124 Search Results for "Prezza, Nicola"

Volume

LIPIcs, Volume 369

37th Annual Symposium on Combinatorial Pattern Matching (CPM 2026)

CPM 2026, Copenhagen, Denmark, June 15-17, 2026

Editors: Philip Bille and Nicola Prezza

Volume

LIPIcs, Volume 338

23rd International Symposium on Experimental Algorithms (SEA 2025)

SEA 2025, July 22-24, 2025, Venice, Italy

Editors: Petra Mutzel and Nicola Prezza

Artifact
Software
DOI: 10.4230/artifacts.26761
STPD-index

Authors: Ruben Becker, Davide Cenzato, Travis Gagie, Ragnar Groot Koerkamp, Sung-Hwan Kim, Giovanni Manzini, and Nicola Prezza

Abstract
Cite as

Ruben Becker, Davide Cenzato, Travis Gagie, Ragnar Groot Koerkamp, Sung-Hwan Kim, Giovanni Manzini, Nicola Prezza. STPD-index (Software, Source Code). Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@misc{dagstuhl-artifact-26761,
   title = {{STPD-index}}, 
   author = {Becker, Ruben and Cenzato, Davide and Gagie, Travis and Groot Koerkamp, Ragnar and Kim, Sung-Hwan and Manzini, Giovanni and Prezza, Nicola},
   note = {Software, Funded by the European Union (ERC, REGINDEX, 101039208), swhId: \href{https://archive.softwareheritage.org/swh:1:dir:d4f76a2be744c622f98d403443e3f4507ae9b536;origin=https://github.com/regindex/STPD-index;visit=swh:1:snp:15232c90524e31eb789f2fce1686ae9a23d5f70f;anchor=swh:1:rev:4d8522e4fc1e7bc9781724352e4dcdefb0b8579d}{\texttt{swh:1:dir:d4f76a2be744c622f98d403443e3f4507ae9b536}} (visited on 2026-07-01)},
   url = {https://github.com/regindex/STPD-index},
   doi = {10.4230/artifacts.26761},
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2026.24
Compressing Suffix Trees by Path Decompositions

Authors: Ruben Becker, Davide Cenzato, Travis Gagie, Ragnar Groot Koerkamp, Sung-Hwan Kim, Giovanni Manzini, and Nicola Prezza

Published in: LIPIcs, Volume 374, 53rd International Colloquium on Automata, Languages, and Programming (ICALP 2026)

Abstract
The suffix tree is arguably the most fundamental data structure on strings: introduced by Weiner (SWAT 1973) and McCreight (JACM 1976), it allows solving a myriad of computational problems on strings in linear time. Motivated by its large space usage, subsequent research focused first on reducing its size by a constant factor via Suffix Arrays, and later on reaching space proportional to the size of the compressed string. Modern compressed indexes, such as the r-index (Gagie et al., JACM 2020), fit in space proportional to r, the number of runs in the Burrows-Wheeler transform (a strong and universal repetitiveness measure). These advances, however, came with a price: while modern compressed indexes boast optimal bounds in the RAM model, they are often orders of magnitude slower than uncompressed counterparts in practice due to catastrophic cache locality. This reality gap highlights that Big-O complexity in the RAM model has become a misleading predictor of real-world performance, leaving a critical question unanswered: can we design compressed indexes that are efficient in the I/O model of computation? We answer this in the affirmative by introducing a new Suffix Array sampling technique based on particular path decompositions of the suffix tree. We prove that sorting the suffix tree leaves by specific priority functions induces a decomposition where the number of distinct paths (each corresponding to a string suffix) is bounded by r. This allows us to solve indexed pattern matching efficiently in the I/O model using a Suffix Array sample of size at most r, strictly improving upon the (tight) 2r bound of Suffixient Arrays, another recent compressed Suffix Array sampling technique. Experiments confirm that this theoretical I/O efficiency translates to practice in pangenomic applications: our index locates pattern occurrences using less space and orders of magnitude less time than the r-index when performing pattern matching on repetitive DNA collections. Beyond this, our contributions are twofold: (i) unlike Suffixient Arrays, our technique supports most standard suffix tree operations in O(r) space on top of the text while matching the I/O complexity of uncompressed suffix trees; and (ii) we establish a general framework where any valid path decomposition induces a Suffix Array sampling whose size is a new strong repetitiveness measure; we provide a universal mechanism for locating all pattern occurrences for each such path decomposition.
Cite as

