{\'\i}az-Dom{\'\i}nguez, Diego and Egidi, Lavinia and Guerrini, Veronica and Louza, Felipe A. and Rosone, Giovanna},
  title =	{{Algorithms for Computing Very Large BWTs: a Short Survey}},
  booktitle =	{The Expanding World of Compressed Data: A Festschrift for Giovanni Manzini's 60th Birthday},
  pages =	{7:1--7:28},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-95977-390-4},
  ISSN =	{2190-6807},
  year =	{2025},
  volume =	{131},
  editor =	{Ferragina, Paolo and Gagie, Travis and Navarro, Gonzalo},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.Manzini.7},
  URN =		{urn:nbn:de:0030-drops-239151},
  doi =		{10.4230/OASIcs.Manzini.7},
  annote =	{Keywords: Burrows-Wheeler transform, Extended Burrows-Wheeler transform, external memory, text compression, longest common prefix}
}
Document
DOI: 10.4230/OASIcs.Manzini.12
Wheeler Graphs and Wheeler Languages

Authors: Nicola Cotumaccio, Giovanna D'Agostino, Daniel Gibney, Alberto Policriti, Nicola Prezza, and Sharma V. Thankachan

Published in: OASIcs, Volume 131, The Expanding World of Compressed Data: A Festschrift for Giovanni Manzini's 60th Birthday (2025)

Abstract
Suffix sorting stands at the core of the most efficient solutions for indexed pattern matching: the suffix tree, the suffix array, compressed indexes based on the Burrows-Wheeler transform, and so on. In [Gagie, Manzini, Sirén, TCS 2017] this concept was extended to labeled graphs, obtaining the rich class of Wheeler graphs. This work opened a very fruitful line of research, ultimately generating results able to bridge the fields of compressed data structures, graph theory, and regular language theory. In a Wheeler graph, nodes are sorted according to the alphabetic order of their incoming labels, propagating this order through pairs of equally-labeled edges. This apparently-simple definition makes it possible to solve on Wheeler graphs problems (including, but not limited to: compression, subpath queries, NFA equivalence, determinization, minimization) that on general labeled graphs are extremely hard to solve, and induces a rich structure in the class of regular languages (Wheeler languages) recognized by automata whose state transition is a Wheeler graph. The goal of this survey is to provide a summary of (and intuitions behind) the results on Wheeler graphs that appeared in the literature since their introduction, in addition to a discussion of interesting problems that are still open in the field.
Cite as

Nicola Cotumaccio, Giovanna D'Agostino, Daniel Gibney, Alberto Policriti, Nicola Prezza, and Sharma V. Thankachan. Wheeler Graphs and Wheeler Languages. In The Expanding World of Compressed Data: A Festschrift for Giovanni Manzini's 60th Birthday. Open Access Series in Informatics (OASIcs), Volume 131, pp. 12:1-12:28, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{cotumaccio_et_al:OASIcs.Manzini.12,
  author =	{Cotumaccio, Nicola and D'Agostino, Giovanna and Gibney, Daniel and Policriti, Alberto and Prezza, Nicola and Thankachan, Sharma V.},
  title =	{{Wheeler Graphs and Wheeler Languages}},
  booktitle =	{The Expanding World of Compressed Data: A Festschrift for Giovanni Manzini's 60th Birthday},
  pages =	{12:1--12:28},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-95977-390-4},
  ISSN =	{2190-6807},
  year =	{2025},
  volume =	{131},
  editor =	{Ferragina, Paolo and Gagie, Travis and Navarro, Gonzalo},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.Manzini.12},
  URN =		{urn:nbn:de:0030-drops-239205},
  doi =		{10.4230/OASIcs.Manzini.12},
  annote =	{Keywords: Wheeler languages, Wheeler graphs, pattern matching, indexing, compressed data structures}
}
Document
DOI: 10.4230/OASIcs.Manzini.14
BWT Indexes for Optimal Joins in Graph Databases

Authors: Diego Arroyuelo and Gonzalo Navarro

Published in: OASIcs, Volume 131, The Expanding World of Compressed Data: A Festschrift for Giovanni Manzini's 60th Birthday (2025)

