18 Search Results for "Pop, Mihai"

Document
DOI: 10.4230/LIPIcs.SEA.2026.20
QuadRank: Engineering a High Throughput Rank

Authors: Ragnar Groot Koerkamp

Published in: LIPIcs, Volume 371, 24th International Symposium on Experimental Algorithms (SEA 2026)

Abstract
Motivation. Given a text, a query rank(q, c) counts the number of occurrences of character c among the first q characters of the text. Space-efficient methods to answer these rank queries form an important building block in many succinct data structures. For example, the FM-index [Ferragina and Manzini, 2000] is a widely used data structure that uses rank queries to locate all occurrences of a pattern in a text. In bioinformatics applications, the goal is usually to process large inputs as fast as possible. Thus, data structures should have high throughput when used with many threads. Contributions. We first survey existing results on rank data structures. For the σ = 2 binary alphabet, we then develop BiRank, which has 3.28% space overhead. BiRank merges the central ideas of two recent papers: (1) we interleave (inline) offsets in each cache line of the underlying bit vector [Laws et al., 2024], reducing cache misses, and (2) these offsets are to the middle of each block so that only half of each needs popcounting [Gottlieb and Reinert, 2025]. In QuadRank (14.4% overhead), we extend these techniques to the σ = 4 (DNA) alphabet. Both data structures typically require only a single cache miss per query, making them highly suitable for high-throughput and memory-bound settings. To enable efficient batch-processing, we support prefetching the cache lines required to answer upcoming queries. Results. BiRank and QuadRank are around 1.5× and 2× faster than similar-overhead methods that do not use interleaving. Prefetching gives an additional 2× speedup, at which point the dual-channel DDR4 RAM bandwidth becomes a hard limit on the total throughput. With prefetching, both methods outperform all other methods apart from SPIDER [Laws et al., 2024] by 2×. When using QuadRank with prefetching in a toy count-only FM-index, QuadFm, this results in a smaller size and up to 4× speedup over Genedex, a state-of-the-art batching FM-index implementation. Conclusion. Optimizing data structures for high throughput, by minimizing cache misses and branch-misses and adding support for prefetching, can result in significant speedups when benchmarks are adjusted accordingly.
Cite as

Ragnar Groot Koerkamp. QuadRank: Engineering a High Throughput Rank. In 24th International Symposium on Experimental Algorithms (SEA 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 371, pp. 20:1-20:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{grootkoerkamp:LIPIcs.SEA.2026.20,
  author =	{Groot Koerkamp, Ragnar},
  title =	{{QuadRank: Engineering a High Throughput Rank}},
  booktitle =	{24th International Symposium on Experimental Algorithms (SEA 2026)},
  pages =	{20:1--20:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-422-2},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{371},
  editor =	{Aum\"{u}ller, Martin and Finocchi, Irene},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SEA.2026.20},
  URN =		{urn:nbn:de:0030-drops-260248},
  doi =		{10.4230/LIPIcs.SEA.2026.20},
  annote =	{Keywords: Rank, Succinct Data Structures, Cache Performance, Prefetching}
}
Document
DOI: 10.4230/LIPIcs.CPM.2026.17
Sensitivity of Repetitiveness Measures to String Reversal

Authors: Hideo Bannai, Yuto Fujie, Peaker Guo, Shunsuke Inenaga, Yuto Nakashima, Simon J. Puglisi, and Cristian Urbina

Published in: LIPIcs, Volume 369, 37th Annual Symposium on Combinatorial Pattern Matching (CPM 2026)

Abstract
We study the impact that string reversal can have on several repetitiveness measures. First, we exhibit an infinite family of strings where the number, r, of runs in the run-length encoding of the Burrows-Wheeler transform (BWT) can increase additively by Θ(n) when reversing the string. This substantially improves the known Ω(log n) lower-bound for the additive sensitivity of r and it is asymptotically tight. We generalize our result to other variants of the BWT, including the variant with an appended end-of-string symbol and the bijective BWT. We show that an analogous result holds for the size z of the Lempel-Ziv 77 (LZ) parsing of the text, and also for some of its variants, including the non-overlapping LZ parsing, and the LZ-end parsing. Moreover, we describe a family of strings for which the ratio z(w^R)/z(w) approaches 3 from below as |w| → ∞. We also show an asymptotically tight lower-bound of Θ(n) for the additive sensitivity of the size v of the smallest lexicographic parsing to string reversal. Finally, we show that the multiplicative sensitivity of v to reversing the string is Θ(log n), and this lower-bound is also tight. Overall, our results expose the limitations of repetitiveness measures that are widely used in practice, against string reversal - a simple and natural data transformation.
Cite as

