Volume
OASIcs, Volume 131
The Expanding World of Compressed Data: A Festschrift for Giovanni Manzini's 60th Birthday
-
Part of:
Series:
Open Access Series in Informatics (OASIcs)
Conference: Giovanni Manzini's Festschrift
Event
Manzini's Festschrift, July 25, 2025, Venice, ItalyEditors
Publication Details
- published at: 2025-08-08
- Publisher: Schloss Dagstuhl – Leibniz-Zentrum für Informatik
- ISBN: 978-3-95977-390-4
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Document
Complete Volume
OASIcs, Volume 131, Manzini's Festschrift, Complete Volume
Abstract
OASIcs, Volume 131, Manzini's Festschrift, Complete Volume
Cite as
The Expanding World of Compressed Data: A Festschrift for Giovanni Manzini's 60th Birthday. Open Access Series in Informatics (OASIcs), Volume 131, pp. 1-324, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
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@Proceedings{ferragina_et_al:OASIcs.Manzini,
title = {{OASIcs, Volume 131, Manzini's Festschrift, Complete Volume}},
booktitle = {The Expanding World of Compressed Data: A Festschrift for Giovanni Manzini's 60th Birthday},
pages = {1--324},
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},
URN = {urn:nbn:de:0030-drops-243407},
doi = {10.4230/OASIcs.Manzini},
annote = {Keywords: OASIcs, Volume 131, Manzini's Festschrift, Complete Volume}
}
Document
Front Matter
Front Matter, Table of Contents, Preface, Conference Organization
Abstract
Front Matter, Table of Contents, Preface, Conference Organization
Cite as
The Expanding World of Compressed Data: A Festschrift for Giovanni Manzini's 60th Birthday. Open Access Series in Informatics (OASIcs), Volume 131, pp. 0:i-0:xvi, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
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@InProceedings{ferragina_et_al:OASIcs.Manzini.0,
author = {Ferragina, Paolo and Gagie, Travis and Navarro, Gonzalo},
title = {{Front Matter, Table of Contents, Preface, Conference Organization}},
booktitle = {The Expanding World of Compressed Data: A Festschrift for Giovanni Manzini's 60th Birthday},
pages = {0:i--0:xvi},
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.0},
URN = {urn:nbn:de:0030-drops-239230},
doi = {10.4230/OASIcs.Manzini.0},
annote = {Keywords: Front Matter, Table of Contents, Preface, Conference Organization}
}
Document
BWT and Combinatorics on Words
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.
Cite as
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
A Survey of the Bijective Burrows-Wheeler Transform
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.
Cite as
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
BWT for String Collections
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
Wavelet Tree, Part II: Text Indexing
Abstract
The Wavelet Tree data structure introduced in Grossi, Gupta, and Vitter [Grossi et al., 2003] is a space-efficient technique for rank and select queries that generalizes from binary symbols to an arbitrary multisymbol alphabet. Over the last two decades, it has become a pivotal tool in modern full-text indexing and data compression because of its properties and capabilities in compressing and indexing data, with many applications to information retrieval, genome analysis, data mining, and web search. In this paper, we survey the fascinating history and impact of Wavelet Trees; no doubt many more developments are yet to come. Our survey borrows some content from the authors' earlier works.
This paper is divided into two parts: The first part gives a brief history of Wavelet Trees, including its varieties and practical implementations, which appears in the Festschrift dedicated to Roberto Grossi; the second part (this one) deals with Wavelet Tree-based text indexing and is included in the Festschrift dedicated to Giovanni Manzini.
Cite as
Paolo Ferragina, Raffaele Giancarlo, Roberto Grossi, Giovanna Rosone, Rossano Venturini, and Jeffrey Scott Vitter. Wavelet Tree, Part II: Text Indexing. In The Expanding World of Compressed Data: A Festschrift for Giovanni Manzini's 60th Birthday. Open Access Series in Informatics (OASIcs), Volume 131, pp. 4:1-4:10, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
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@InProceedings{ferragina_et_al:OASIcs.Manzini.4,
author = {Ferragina, Paolo and Giancarlo, Raffaele and Grossi, Roberto and Rosone, Giovanna and Venturini, Rossano and Vitter, Jeffrey Scott},
title = {{Wavelet Tree, Part II: Text Indexing}},
booktitle = {The Expanding World of Compressed Data: A Festschrift for Giovanni Manzini's 60th Birthday},
pages = {4:1--4:10},
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.4},
URN = {urn:nbn:de:0030-drops-239127},
doi = {10.4230/OASIcs.Manzini.4},
annote = {Keywords: Wavelet tree, data compression, text indexing, compressed suffix array, Burrows-Wheeler transform, rank and select}
}
Document
FM-Adaptive: A Practical Data-Aware FM-Index
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
Optimizing the Performance of the FM-Index for Large-Scale Data
Abstract
The FM-index is a fundamental data structure used in bioinformatics to efficiently search for strings and index genomes. However, the FM-index can pose computational challenges, particularly in the context of large-scale genomic datasets, due to the complexity of its underlying components and data encodings. In this paper, we present a comprehensive review of efficient variants of the FM-index and the encoding strategies used to improve performance. We examine hardware-accelerated techniques, such as memory-efficient data layouts and cache-aware structures, as well as software-level innovations, including algorithmic refinements and compact representations. The reviewed work demonstrates substantial gains in both speed and scalability, making methods that use the FM-index more practical for high-throughput genomic applications. By analyzing the trade-offs and design choices of these variants, we highlight how combining hardware-aware and software-centric strategies enables more efficient FM-index construction and usage across a range of bioinformatics tasks.
