20 Search Results for "Romana, Giuseppe"

Document
DOI: 10.4230/LIPIcs.CPM.2026.13
Totally Unclustered BWT Images of Any Length over Non-Binary Alphabets

Authors: Gabriele Fici, Estéban Gabory, Giuseppe Romana, and Marinella Sciortino

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

Abstract
We prove that for every integer n > 0 and for every alphabet Σ_k of size k ≥ 3, there exist words of length n whose Burrows-Wheeler Transform (BWT) is totally unclustered, i.e., it consists of exactly n runs with no two consecutive equal symbols. These words represent the worst-case behavior of the clustering effect of the BWT. We also establish a lower bound on their number. This contrasts with the binary case, where the existence of infinitely many totally unclustered BWT images is still an open problem, related to Artin’s conjecture on primitive roots.
Cite as

Gabriele Fici, Estéban Gabory, Giuseppe Romana, and Marinella Sciortino. Totally Unclustered BWT Images of Any Length over Non-Binary Alphabets. In 37th Annual Symposium on Combinatorial Pattern Matching (CPM 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 369, pp. 13:1-13:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{fici_et_al:LIPIcs.CPM.2026.13,
  author =	{Fici, Gabriele and Gabory, Est\'{e}ban and Romana, Giuseppe and Sciortino, Marinella},
  title =	{{Totally Unclustered BWT Images of Any Length over Non-Binary Alphabets}},
  booktitle =	{37th Annual Symposium on Combinatorial Pattern Matching (CPM 2026)},
  pages =	{13:1--13:17},
  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.2026.13},
  URN =		{urn:nbn:de:0030-drops-259399},
  doi =		{10.4230/LIPIcs.CPM.2026.13},
  annote =	{Keywords: Burrows-Wheeler Transform, BWT-runs, Repetitiveness Measure, Clustering Effect, Generalized de Bruijn Words}
}
Document
DOI: 10.4230/LIPIcs.CPM.2026.8
Constant Multiplicative Sensitivity on the CDAWGs

Authors: Rikuya Hamai, Hiroto Fujimaru, and Shunsuke Inenaga

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

Abstract
Compact directed acyclic word graphs (CDAWGs) [Blumer et al. 1987] are a fundamental data structure on strings with applications in text pattern searching, data compression, and pattern discovery. Intuitively, the CDAWG of a string T is obtained by merging isomorphic subtrees of the suffix tree [Weiner 1973] of the same string T, and thus CDAWGs are a compact indexing structure. Indeed, the CDAWG size 𝖾 can be sublinear in n for some highly repetitive strings. Of its various applications, the CDAWG allows for computing pattern occurrences, maximal exact matches (MEMs), minimal absent words (MAWs), and minimal unique substrings (MUSs) in optimal time using O(𝖾) space. For designing space-efficient data storage, it is crucial that the underlying data structure is robust against data edits and errors. As a mathematical measure for this, the notion of compression sensitivity [Akagi et al. 2023] was introduced as the maximum of the size increase in the compressed data structures after edits operations. In this paper, we investigate the sensitivity of CDAWGs when a single character edit operation is performed at an arbitrary position in the input string T. We show that the size of the CDAWG after an edit operation on T is asymptotically at most 8 times larger than the original CDAWG before the edit. This O(1) upper bound significantly improves on the only known upper bound O(n/log n) for the problem.
Cite as

Rikuya Hamai, Hiroto Fujimaru, and Shunsuke Inenaga. Constant Multiplicative Sensitivity on the CDAWGs. In 37th Annual Symposium on Combinatorial Pattern Matching (CPM 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 369, pp. 8:1-8:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{hamai_et_al:LIPIcs.CPM.2026.8,
  author =	{Hamai, Rikuya and Fujimaru, Hiroto and Inenaga, Shunsuke},
  title =	{{Constant Multiplicative Sensitivity on the CDAWGs}},
  booktitle =	{37th Annual Symposium on Combinatorial Pattern Matching (CPM 2026)},
  pages =	{8:1--8:17},
  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.2026.8},
  URN =		{urn:nbn:de:0030-drops-259345},
  doi =		{10.4230/LIPIcs.CPM.2026.8},
  annote =	{Keywords: string data structures, maximal repeats, data compression, compression sensitivity, CDAWGs}
}
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.CPM.2026.24
On Occurrence-Preserving Morphisms