Hideo Bannai, Yuto Fujie, Peaker Guo, Shunsuke Inenaga, Yuto Nakashima, Simon J. Puglisi, and Cristian Urbina. Sensitivity of Repetitiveness Measures to String Reversal. In 37th Annual Symposium on Combinatorial Pattern Matching (CPM 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 369, pp. 17:1-17:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{bannai_et_al:LIPIcs.CPM.2026.17,
  author =	{Bannai, Hideo and Fujie, Yuto and Guo, Peaker and Inenaga, Shunsuke and Nakashima, Yuto and Puglisi, Simon J. and Urbina, Cristian},
  title =	{{Sensitivity of Repetitiveness Measures to String Reversal}},
  booktitle =	{37th Annual Symposium on Combinatorial Pattern Matching (CPM 2026)},
  pages =	{17:1--17:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-420-8},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{369},
  editor =	{Bille, Philip 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.CPM.2026.17},
  URN =		{urn:nbn:de:0030-drops-259434},
  doi =		{10.4230/LIPIcs.CPM.2026.17},
  annote =	{Keywords: String reversal, Repetitiveness measures, Burrows-Wheeler transform, Lempel-Ziv parsing, Lexicographic parsings}
}
Document
DOI: 10.4230/LIPIcs.STACS.2026.62
Relative Compressed Reverse Suffix Array

Authors: Muhammed Oguzhan Kulekci, Mano Prakash Parthasarathi, Rahul Shah, and Sharma V. Thankachan

Published in: LIPIcs, Volume 364, 43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026)

Abstract
Suffix trees and suffix arrays are two fundamental data structures in the field of string algorithms. For a string (a.k.a. text or sequence) of length n over an alphabet of size σ, these structures typically require O(nlog n) bits of space. The FM-index provides a compressed representation of the suffix array in ≈ nlog σ bits, allowing for efficient queries on both the suffix array and its inverse array in near logarithmic time. In certain applications, such as approximate pattern matching (i.e., with wildcards, mismatches, edits), there is a need to access the suffix array of a text, as well as the suffix array of text’s reverse. Motivated by this, we explore the possibility of encoding the suffix array of the reversed text in a compact form, assuming the availability of the FM-index for the original text. Our first solution is an O(n)-bit (relative) encoding of the suffix array of the reversed text, with the time for decoding an entry being only O(log^*n) times that of decoding an entry in the text’s suffix array using FM-index. We then demonstrate how to reduce the space to O(n/κ) bits for a parameter κ, while multiplicative factor in time becomes approximately O(κlog^*n+κ³). We can also support inverse suffix array and longest common extension queries on the reversed text. These results are achieved through some careful and non-trivial application of various succinct data structure techniques.
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Muhammed Oguzhan Kulekci, Mano Prakash Parthasarathi, Rahul Shah, and Sharma V. Thankachan. Relative Compressed Reverse Suffix Array. In 43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 364, pp. 62:1-62:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{kulekci_et_al:LIPIcs.STACS.2026.62,
  author =	{Kulekci, Muhammed Oguzhan and Parthasarathi, Mano Prakash and Shah, Rahul and Thankachan, Sharma V.},
  title =	{{Relative Compressed Reverse Suffix Array}},
  booktitle =	{43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026)},
  pages =	{62:1--62:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-412-3},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{364},
  editor =	{Mahajan, Meena and Manea, Florin and McIver, Annabelle and Thắng, Nguy\~{ê}n Kim},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2026.62},
  URN =		{urn:nbn:de:0030-drops-255512},
  doi =		{10.4230/LIPIcs.STACS.2026.62},
  annote =	{Keywords: String Matching, Text Indexing, Data Structures, Suffix Trees}
}
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
Invited Talk
DOI: 10.4230/LIPIcs.WABI.2025.2
We Are What We Index; a Primer for the Wheeler Graph Era (Invited Talk)