Cite as
Eddie Ferro and Christina Boucher. Optimizing the Performance of the FM-Index for Large-Scale Data. In The Expanding World of Compressed Data: A Festschrift for Giovanni Manzini's 60th Birthday. Open Access Series in Informatics (OASIcs), Volume 131, pp. 6:1-6:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
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@InProceedings{ferro_et_al:OASIcs.Manzini.6,
author = {Ferro, Eddie and Boucher, Christina},
title = {{Optimizing the Performance of the FM-Index for Large-Scale Data}},
booktitle = {The Expanding World of Compressed Data: A Festschrift for Giovanni Manzini's 60th Birthday},
pages = {6:1--6:21},
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.6},
URN = {urn:nbn:de:0030-drops-239140},
doi = {10.4230/OASIcs.Manzini.6},
annote = {Keywords: FM-Index Acceleration, Run-Length Encoding, Suffix Array Optimization, Burrows-Wheeler Transform, Efficient Backward Search}
}
Document
Algorithms for Computing Very Large BWTs: a Short Survey
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
A Taxonomy of LCP-Array Construction Algorithms
Abstract
The combination of the suffix array and the LCP-array can be used to solve many string processing problems efficiently. We review some of the most important sequential LCP-array construction algorithms in random access memory.
Cite as
Johannes Fischer and Enno Ohlebusch. A Taxonomy of LCP-Array Construction Algorithms. In The Expanding World of Compressed Data: A Festschrift for Giovanni Manzini's 60th Birthday. Open Access Series in Informatics (OASIcs), Volume 131, pp. 8:1-8:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
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@InProceedings{fischer_et_al:OASIcs.Manzini.8,
author = {Fischer, Johannes and Ohlebusch, Enno},
title = {{A Taxonomy of LCP-Array Construction Algorithms}},
booktitle = {The Expanding World of Compressed Data: A Festschrift for Giovanni Manzini's 60th Birthday},
pages = {8:1--8:17},
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.8},
URN = {urn:nbn:de:0030-drops-239166},
doi = {10.4230/OASIcs.Manzini.8},
annote = {Keywords: longest common prefix array, suffix array, Burrows-Wheeler transform}
}
Document
Search Schemes for Approximate Pattern Matching: An Overview
Abstract
We provide a brief survey of results on solving the approximate pattern matching problem using search schemes, as introduced by Kucherov et al. (2016). We demonstrate that search schemes constitute a flexible and versatile tool that enable the specification of various search strategies, including several known filtering methods. We present approaches for designing efficient search schemes and for implementing them effectively. Finally, we conclude with experimental results comparing multiple search schemes on DNA sequencing data using the Columba software by Renders et al. (2021).
Cite as
Lore Depuydt, Jan Fostier, Simon Gottlieb, Gregory Kucherov, Knut Reinert, and Luca Renders. Search Schemes for Approximate Pattern Matching: An Overview. In The Expanding World of Compressed Data: A Festschrift for Giovanni Manzini's 60th Birthday. Open Access Series in Informatics (OASIcs), Volume 131, pp. 9:1-9:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
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@InProceedings{depuydt_et_al:OASIcs.Manzini.9,
author = {Depuydt, Lore and Fostier, Jan and Gottlieb, Simon and Kucherov, Gregory and Reinert, Knut and Renders, Luca},
title = {{Search Schemes for Approximate Pattern Matching: An Overview}},
booktitle = {The Expanding World of Compressed Data: A Festschrift for Giovanni Manzini's 60th Birthday},
pages = {9:1--9:16},
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.9},
URN = {urn:nbn:de:0030-drops-239172},
doi = {10.4230/OASIcs.Manzini.9},
annote = {Keywords: FM-index, bidirectional index, approximate pattern matching, search scheme}
}
Document
Phasing Data from Genotype Queries via the μ-PBWT
Abstract
Genotype phasing - the process of reconstructing haplotypes from genotype data - is a fundamental problem in genomics with applications in ancestry inference, imputation, and disease association. Traditional phasing methods rely on statistical models or combinatorial approaches which can be computationally expensive, particularly when applied to large-scale reference panels.