Abstract
Graph databases represent data as a labeled directed graph, where the labels refer to properties that connect the entities represented by their source and target vertices. Queries feature, most prominently, sets of edges where source, target, and/or label can be variables; each instantiation of the variables where all the edges occur in the graph is a solution to the query. Worst-case-optimal algorithms to solve those queries have been devised, but they pose significant space requirements. This overhead has hindered the adoption of worst-case-optimal algorithms in real systems. We show that a representation of the graph based on the extended BWT (eBWT), where each edge is seen as an independent string of length 3 (source, label, target) supports worst-case-optimal algorithms while using almost no extra space on top of the raw data. We then show how the idea is generalized to the relational model, where the strings can be longer than 3 and several eBWTs are needed to obtain worst-case optimality. The aim to minimize the amount of space in that case leads to consider novel eBWT variants, where columns other than the last can be chosen. Finally, we show how the same graph representation can be used to solve other typical queries, like finding graph paths that match regular expressions.
Cite as

Diego Arroyuelo and Gonzalo Navarro. BWT Indexes for Optimal Joins in Graph Databases. In The Expanding World of Compressed Data: A Festschrift for Giovanni Manzini's 60th Birthday. Open Access Series in Informatics (OASIcs), Volume 131, pp. 14:1-14:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{arroyuelo_et_al:OASIcs.Manzini.14,
  author =	{Arroyuelo, Diego and Navarro, Gonzalo},
  title =	{{BWT Indexes for Optimal Joins in Graph Databases}},
  booktitle =	{The Expanding World of Compressed Data: A Festschrift for Giovanni Manzini's 60th Birthday},
  pages =	{14:1--14:19},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-95977-390-4},
  ISSN =	{2190-6807},
  year =	{2025},
  volume =	{131},
  editor =	{Ferragina, Paolo and Gagie, Travis and Navarro, Gonzalo},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.Manzini.14},
  URN =		{urn:nbn:de:0030-drops-239222},
  doi =		{10.4230/OASIcs.Manzini.14},
  annote =	{Keywords: Graph databases, Ring index, extended BWT, compact data structures}
}
Document
DOI: 10.4230/LIPIcs.SEA.2025.13
Pangenome Graph Indexing via the Multidollar-BWT

Authors: Davide Cozzi, Brian Riccardi, Luca Denti, Simone Ciccolella, Kunihiko Sadakane, and Paola Bonizzoni

Published in: LIPIcs, Volume 338, 23rd International Symposium on Experimental Algorithms (SEA 2025)

Abstract
Indexing pangenome graphs is a major algorithmic challenge in computational pangenomics, a recent and active research field that seeks to use graphs as representations of multiple genomes. Since these graphs are constructed from whole genome sequences of a species population, they can become very large, making indexing one of the most challenging problems. In this paper, we propose gindex, a novel indexing approach to solve the Graph Pattern Matching Problem based on the multidollar-BWT. Specifically, gindex aims to find all occurrences of a pattern in a sequence-labeled graph by overcoming two main limitations of GCSA2, one of the most widely used graph indexes: handling queries of arbitrary length and scaling to large graphs without pruning any complex regions. Moreover, we show how a smart preprocessing step can optimize the use of multidollar-BWT to skip small redundant sub-patterns and enhance gindex’s querying capabilities. We demonstrate the effectiveness of our approach by comparing it to GCSA2 in terms of index construction and query time, using different preprocessing modes on three pangenome graphs: one built from Drosophila genomes and two produced by the Human Pangenome Reference Consortium. The results show that gindex can scale on human pangenome graphs - which GCSA2 cannot index using large amounts of RAM - with acceptable memory and time requirements. Moreover, gindex achieves fast query times, although not as fast as GCSA2, which may produce false positives.
Cite as

Davide Cozzi, Brian Riccardi, Luca Denti, Simone Ciccolella, Kunihiko Sadakane, and Paola Bonizzoni. Pangenome Graph Indexing via the Multidollar-BWT. In 23rd International Symposium on Experimental Algorithms (SEA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 338, pp. 13:1-13:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{cozzi_et_al:LIPIcs.SEA.2025.13,
  author =	{Cozzi, Davide and Riccardi, Brian and Denti, Luca and Ciccolella, Simone and Sadakane, Kunihiko and Bonizzoni, Paola},
  title =	{{Pangenome Graph Indexing via the Multidollar-BWT}},
  booktitle =	{23rd International Symposium on Experimental Algorithms (SEA 2025)},
  pages =	{13:1--13:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-375-1},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{338},
  editor =	{Mutzel, Petra and Prezza, Nicola},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SEA.2025.13},
  URN =		{urn:nbn:de:0030-drops-232515},
  doi =		{10.4230/LIPIcs.SEA.2025.13},
  annote =	{Keywords: Multidollar-BWT, Graph Index, Graph Pattern Matching, Pangenome Graph}
}
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