Authors: Kaisei Kishi, Peaker Guo, Cristian Urbina, and Hideo Bannai

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

Abstract
A morphism is a mapping that transforms words through letter-wise substitution, where each symbol is consistently replaced by a fixed word. In the field of combinatorics on words, one topic that has attracted considerable attention is the characterization of morphisms that preserve specific properties, such as overlap-freeness, square-freeness, lexicographic order, and primitivity. Continuing this direction, we initiate the study on occurrence-preserving morphisms, which address the following fundamental question: given a morphism ϕ, two words u and v, and k ≥ 1, under what conditions does the number of occurrences of u in v equal the number of occurrences of ϕ^k(u) in ϕ^k(v)? To answer this question, we introduce the notion of interference-free morphisms, examine their properties, and uncover a connection to recognizable morphisms. We then present a precise characterization of occurrence-preserving morphisms in terms of interference-freeness. As applications of our characterization, we first show that there exists a bijection between the starting positions of the occurrences of u in v and those of ϕ^k(u) in ϕ^k(v). We then apply the characterization to the Fibonacci and Thue-Morse words to identify their minimal unique substrings (MUSs). Finally, we exploit the connection between MUSs and net occurrences to simplify existing proofs on net occurrences in these words.
Cite as

Kaisei Kishi, Peaker Guo, Cristian Urbina, and Hideo Bannai. On Occurrence-Preserving Morphisms. In 37th Annual Symposium on Combinatorial Pattern Matching (CPM 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 369, pp. 24:1-24:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{kishi_et_al:LIPIcs.CPM.2026.24,
  author =	{Kishi, Kaisei and Guo, Peaker and Urbina, Cristian and Bannai, Hideo},
  title =	{{On Occurrence-Preserving Morphisms}},
  booktitle =	{37th Annual Symposium on Combinatorial Pattern Matching (CPM 2026)},
  pages =	{24:1--24:16},
  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.2026.24},
  URN =		{urn:nbn:de:0030-drops-259504},
  doi =		{10.4230/LIPIcs.CPM.2026.24},
  annote =	{Keywords: Property-preserving morphisms, interference-free morphisms, recognizable morphisms, injective morphisms, Fibonacci words, Thue-Morse words, minimal unique substrings (MUSs), net occurrences}
}
Document
DOI: 10.4230/LIPIcs.CPM.2026.32
Balancing Two-Dimensional Straight-Line Programs

Authors: Itai Boneh, Estéban Gabory, Paweł Gawrychowski, and Adam Górkiewicz

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

Abstract
We consider building, given a straight-line program (SLP) consisting of g productions deriving a two-dimensional string T of size N× N, a structure capable of providing random access to any character of T. For one-dimensional strings, it is now known how to build a structure of size 𝒪(g) that provides random access in 𝒪(log N) time. In fact, it is known that this can be obtained by building an equivalent SLP of size 𝒪(g) and depth 𝒪(log N) [Ganardi, Jeż, Lohrey, JACM 2021]. We consider the analogous question for two-dimensional strings: can we build an equivalent SLP of roughly the same size and small depth? We show that the answer is negative: there exists an infinite family of two-dimensional strings of size N× N described by a 2D SLP of size g such that any 2D SLP of depth 𝒪(log N) describing the same string must be of size Ω(g⋅ N/log³N). We complement this with an upper bound showing how to construct such a 2D SLP of size 𝒪(g⋅ N). Next, we observe that one can naturally define a generalization of 2D SLP, which we call 2D SLP with holes. We show that a known general balancing theorem by [Ganardi, Jeż, Lohrey, JACM 2021] immediately implies that, given a 2D SLP of size g deriving a string of size N× N, we can construct a 2D SLP with holes of depth 𝒪(log N) and size 𝒪(g). This allows us to conclude that there is a structure of size 𝒪(g) providing random access in 𝒪(log N) time for such a 2D SLP. Further, this can be extended (analogously as for a 1D SLP) to obtain a structure of size 𝒪(g log^ε N) providing random access in 𝒪(log N/log log N) time, for any ε > 0. The same (optimal) random access time was very recently achieved by [De and Kempa, SODA 2026], but with a significantly larger structure of size 𝒪(g log^{2+ε} N).
Cite as