In this paper, we present a first exploration of using the μ-PBWT (a run-length encoded Positional Burrows-Wheeler Transform) to solve the genotype phasing problem with a reference panel. Leveraging our previous results on positional substrings, we propose an approach that can explain a query genotype if the corresponding haplotype pair exists in the input panel. Moreover, our method is extended to cases where such a pair does not exist, even though some regions should remain unphased if they cannot be explicitly explained using the reference panel.
We implemented this method and compared it against Beagle, a state-of-the-art phasing tool, demonstrating that, in the absence of mutations and recombinations, our approach correctly identifies the haplotype pair that explains a genotype query while using seven times less memory than Beagle. However, we also observe that as mutation rates increase, the quality of the phasing decreases as a result of the growing difficulty of identifying consistent haplotype pairs in the presence of sequence variation.
These findings highlight the potential of μ-PBWT as an efficient alternative for genotype phasing, particularly in settings where computational resources are limited. The source code is publicly available at https://github.com/dlcgold/muPBWT/tree/phase.
Cite as
Davide Cozzi, Paola Bonizzoni, Christina Boucher, Ben Langmead, and Yuri Pirola. Phasing Data from Genotype Queries via the μ-PBWT. In The Expanding World of Compressed Data: A Festschrift for Giovanni Manzini's 60th Birthday. Open Access Series in Informatics (OASIcs), Volume 131, pp. 10:1-10:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
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@InProceedings{cozzi_et_al:OASIcs.Manzini.10,
author = {Cozzi, Davide and Bonizzoni, Paola and Boucher, Christina and Langmead, Ben and Pirola, Yuri},
title = {{Phasing Data from Genotype Queries via the \mu-PBWT}},
booktitle = {The Expanding World of Compressed Data: A Festschrift for Giovanni Manzini's 60th Birthday},
pages = {10:1--10:17},
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.10},
URN = {urn:nbn:de:0030-drops-239183},
doi = {10.4230/OASIcs.Manzini.10},
annote = {Keywords: Positional Burrows-Wheeler Transform, r-index, minimal position substring cover, set-maximal exact matches, genotype phasing}
}
Document
Circular Dictionary Matching Using Extended BWT
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
Wheeler Graphs and Wheeler Languages
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
Graph Indexing Beyond Wheeler Graphs
Abstract
After the discovery of the FM index, which linked the Burrows-Wheeler transform (BWT) to pattern matching on strings, several contemporaneous strands of research began on indexing more complex structures with the BWT, such as tries, finite languages, de Bruijn graphs, and aligned sequences. These directions can now be viewed as culminating in the theory of Wheeler Graphs, but sometimes they go beyond. This chapter reviews the significant body of "proto Wheeler Graph" indexes, many of which exploit characteristics of their specific case to outperform Wheeler graphs, especially in practice.
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Jarno N. Alanko, Elena Biagi, Massimo Equi, Veli Mäkinen, Simon J. Puglisi, Nicola Rizzo, Kunihiko Sadakane, and Jouni Sirén. Graph Indexing Beyond Wheeler Graphs. In The Expanding World of Compressed Data: A Festschrift for Giovanni Manzini's 60th Birthday. Open Access Series in Informatics (OASIcs), Volume 131, pp. 13:1-13:29, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
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@InProceedings{alanko_et_al:OASIcs.Manzini.13,
author = {Alanko, Jarno N. and Biagi, Elena and Equi, Massimo and M\"{a}kinen, Veli and Puglisi, Simon J. and Rizzo, Nicola and Sadakane, Kunihiko and Sir\'{e}n, Jouni},
title = {{Graph Indexing Beyond Wheeler Graphs}},
booktitle = {The Expanding World of Compressed Data: A Festschrift for Giovanni Manzini's 60th Birthday},
pages = {13:1--13:29},
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.13},
URN = {urn:nbn:de:0030-drops-239215},
doi = {10.4230/OASIcs.Manzini.13},
annote = {Keywords: indexing, compression, compressed data structures, string algorithms, pattern matching}
}
Document
BWT Indexes for Optimal Joins in Graph Databases
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}
}