Authors: Ben Langmead

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

Abstract
Since the arrival of second-generation sequencing, we have needed to build indexes over reference sequences - e.g. genomes and transcriptomes - in order to solve read alignment and classification problems efficiently [Langmead et al., 2009; Li and Durbin, 2009; Li et al., 2009]. The rule has been: what we can index determines what we can do. When indexing strings, we can use methods like suffix arrays [Manber and Myers, 1993], the Burrows-Wheeler Transform (BWT) [Burrows and Wheeler, 1994] / FM Index [Ferragina and Manzini, 2000], or k-mer indexes [Marchet et al., 2021]. What if we want to index objects more complex than strings? A pangenome, for example, is a large collection of similar strings, e.g. the hundreds of assemblies that make up the Human Pangenome Reference [Liao et al., 2023] or all the bacteria in the Refseq database [Goldfarb et al., 2025]. We may wish to combine these strings into a multiple sequence alignment (MSA) or a graph first. Can we index those efficiently? In many useful cases the answer is "yes," but in others the answer is "no." The story of how we learned exactly when the answer is "yes" versus "no" unfolded through a sequence of insights. Here we review this story, eventually arriving at the definition of Wheeler graphs as discovered and formalized by Gagie, Manzini and Sirén [Gagie et al., 2017]. We will focus on indexes based on the BWT, since these (a) are lossless full-text indexes, (b) are widely used in practice [Langmead et al., 2009; Li and Durbin, 2009], and (c) form the theoretical throughline for all the indexing strategies on the path to Wheeler graphs. We will trace the BWT-based indexing story from the early days of the FM Index, though its step-by-step gobbling up of trees (XBW-transform [Ferragina et al., 2005]) and de Bruijn Graphs (BOSS representation [Bowe et al., 2012]), and to the eventual formalization of Wheeler graphs [Gagie et al., 2017]. Along the way, we will define and update our notions of what it means to track a consecutive range of elements in the structure, and what it means for an index to be efficient. We will also connect these notions to automata [Sipser, 1996], noting how the indexability of Wheeler graphs (also called Wheeler automata) is connected to the mechanics of how to efficiently represent and simulate a finite automaton [Alanko et al., 2021]. With this context, we can imagine improved indexes for the future of genomics and pangenomics. De Bruijn are extremely practical and are the most widely used among the non-string data structures that are also Wheeler graphs. But we might prefer other options. For example, de Bruijn graphs have the undesirable property that they usually encode not only the true longer-than-k substrings of the original text, but also "false" substrings that span repeats. Related to this, paths through the de Bruijn graph can "glue" substrings together that are horizontally distant in the MSA. Could other Wheeler graphs be practical alternatives to de Bruijn graphs? For instance, the original GCSA study by Sirén, Välimäki and Mäkinen proposed a way to convert a multiple alignment into an automaton that either is a Wheeler graph or can be made into one [Sirén et al., 2014]. This warrants further exploration, possibly with the help of improved tools for solving the NP-complete problem of recognizing whether a graph is a Wheeler graph [Chao et al., 2023]. The notion of BWT tunnels [Baier, 2018] gives another route: we can begin with a concatenated pangenome strings and compress it by identifying and collapsing BWT tunnels. This yields a Wheeler graph that is compressed like the de Bruijn graph, but without departing from the exact contents or coordinate systems of the original genomes. The future might need us to explore all these Wheeler-graph indexes, along with the also highly practical and always-improving world of indexes buiover collections of strings [Gagie et al., 2018].
Cite as

Ben Langmead. We Are What We Index; a Primer for the Wheeler Graph Era (Invited Talk). In 25th International Conference on Algorithms for Bioinformatics (WABI 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 344, pp. 2:1-2:2, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{langmead:LIPIcs.WABI.2025.2,
  author =	{Langmead, Ben},
  title =	{{We Are What We Index; a Primer for the Wheeler Graph Era}},
  booktitle =	{25th International Conference on Algorithms for Bioinformatics (WABI 2025)},
  pages =	{2:1--2:2},
  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.2025.2},
  URN =		{urn:nbn:de:0030-drops-239288},
  doi =		{10.4230/LIPIcs.WABI.2025.2},
  annote =	{Keywords: Indexing, Burrows-Wheeler Transform}
}
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.6
Optimizing the Performance of the FM-Index for Large-Scale Data

Authors: Eddie Ferro and Christina Boucher

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

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.
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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
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.
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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.9
Search Schemes for Approximate Pattern Matching: An Overview

Authors: Lore Depuydt, Jan Fostier, Simon Gottlieb, Gregory Kucherov, Knut Reinert, and Luca Renders

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

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
DOI: 10.4230/LIPIcs.SEA.2025.2
IBB: Fast Burrows-Wheeler Transform Construction for Length-Diverse DNA Data