Ruben Becker, Davide Cenzato, Travis Gagie, Ragnar Groot Koerkamp, Sung-Hwan Kim, Giovanni Manzini, and Nicola Prezza. Compressing Suffix Trees by Path Decompositions. In 53rd International Colloquium on Automata, Languages, and Programming (ICALP 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 374, pp. 24:1-24:25, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{becker_et_al:LIPIcs.ICALP.2026.24,
  author =	{Becker, Ruben and Cenzato, Davide and Gagie, Travis and Groot Koerkamp, Ragnar and Kim, Sung-Hwan and Manzini, Giovanni and Prezza, Nicola},
  title =	{{Compressing Suffix Trees by Path Decompositions}},
  booktitle =	{53rd International Colloquium on Automata, Languages, and Programming (ICALP 2026)},
  pages =	{24:1--24:25},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-428-4},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{374},
  editor =	{Bhattacharya, Sayan and Nanongkai, Danupon and Benedikt, Michael and Puppis, Gabriele},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2026.24},
  URN =		{urn:nbn:de:0030-drops-264139},
  doi =		{10.4230/LIPIcs.ICALP.2026.24},
  annote =	{Keywords: Text indexing, suffix tree, I/O-efficient, Compressed Data Structures}
}
Document
DOI: 10.4230/LIPIcs.SEA.2026.13
Practical Parallel Block Tree Construction

Authors: Robert Clausecker, Florian Kurpicz, and Etienne Palanga

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

Abstract
The block tree [Belazzougui et al., J. Comput. Syst. Sci. '21] is a compressed representation of a length-n text that supports access, rank, and select queries while requiring only O(z log n/z) words of space, where z is the number of Lempel-Ziv factors of the text. In other words, its space requirements are asymptotically comparable to those of the compressed text itself. In practice, block trees offer query performance comparable to that of state-of-the-art compressed rank and select indices. However, their construction is significantly slower, and the fastest known construction algorithms additionally require a significant amount of working memory. To address these limitations, we propose fast and lightweight parallel algorithms for the efficient construction of block trees. Our algorithm achieves similar construction speed than the currently fastest block tree construction algorithm on a single core and is up to eight times faster using 64 cores, while requiring an order of magnitude less memory. Overall, we achieve a speedup of up to 15.5 on 64 cores, which is in line with the parallel construction of the Lempel-Ziv compression.
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Robert Clausecker, Florian Kurpicz, and Etienne Palanga. Practical Parallel Block Tree Construction. In 24th International Symposium on Experimental Algorithms (SEA 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 371, pp. 13:1-13:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{clausecker_et_al:LIPIcs.SEA.2026.13,
  author =	{Clausecker, Robert and Kurpicz, Florian and Palanga, Etienne},
  title =	{{Practical Parallel Block Tree Construction}},
  booktitle =	{24th International Symposium on Experimental Algorithms (SEA 2026)},
  pages =	{13:1--13:19},
  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.2026.13},
  URN =		{urn:nbn:de:0030-drops-260175},
  doi =		{10.4230/LIPIcs.SEA.2026.13},
  annote =	{Keywords: block tree, shared memory, compression, SIMD, Karp-Rabin fingerprints}
}
Document
DOI: 10.4230/LIPIcs.SEA.2026.11
Wavelet Forests Revisited

Authors: Eric Chiu and Dominik Kempa

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

Abstract
Rank and select queries are basic operations on sequences, with applications in compressed text indexes and other space-efficient data structures. One of the standard data structures supporting these queries is the wavelet tree. In this paper, we study wavelet forests, that is, wavelet-tree structures based on the fixed-block compression boosting technique. Such structures partition the input sequence into fixed-size blocks and build a separate wavelet tree for each block. Previous work showed that this approach yields strong practical performance for rank queries. We extend wavelet forests to support select queries. We show that select support can be added with little additional space overhead and that the resulting structures remain practically efficient. In experiments on a range of non-repetitive and repetitive inputs, wavelet forests are competitive with, and in most cases outperform, standalone wavelet-tree implementations. We also study the effect of internal parameters, including superblock size and navigational data, on select-query performance.
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Eric Chiu and Dominik Kempa. Wavelet Forests Revisited. In 24th International Symposium on Experimental Algorithms (SEA 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 371, pp. 11:1-11:11, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{chiu_et_al:LIPIcs.SEA.2026.11,
  author =	{Chiu, Eric and Kempa, Dominik},
  title =	{{Wavelet Forests Revisited}},
  booktitle =	{24th International Symposium on Experimental Algorithms (SEA 2026)},
  pages =	{11:1--11:11},
  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.2026.11},
  URN =		{urn:nbn:de:0030-drops-260152},
  doi =		{10.4230/LIPIcs.SEA.2026.11},
  annote =	{Keywords: wavelet tree, wavelet forest, select queries}
}
Document
DOI: 10.4230/LIPIcs.SEA.2026.9
Bounding the Average Move Structure Query for Faster and Smaller RLBWT Permutations