Itai Boneh, Estéban Gabory, Paweł Gawrychowski, and Adam Górkiewicz. Balancing Two-Dimensional Straight-Line Programs. In 37th Annual Symposium on Combinatorial Pattern Matching (CPM 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 369, pp. 32:1-32:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{boneh_et_al:LIPIcs.CPM.2026.32,
  author =	{Boneh, Itai and Gabory, Est\'{e}ban and Gawrychowski, Pawe{\l} and G\'{o}rkiewicz, Adam},
  title =	{{Balancing Two-Dimensional Straight-Line Programs}},
  booktitle =	{37th Annual Symposium on Combinatorial Pattern Matching (CPM 2026)},
  pages =	{32:1--32:20},
  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.2026.32},
  URN =		{urn:nbn:de:0030-drops-259582},
  doi =		{10.4230/LIPIcs.CPM.2026.32},
  annote =	{Keywords: Two-dimensional string, straight-line program, random access}
}
Document
DOI: 10.4230/LIPIcs.CPM.2026.33
The Smallest String Attractors of Fibonacci and Period-Doubling Words

Authors: Mutsunori Banbara, Hideo Bannai, Peaker Guo, Dominik Köppl, Takuya Mieno, and Yoshio Okamoto

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

Abstract
A string attractor of a string T[1..|T|] is a set of positions Γ of T such that any substring w of T has an occurrence that crosses a position in Γ, i.e., there is a position i such that w = T[i..i+|w|-1] and the intersection [i,i+|w|-1]∩ Γ is nonempty. The size of the smallest string attractor of Fibonacci words is known to be 2. We completely characterize the set of all smallest string attractors of Fibonacci words, and show a recursive formula describing the 2^{n-4} + 2^{⌈n/2⌉ - 2} distinct position pairs that are the smallest string attractors of the nth Fibonacci word for n ≥ 7. Similarly, the size of the smallest string attractor of period-doubling words is known to be 2. We also completely characterize the set of all smallest string attractors of period-doubling words, and show a formula describing the two distinct position pairs that are the smallest string attractors of the nth period-doubling word for n ≥ 2. Our results show that strings with the same smallest attractor size can have a drastically different number of distinct smallest attractors.
Cite as

Mutsunori Banbara, Hideo Bannai, Peaker Guo, Dominik Köppl, Takuya Mieno, and Yoshio Okamoto. The Smallest String Attractors of Fibonacci and Period-Doubling Words. In 37th Annual Symposium on Combinatorial Pattern Matching (CPM 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 369, pp. 33:1-33:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{banbara_et_al:LIPIcs.CPM.2026.33,
  author =	{Banbara, Mutsunori and Bannai, Hideo and Guo, Peaker and K\"{o}ppl, Dominik and Mieno, Takuya and Okamoto, Yoshio},
  title =	{{The Smallest String Attractors of Fibonacci and Period-Doubling Words}},
  booktitle =	{37th Annual Symposium on Combinatorial Pattern Matching (CPM 2026)},
  pages =	{33:1--33:21},
  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.2026.33},
  URN =		{urn:nbn:de:0030-drops-259599},
  doi =		{10.4230/LIPIcs.CPM.2026.33},
  annote =	{Keywords: String attractors, Fibonacci words, Period-doubling words, Combinatorics on words}
}
Document
DOI: 10.4230/LIPIcs.CPM.2026.30
Constructing Suffixient Arrays Revisited

Authors: Paola Bonizzoni, Younan Gao, and Brian Riccardi

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

Abstract
Recently, Cenzato et al. proposed a new text index, called the suffixient array, which is a subset of the suffix array and supports locating a single pattern occurrence or finding its maximal exact matches (MEMs), assuming random access to the input text T[1..n] is available. They show that, given the suffix array, the longest common prefix array, and the Burrows-Wheeler transform (BWT) of the reverse of T[1..n] over an alphabet {1,…,σ}, a suffixient array can be constructed in linear time. However, their construction algorithms require multiple scans of these arrays. When restricted to a single pass over the arrays, they present an alternative construction algorithm running in O(n + r log σ) time, where r is the number of runs in the BWT of the reversed text. In this paper, we present a new one-pass algorithm that constructs a suffixient array in linear time under the standard RAM model.
Cite as