Authors: Enno Adler, Stefan Böttcher, Rita Hartel, and Cederic Alexander Steininger

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

Abstract
The Burrows-Wheeler transform (BWT) is integral to the FM-index, which is used extensively in text compression, indexing, pattern search, and bioinformatic problems as de novo assembly and read alignment. Thus, efficient construction of the BWT in terms of time and memory usage is key to these applications. We present a novel external-memory algorithm called Improved-Bucket Burrows-Wheeler transform (IBB) for constructing the BWT of DNA datasets with highly diverse sequence lengths. IBB uses a right-aligned approach to efficiently handle sequences of varying lengths, a tree-based data structure to manage relative insert positions and ranks, and fine buckets to reduce the necessary amount of input and output to external memory. Our experiments demonstrate that IBB is 10% to 40% faster than the best existing state-of-the-art BWT construction algorithms on most datasets while maintaining competitive memory consumption.
Cite as

Enno Adler, Stefan Böttcher, Rita Hartel, and Cederic Alexander Steininger. IBB: Fast Burrows-Wheeler Transform Construction for Length-Diverse DNA Data. In 23rd International Symposium on Experimental Algorithms (SEA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 338, pp. 2:1-2:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{adler_et_al:LIPIcs.SEA.2025.2,
  author =	{Adler, Enno and B\"{o}ttcher, Stefan and Hartel, Rita and Steininger, Cederic Alexander},
  title =	{{IBB: Fast Burrows-Wheeler Transform Construction for Length-Diverse DNA Data}},
  booktitle =	{23rd International Symposium on Experimental Algorithms (SEA 2025)},
  pages =	{2:1--2:18},
  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.2025.2},
  URN =		{urn:nbn:de:0030-drops-232402},
  doi =		{10.4230/LIPIcs.SEA.2025.2},
  annote =	{Keywords: burrows-wheeler transform, self-indexes, external-memory}
}
Document
DOI: 10.4230/LIPIcs.CPM.2025.17
On the Compressiveness of the Burrows-Wheeler Transform

Authors: Hideo Bannai, Tomohiro I, and Yuto Nakashima

Published in: LIPIcs, Volume 331, 36th Annual Symposium on Combinatorial Pattern Matching (CPM 2025)

Abstract
The Burrows-Wheeler transform (BWT) is a reversible transform that converts a string w into another string BWT(w). The size of the run-length encoded BWT (RLBWT) can be interpreted as a measure of repetitiveness in the class of representations called dictionary compression which are essentially representations based on copy and paste operations. In this paper, we shed new light on the compressiveness of BWT and the bijective BWT (BBWT). We first extend previous results on the relations of their run-length compressed sizes r and r_B. We also show that the so-called "clustering effect" of BWT and BBWT can be captured by measures other than empirical entropy or run-length encoding. In particular, we show that BWT and BBWT do not increase the repetitiveness of the string with respect to various measures based on dictionary compression by more than a polylogarithmic factor. Furthermore, we show that there exists an infinite family of strings that are maximally incompressible by any dictionary compression measure, but become very compressible after applying BBWT. An interesting implication of this result is that it is possible to transcend dictionary compression in some cases by simply applying BBWT before applying dictionary compression.
Cite as

Hideo Bannai, Tomohiro I, and Yuto Nakashima. On the Compressiveness of the Burrows-Wheeler Transform. In 36th Annual Symposium on Combinatorial Pattern Matching (CPM 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 331, pp. 17:1-17:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{bannai_et_al:LIPIcs.CPM.2025.17,
  author =	{Bannai, Hideo and I, Tomohiro and Nakashima, Yuto},
  title =	{{On the Compressiveness of the Burrows-Wheeler Transform}},
  booktitle =	{36th Annual Symposium on Combinatorial Pattern Matching (CPM 2025)},
  pages =	{17:1--17:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-369-0},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{331},
  editor =	{Bonizzoni, Paola and M\"{a}kinen, Veli},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CPM.2025.17},
  URN =		{urn:nbn:de:0030-drops-231116},
  doi =		{10.4230/LIPIcs.CPM.2025.17},
  annote =	{Keywords: Data Compression, Bijective Burrows-Wheeler Transform, Fibonacci words}
}
Document
DOI: 10.4230/LIPIcs.CPM.2025.12
Shortest Undirected Paths in de Bruijn Graphs