Authors: Nathaniel K. Brown and Ben Langmead

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

Abstract
The move structure represents permutations with long contiguously permuted intervals in compressed space with optimal query time. They have become an important feature of compressed text indexes using space proportional to the number of Burrows-Wheeler Transform (BWT) runs, often applied in genomics. This is in thanks not only to theoretical improvements over past approaches, but great cache efficiency and average case query time in practice. This is true even without using the worst case guarantees provided by the interval splitting balancing of the original result. In this paper, we show that an even simpler type of splitting, length capping by truncating long intervals, bounds the average move structure query time to optimal whilst obtaining a superior construction time than the traditional approach. This also proves constant query time when amortized over a full traversal of a single cycle permutation from an arbitrary starting position. Such a scheme has surprising benefits both in theory and practice. For a move structure with r runs over a domain n, we replace all O(r log n)-bit components to reduce the overall representation by O(r log r)-bits. The worst case query time is also improved to O(log n/r) without balancing. An O(r)-time and space construction lets us apply the method to run-length encoded BWT (RLBWT) permutations such as LF and ϕ to obtain optimal-time algorithms for BWT inversion and suffix array (SA) enumeration in O(r) working space. Finally, we introduce the Orbit library, providing flexible plug and play move structure support, and use it to evaluate our splitting approach. Experiments find length capping construction is faster and uses less memory than balancing, and results in faster move structure queries: up to ∼ 17 times faster when compared to an unbalanced representation of ϕ. We also see a space reduction in practice, with at least a ∼ 40% disk size decrease for LF across large repetitive genomic collections when compared to a balanced/unbalanced move structure.
Cite as

Nathaniel K. Brown and Ben Langmead. Bounding the Average Move Structure Query for Faster and Smaller RLBWT Permutations. In 24th International Symposium on Experimental Algorithms (SEA 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 371, pp. 9:1-9:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{brown_et_al:LIPIcs.SEA.2026.9,
  author =	{Brown, Nathaniel K. and Langmead, Ben},
  title =	{{Bounding the Average Move Structure Query for Faster and Smaller RLBWT Permutations}},
  booktitle =	{24th International Symposium on Experimental Algorithms (SEA 2026)},
  pages =	{9:1--9:15},
  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.2026.9},
  URN =		{urn:nbn:de:0030-drops-260136},
  doi =		{10.4230/LIPIcs.SEA.2026.9},
  annote =	{Keywords: Move Structure, Burrows-Wheeler Transform, Permutation}
}
Document
DOI: 10.4230/LIPIcs.SEA.2026.16
Efficient Large-Scale Text Precompression via Approximate LZ77 Parsings

Authors: Patrick Dinklage

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

Abstract
The LZ77 [Lempel and Ziv, 1977] compression scheme is ubiquitous: it lies at the core of everyday general-purpose standard compressors such as gzip or zstd, but also behind the scenes of many applications such as the compression of payloads transmitted in networks. Computing the exact LZ77 parsing is largely solved in theory: it can be done in sublinear time and space, in compressed space and in external memory, to name but some scenarios. However, these approaches are often impractical for everyday use due to their intensive time or space requirements. Standard compressors tackle this issue by introducing heuristics that go hand in hand with sophisticated encoding schemes to achieve very good compression fast and in small space, however, they only have a local view (e.g., a sliding window) on the input, potentially missing out on long-range repetitions that may be located far apart from one another. In this work, we design and implement - in C++ and leveraging shared-memory parallelism - compression pipelines that first precompress the input using an approximate LZ77 parsing taking care of long-range repetitions. This then serves as an assist to standard compressors for producing a succinct encoding of the remaining short and local repetitions. Similar approaches have been considered by [Kosolobov et al., 2020] and [Nalbach, 2024], respectively using Relative Lempel Ziv [Kuruppu et al. 2010] or the string synchronizing set [Kempa & Kociumaka, 2019]. We fill a gap taking the route via the prefix-free parsing [Boucher et al., 2019], using an intermediate result of [Hong et al., 2023]. On large repetitive inputs of tens of gigabytes, our pipelines are orders of magnitudes faster than the state of the art for computing the exact LZ77 parsing, use space less than the input size and still - despite producing more phrases - achieve the best overall compression in comparison to related work.
Cite as