Paola Bonizzoni, Younan Gao, and Brian Riccardi. Constructing Suffixient Arrays Revisited. In 37th Annual Symposium on Combinatorial Pattern Matching (CPM 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 369, pp. 30:1-30:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{bonizzoni_et_al:LIPIcs.CPM.2026.30,
  author =	{Bonizzoni, Paola and Gao, Younan and Riccardi, Brian},
  title =	{{Constructing Suffixient Arrays Revisited}},
  booktitle =	{37th Annual Symposium on Combinatorial Pattern Matching (CPM 2026)},
  pages =	{30:1--30:18},
  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.2026.30},
  URN =		{urn:nbn:de:0030-drops-259564},
  doi =		{10.4230/LIPIcs.CPM.2026.30},
  annote =	{Keywords: Suffixient set, suffixient array, right-maximal substring, linear-time algorithm}
}
Document
Research
DOI: 10.4230/TGDK.4.1.3
Semantically Reflected Programs

Authors: Eduard Kamburjan, Vidar Norstein Klungre, Yuanwei Qu, Rudolf Schlatte, Egor V. Kostylev, Martin Giese, and Einar Broch Johnsen

Published in: TGDK, Volume 4, Issue 1 (2026). Transactions on Graph Data and Knowledge, Volume 4, Issue 1

Abstract
This paper addresses the dichotomy between the formalization of structural and the formalization of executable behavioral knowledge by means of semantically lifted programs, which explore an intuitive connection between imperative programs and knowledge graphs. While knowledge graphs and ontologies are eminently useful to represent formal knowledge about a system’s individuals and universals, programming languages are designed to describe the system’s evolution. To address this dichotomy, we introduce a semantic lifting of the program states of an executing progam into a knowledge graph, for an object-oriented programming language. The resulting graph is exposed as a semantic reflection layer within the programming language, allowing programmers to leverage knowledge of the application domain in their programs during execution. In this paper, we formalize semantic lifting and semantic reflection for a small imperative programming language, SMOL, explain the operational aspects of the language, and consider type correctness and virtualization for runtime program queries through the semantic reflection layer. We illustrate semantic lifting and semantic reflection through a case study of geological modeling and discuss different applications of the technique. The language implementation is open source and available online.
Cite as

Eduard Kamburjan, Vidar Norstein Klungre, Yuanwei Qu, Rudolf Schlatte, Egor V. Kostylev, Martin Giese, and Einar Broch Johnsen. Semantically Reflected Programs. In Transactions on Graph Data and Knowledge (TGDK), Volume 4, Issue 1, pp. 3:1-3:52, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@Article{kamburjan_et_al:TGDK.4.1.3,
  author =	{Kamburjan, Eduard and Klungre, Vidar Norstein and Qu, Yuanwei and Schlatte, Rudolf and Kostylev, Egor V. and Giese, Martin and Johnsen, Einar Broch},
  title =	{{Semantically Reflected Programs}},
  journal =	{Transactions on Graph Data and Knowledge},
  pages =	{3:1--3:52},
  ISSN =	{2942-7517},
  year =	{2026},
  volume =	{4},
  number =	{1},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/TGDK.4.1.3},
  URN =		{urn:nbn:de:0030-drops-256884},
  doi =		{10.4230/TGDK.4.1.3},
  annote =	{Keywords: Knowledge Graphs, Ontologies, Object-Oriented Modelling, Imperative Programming Languages, Reflection, Type Safety}
}
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.GIScience.2025.16
What, When, and Where Do You Mean? Detecting Spatio-Temporal Concept Drift in Scientific Texts

Authors: Meilin Shi, Krzysztof Janowicz, Zilong Liu, Mina Karimi, Ivan Majic, and Alexandra Fortacz

Published in: LIPIcs, Volume 346, 13th International Conference on Geographic Information Science (GIScience 2025)