Authors: Wiktor Zuba, Oded Lachish, and Solon P. Pissis

Published in: LIPIcs, Volume 331, 36th Annual Symposium on Combinatorial Pattern Matching (CPM 2025)

Abstract
Computing shortest directed paths in de Bruijn graphs is well studied and well understood. This is not the case for computing undirected paths, which is much more challenging algorithmically. In this paper, we present a general framework for computing shortest undirected paths in arbitrary de Bruijn graphs, that is, arbitrary subgraphs of the complete de Bruijn graph. We then present an application of our techniques for making any arbitrary order-k de Bruijn graph G(V,E) weakly connected by adding a set of edges of minimum total cost. This improves the running time of the recent (2-2/d)-approximation algorithm by Bernardini et al. [CPM 2024] from 𝒪(k|V|²) to 𝒪(k|V|log d) time, where d is the number of weakly connected components of graph G.
Cite as

Wiktor Zuba, Oded Lachish, and Solon P. Pissis. Shortest Undirected Paths in de Bruijn Graphs. In 36th Annual Symposium on Combinatorial Pattern Matching (CPM 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 331, pp. 12:1-12:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{zuba_et_al:LIPIcs.CPM.2025.12,
  author =	{Zuba, Wiktor and Lachish, Oded and Pissis, Solon P.},
  title =	{{Shortest Undirected Paths in de Bruijn Graphs}},
  booktitle =	{36th Annual Symposium on Combinatorial Pattern Matching (CPM 2025)},
  pages =	{12:1--12:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-369-0},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{331},
  editor =	{Bonizzoni, Paola and M\"{a}kinen, Veli},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CPM.2025.12},
  URN =		{urn:nbn:de:0030-drops-231060},
  doi =		{10.4230/LIPIcs.CPM.2025.12},
  annote =	{Keywords: string algorithm, graph algorithm, de Bruijn graph, Eulerian graph}
}
Document
DOI: 10.4230/LIPIcs.CPM.2018.5
Fast Matching-based Approximations for Maximum Duo-Preservation String Mapping and its Weighted Variant

Authors: Brian Brubach

Published in: LIPIcs, Volume 105, 29th Annual Symposium on Combinatorial Pattern Matching (CPM 2018)

Abstract
We present a new approach to approximating the Maximum Duo-Preservation String Mapping Problem (MPSM) based on massaging the constraints into a tractable matching problem. MPSM was introduced in Chen, Chen, Samatova, Peng, Wang, and Tang [Chen et al., 2014] as the complement to the well-studied Minimum Common String Partition problem (MCSP). Prior work also considers the k-MPSM and k-MCSP variants in which each letter occurs at most k times in each string. The authors of [Chen et al., 2014] showed a k^2-appoximation for k >= 3 and 2-approximation for k = 2. Boria, Kurpisz, Leppänen, and Mastrolilli [Boria et al., 2014] gave a 4-approximation independent of k and showed that even 2-MPSM is APX-Hard. A series of improvements led to the current best bounds of a (2 + epsilon)-approximation for any epsilon > 0 in n^{O(1/epsilon)} time for strings of length n and a 2.67-approximation running in O(n^2) time, both by Dudek, Gawrychowski, and Ostropolski-Nalewaja [Dudek et al., 2017]. Here, we show that a 2.67-approximation can surprisingly be achieved in O(n) time for alphabets of constant size and O(n + alpha^7) for alphabets of size alpha. Recently, Mehrabi [Mehrabi, 2017] introduced the more general weighted variant, Maximum Weight Duo-Preservation String Mapping (MWPSM) and provided a 6-approximation. Our approach gives a 2.67-approximation to this problem running in O(n^3) time. This approach can also find an 8/(3(1-epsilon))-approximation to MWPSM for any epsilon > 0 in O(n^2 epsilon^{-1} lg{epsilon^{-1}}) time using the approximate weighted matching algorithm of Duan and Pettie [Duan and Pettie, 2014]. Finally, we introduce the first streaming algorithm for MPSM. We show that a single pass suffices to find a 4-approximation on the size of an optimal solution using only O(alpha^2 lg{n}) space.
Cite as