Patrick Dinklage. Efficient Large-Scale Text Precompression via Approximate LZ77 Parsings. In 24th International Symposium on Experimental Algorithms (SEA 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 371, pp. 16:1-16:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{dinklage:LIPIcs.SEA.2026.16,
  author =	{Dinklage, Patrick},
  title =	{{Efficient Large-Scale Text Precompression via Approximate LZ77 Parsings}},
  booktitle =	{24th International Symposium on Experimental Algorithms (SEA 2026)},
  pages =	{16:1--16:20},
  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.2026.16},
  URN =		{urn:nbn:de:0030-drops-260204},
  doi =		{10.4230/LIPIcs.SEA.2026.16},
  annote =	{Keywords: compression, algorithm engineering, parallel computation}
}
Document
DOI: 10.4230/LIPIcs.CPM.2026.2
Near-Real-Time Solutions for Online String Problems

Authors: Dominik Köppl and Gregory Kucherov

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

Abstract
Based on the Breslauer-Italiano online suffix tree construction algorithm (2013) with double logarithmic worst-case guarantees on the update time per letter, we develop near-real-time algorithms for several classical problems on strings, including the computation of the longest repeating suffix array, the (reversed) Lempel-Ziv 77 factorization, and the maintenance of minimal unique substrings, all in an online manner. Our solutions improve over the best known running times for these problems in terms of the worst-case time per letter, for which we achieve a poly-log-logarithmic time complexity, within a linear space. Best known results for these problems require a poly-logarithmic time complexity per letter or only provide amortized complexity bounds. As a result of independent interest, we give conversions between the longest previous factor array and the longest repeating suffix array in space and time bounds based on their irreducible representations, which can have sizes sublinear in the length of the input string.
Cite as

Dominik Köppl and Gregory Kucherov. Near-Real-Time Solutions for Online String Problems. In 37th Annual Symposium on Combinatorial Pattern Matching (CPM 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 369, pp. 2:1-2:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{koppl_et_al:LIPIcs.CPM.2026.2,
  author =	{K\"{o}ppl, Dominik and Kucherov, Gregory},
  title =	{{Near-Real-Time Solutions for Online String Problems}},
  booktitle =	{37th Annual Symposium on Combinatorial Pattern Matching (CPM 2026)},
  pages =	{2:1--2:17},
  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.2026.2},
  URN =		{urn:nbn:de:0030-drops-259287},
  doi =		{10.4230/LIPIcs.CPM.2026.2},
  annote =	{Keywords: online algorithms, string algorithms, suffix tree, real-time computation, Lempel-Ziv factorization, minimal unique substrings}
}
Document
DOI: 10.4230/LIPIcs.CPM.2026.3
Computing k-mers in Graphs

Authors: Jarno N. Alanko and Máximo Pérez-López

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

Abstract
We initiate the study of computational problems on k-mers (strings of length k) in labeled graphs. As a starting point, we consider the problem of counting the number of distinct k-mers found on the walks of a graph. We establish that this is #P-hard, even on connected deterministic DAGs. However, in the class of deterministic Wheeler graphs (Gagie, Manzini, and Sirén, TCS 2017), we show that distinct k-mers of such a graph W = (V, E) can be counted using O(|W|k) or O(n⁴ log k) arithmetic operations, where n = |V|, m = |E| and |W| = n+m. The latter result uses a new generalization of the technique of prefix doubling to Wheeler graphs. To generalize our results beyond Wheeler graphs, we discuss ways to transform a graph into a Wheeler graph in a manner that preserves the k-mers. As an application of our k-mer counting algorithms, we construct a representation of the de Bruijn graph of the k-mers that occupies O(n_k + |W|k log(max_{1 ≤ 𝓁 ≤ k} n_𝓁) + σlog m) bits of space, where n_𝓁 is the number of distinct 𝓁-mers in the Wheeler graph, and σ is the size of the alphabet. We show how to construct it in the same time complexity. Given that the Wheeler graph can be exponentially smaller than the de Bruijn graph, for large k this provides a theoretical improvement over previous de Bruijn graph construction methods from graphs, which must spend Ω(k) time per k-mer in the graph.
Cite as