Abstract
Inundated by the rapidly expanding AI research nowadays, the research community requires more effective research data management than ever. A key challenge lies in the evolving nature of concepts embedded in the growing body of research publications. As concepts evolve over time (e.g., keywords like global warming become more commonly referred to as climate change), past research may become harder to find and interpret in a modern context. This phenomenon, known as concept drift, affects how research topics and keywords are understood, categorized, and retrieved. Beyond temporal drift, such variations also occur across geographic space, reflecting differences in local policies, research priorities, and so forth. In this work, we introduce the notion of spatio-temporal concept drift to capture how concepts in scientific texts evolve across both space and time. Using a scientometric dataset in geographic information science, we detect how research keywords drifted across countries and years using word embeddings. By detecting spatio-temporal concept drift, we can better align archival research and bridge regional differences, ensuring scientific knowledge remains findable and interoperable within evolving research landscapes.
Cite as

Meilin Shi, Krzysztof Janowicz, Zilong Liu, Mina Karimi, Ivan Majic, and Alexandra Fortacz. What, When, and Where Do You Mean? Detecting Spatio-Temporal Concept Drift in Scientific Texts. In 13th International Conference on Geographic Information Science (GIScience 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 346, pp. 16:1-16:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{shi_et_al:LIPIcs.GIScience.2025.16,
  author =	{Shi, Meilin and Janowicz, Krzysztof and Liu, Zilong and Karimi, Mina and Majic, Ivan and Fortacz, Alexandra},
  title =	{{What, When, and Where Do You Mean? Detecting Spatio-Temporal Concept Drift in Scientific Texts}},
  booktitle =	{13th International Conference on Geographic Information Science (GIScience 2025)},
  pages =	{16:1--16:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-378-2},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{346},
  editor =	{Sila-Nowicka, Katarzyna and Moore, Antoni and O'Sullivan, David and Adams, Benjamin and Gahegan, Mark},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.GIScience.2025.16},
  URN =		{urn:nbn:de:0030-drops-238450},
  doi =		{10.4230/LIPIcs.GIScience.2025.16},
  annote =	{Keywords: Concept Drift, Ontology, Large Language Models, Research Data Management}
}
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.
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
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.
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
DOI: 10.4230/LIPIcs.CPM.2025.16
Net Occurrences in Fibonacci and Thue-Morse Words

Authors: Peaker Guo and Kaisei Kishi

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

Abstract
A net occurrence of a repeated string in a text is an occurrence with unique left and right extensions, and the net frequency of the string is the number of its net occurrences in the text. Originally introduced for applications in Natural Language Processing, net frequency has recently gained attention for its algorithmic aspects. Guo et al. [CPM 2024] and Ohlebusch et al. [SPIRE 2024] focus on its computation in the offline setting, while Guo et al. [SPIRE 2024], Inenaga [arXiv 2024], and Mieno and Inenaga [CPM 2025] tackle the online counterpart. Mieno and Inenaga also characterize net occurrences in terms of the minimal unique substrings of the text. Additionally, Guo et al. [CPM 2024] initiate the study of net occurrences in Fibonacci words to establish a lower bound on the asymptotic running time of algorithms. Although there has been notable progress in algorithmic developments and some initial combinatorial insights, the combinatorial aspects of net occurrences have yet to be thoroughly examined. In this work, we make two key contributions. First, we confirm the conjecture that each Fibonacci word contains exactly three net occurrences. Second, we show that each Thue-Morse word contains exactly nine net occurrences. To achieve these results, we introduce the notion of overlapping net occurrence cover, which narrows down the candidate net occurrences in any text. Furthermore, we provide a precise characterization of occurrences of Fibonacci and Thue-Morse words of smaller order, offering structural insights that may have independent interest and potential applications in algorithm analysis and combinatorial properties of these words.
Cite as

Peaker Guo and Kaisei Kishi. Net Occurrences in Fibonacci and Thue-Morse Words. In 36th Annual Symposium on Combinatorial Pattern Matching (CPM 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 331, pp. 16:1-16:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{guo_et_al:LIPIcs.CPM.2025.16,
  author =	{Guo, Peaker and Kishi, Kaisei},
  title =	{{Net Occurrences in Fibonacci and Thue-Morse Words}},
  booktitle =	{36th Annual Symposium on Combinatorial Pattern Matching (CPM 2025)},
  pages =	{16:1--16:22},
  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.2025.16},
  URN =		{urn:nbn:de:0030-drops-231107},
  doi =		{10.4230/LIPIcs.CPM.2025.16},
  annote =	{Keywords: Fibonacci words, Thue-Morse words, net occurrence, net frequency, factorization}
}
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}
}
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