Brian Brubach. Fast Matching-based Approximations for Maximum Duo-Preservation String Mapping and its Weighted Variant. In 29th Annual Symposium on Combinatorial Pattern Matching (CPM 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 105, pp. 5:1-5:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{brubach:LIPIcs.CPM.2018.5,
  author =	{Brubach, Brian},
  title =	{{Fast Matching-based Approximations for Maximum Duo-Preservation String Mapping and its Weighted Variant}},
  booktitle =	{29th Annual Symposium on Combinatorial Pattern Matching (CPM 2018)},
  pages =	{5:1--5:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-074-3},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{105},
  editor =	{Navarro, Gonzalo and Sankoff, David and Zhu, Binhai},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CPM.2018.5},
  URN =		{urn:nbn:de:0030-drops-87066},
  doi =		{10.4230/LIPIcs.CPM.2018.5},
  annote =	{Keywords: approximation algorithm, maximum duo-preservation string mapping, minimum common string partition, string comparison, streaming algorithm, comparative genomics}
}
Document
DOI: 10.4230/LIPIcs.CPM.2018.13
A Succinct Four Russians Speedup for Edit Distance Computation and One-against-many Banded Alignment

Authors: Brian Brubach and Jay Ghurye

Published in: LIPIcs, Volume 105, 29th Annual Symposium on Combinatorial Pattern Matching (CPM 2018)

Abstract
The classical Four Russians speedup for computing edit distance (a.k.a. Levenshtein distance), due to Masek and Paterson [Masek and Paterson, 1980], involves partitioning the dynamic programming table into k-by-k square blocks and generating a lookup table in O(psi^{2k} k^2 |Sigma|^{2k}) time and O(psi^{2k} k |Sigma|^{2k}) space for block size k, where psi depends on the cost function (for unit costs psi = 3) and |Sigma| is the size of the alphabet. We show that the O(psi^{2k} k^2) and O(psi^{2k} k) factors can be improved to O(k^2 lg{k}) time and O(k^2) space. Thus, we improve the time and space complexity of that aspect compared to Masek and Paterson [Masek and Paterson, 1980] and remove the dependence on psi. We further show that for certain problems the O(|Sigma|^{2k}) factor can also be reduced. Using this technique, we show a new algorithm for the fundamental problem of one-against-many banded alignment. In particular, comparing one string of length m to n other strings of length m with maximum distance d can be performed in O(n m + m d^2 lg{d} + n d^3) time. When d is reasonably small, this approaches or meets the current best theoretic result of O(nm + n d^2) achieved by using the best known pairwise algorithm running in O(m + d^2) time [Myers, 1986][Ukkonen, 1985] while potentially being more practical. It also improves on the standard practical approach which requires O(n m d) time to iteratively run an O(md) time pairwise banded alignment algorithm. Regarding pairwise comparison, we extend the classic result of Masek and Paterson [Masek and Paterson, 1980] which computes the edit distance between two strings in O(m^2/log{m}) time to remove the dependence on psi even when edits have arbitrary costs from a penalty matrix. Crochemore, Landau, and Ziv-Ukelson [Crochemore, 2003] achieved a similar result, also allowing for unrestricted scoring matrices, but with variable-sized blocks. In practical applications of the Four Russians speedup wherein space efficiency is important and smaller block sizes k are used (notably k < |Sigma|), Kim, Na, Park, and Sim [Kim et al., 2016] showed how to remove the dependence on the alphabet size for the unit cost version, generating a lookup table in O(3^{2k} (2k)! k^2) time and O(3^{2k} (2k)! k) space. Combining their work with our result yields an improvement to O((2k)! k^2 lg{k}) time and O((2k)! k^2) space.
Cite as

Brian Brubach and Jay Ghurye. A Succinct Four Russians Speedup for Edit Distance Computation and One-against-many Banded Alignment. In 29th Annual Symposium on Combinatorial Pattern Matching (CPM 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 105, pp. 13:1-13:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{brubach_et_al:LIPIcs.CPM.2018.13,
  author =	{Brubach, Brian and Ghurye, Jay},
  title =	{{A Succinct Four Russians Speedup for Edit Distance Computation and One-against-many Banded Alignment}},
  booktitle =	{29th Annual Symposium on Combinatorial Pattern Matching (CPM 2018)},
  pages =	{13:1--13:12},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-074-3},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{105},
  editor =	{Navarro, Gonzalo and Sankoff, David and Zhu, Binhai},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CPM.2018.13},
  URN =		{urn:nbn:de:0030-drops-86965},
  doi =		{10.4230/LIPIcs.CPM.2018.13},
  annote =	{Keywords: edit distance, banded alignment, one-against-many alignment, genomics, method of the Four Russians}
}
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