Jarno N. Alanko and Máximo Pérez-López. Computing k-mers in Graphs. In 37th Annual Symposium on Combinatorial Pattern Matching (CPM 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 369, pp. 3:1-3:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{alanko_et_al:LIPIcs.CPM.2026.3,
  author =	{Alanko, Jarno N. and P\'{e}rez-L\'{o}pez, M\'{a}ximo},
  title =	{{Computing k-mers in Graphs}},
  booktitle =	{37th Annual Symposium on Combinatorial Pattern Matching (CPM 2026)},
  pages =	{3:1--3:17},
  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.2026.3},
  URN =		{urn:nbn:de:0030-drops-259294},
  doi =		{10.4230/LIPIcs.CPM.2026.3},
  annote =	{Keywords: Wheeler graph, Wheeler language, de Bruijn graph, graph, k-mer, q-gram, DFA, #P-hard}
}
Document
DOI: 10.4230/LIPIcs.CPM.2026.4
Compact Representation of Maximal Palindromes

Authors: Takuya Mieno

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

Abstract
Palindromes are strings that read the same forward and backward. The computation of palindromic structures within strings is a fundamental problem in string algorithms, being motivated by potential applications in formal language theory and bioinformatics. Although the number of palindromic factors in a string of length n can be quadratic, they can be implicitly represented in O(n log n) bits of space by storing the lengths of all maximal palindromes in an integer array, which can be computed in O(n) time [Manacher, 1975]. In this paper, we propose a novel O(n)-bit representation of all maximal palindromes in a string, which enables O(1)-time retrieval of the length of the maximal palindrome centered at any given position. The data structure can be constructed in O(n) time from the input string of length n. Since Manacher’s algorithm and the notion of maximal palindromes are widely utilized for solving numerous problems involving palindromic structures, our compact representation will accelerate the development of more space-efficient solutions to such problems. Indeed, as the first application of our compact representation of maximal palindromes, we present a data structure of size O(n) bits that can compute the longest palindrome appearing in any given factor of a string of length n in O(log n) time.
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Takuya Mieno. Compact Representation of Maximal Palindromes. In 37th Annual Symposium on Combinatorial Pattern Matching (CPM 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 369, pp. 4:1-4:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{mieno:LIPIcs.CPM.2026.4,
  author =	{Mieno, Takuya},
  title =	{{Compact Representation of Maximal Palindromes}},
  booktitle =	{37th Annual Symposium on Combinatorial Pattern Matching (CPM 2026)},
  pages =	{4:1--4:12},
  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.2026.4},
  URN =		{urn:nbn:de:0030-drops-259304},
  doi =		{10.4230/LIPIcs.CPM.2026.4},
  annote =	{Keywords: palindromes, succinct data structures, internal queries}
}
Document
DOI: 10.4230/LIPIcs.CPM.2026.5
Efficient Grammar Compression via RLZ-Based RePair

Authors: Rahul Varki, Travis Gagie, and Christina Boucher

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

Abstract
Among grammar-based compression techniques, RePair is a notable offline encoding scheme known for its simplicity and powerful combinatorial properties, producing compact grammars by repeatedly replacing the most frequent adjacent pairs of symbols, known as bigrams. However, RePair’s memory usage scales poorly with input size, as it loads the entire text into memory. In contrast, Relative Lempel-Ziv (RLZ) parsing offers a scalable and lightweight online encoding scheme that losslessly represents a text in terms of phrases that refer to a reference string, but it often fails to expose deeper structural patterns. We introduce an algorithm that produces a RePair grammar from the RLZ parse of the input, leveraging the strengths of both methods. Our method, RLZ-RePair, performs bigram replacements systematically, preserving the integrity of the RLZ phrases throughout the RePair iterations. When the reference is well chosen, our method achieves the same grammar as standard RePair while significantly reducing both memory usage and the number of bigram replacements. In particular, we show that RLZ-RePair can reduce memory usage by more than 80% while incurring only a modest runtime increase compared to RePair. To our knowledge, RLZ-RePair is one of the first scalable methods that constructs exact RePair grammars, resulting in a grammar-based compressor that is both practical for large datasets and faithful to the theoretical elegance of RePair.
Cite as

Rahul Varki, Travis Gagie, and Christina Boucher. Efficient Grammar Compression via RLZ-Based RePair. In 37th Annual Symposium on Combinatorial Pattern Matching (CPM 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 369, pp. 5:1-5:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{varki_et_al:LIPIcs.CPM.2026.5,
  author =	{Varki, Rahul and Gagie, Travis and Boucher, Christina},
  title =	{{Efficient Grammar Compression via RLZ-Based RePair}},
  booktitle =	{37th Annual Symposium on Combinatorial Pattern Matching (CPM 2026)},
  pages =	{5:1--5:15},
  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.2026.5},
  URN =		{urn:nbn:de:0030-drops-259310},
  doi =		{10.4230/LIPIcs.CPM.2026.5},
  annote =	{Keywords: RePair, RLZ, Grammar Compression}
}
Document
DOI: 10.4230/LIPIcs.CPM.2026.6
Improved Bounds on the Maximum Number of Distinct Squares in Circular Words

Authors: Panagiotis Charalampopoulos, Manal Mohamed, Jakub Radoszewski, Wojciech Rytter, Tomasz Waleń, and Wiktor Zuba

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

Abstract
We investigate the asymptotic growth of function CS(n), which maps n to the maximum number of distinct squares in a circular word of length n (that is, the maximum number of distinct squares of length at most n in a word ww of length 2n). We improve upon the lower bound of 1.25n established by Amit and Gawrychowski [SPIRE 2017] and the straightforward upper bound of 2n, which follows from the recent result of Brlek and Li [Comb. Theory, 2025] stating that there are fewer than n squares in standard (i.e., non-circular) words of length n. (Previously, Amit and Gawrychowski gave an upper bound of 32/15n using a weaker upper bound on squares in standard words.) Specifically, we show that CS(n) ≤ ⌈1.8 n⌉ and that, for infinitely many n, CS(n) ≥ 1.5n-𝒪(√n). For the lower bound, we exploit the combinatorial structure of Fibonacci words to construct a family of square-rich circular words. For the upper bound, we exploit density properties of the starting positions of long squares, adapting an approach of Amit and Gawrychowski.
Cite as

Panagiotis Charalampopoulos, Manal Mohamed, Jakub Radoszewski, Wojciech Rytter, Tomasz Waleń, and Wiktor Zuba. Improved Bounds on the Maximum Number of Distinct Squares in Circular Words. In 37th Annual Symposium on Combinatorial Pattern Matching (CPM 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 369, pp. 6:1-6:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{charalampopoulos_et_al:LIPIcs.CPM.2026.6,
  author =	{Charalampopoulos, Panagiotis and Mohamed, Manal and Radoszewski, Jakub and Rytter, Wojciech and Wale\'{n}, Tomasz and Zuba, Wiktor},
  title =	{{Improved Bounds on the Maximum Number of Distinct Squares in Circular Words}},
  booktitle =	{37th Annual Symposium on Combinatorial Pattern Matching (CPM 2026)},
  pages =	{6:1--6:12},
  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.2026.6},
  URN =		{urn:nbn:de:0030-drops-259325},
  doi =		{10.4230/LIPIcs.CPM.2026.6},
  annote =	{Keywords: circular words, squares, repetitions}
}
Document
DOI: 10.4230/LIPIcs.CPM.2026.9
Indexing and Encoding Arrays for Element Distinctness Queries

Authors: Johannes Fischer and Filippo Lari

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

Abstract
We introduce the data structure variant of the well-known element distinctness problem. Given an array of n elements, the goal is to preprocess the array into a data structure that supports queries asking whether all elements within a given query range are distinct. This has applications in text indexing and possibly also in other algorithmic domains. In the indexing model (where access to the input array is allowed), we design a data structure using O((n log b)/b) bits and answering queries in the time needed to solve an online element distinctness instance of size O(b), for any b ≥ 1. As a concrete instantiation of this, there exists an index that answers queries in O(log log log n) time using O({n log²(log log log n)}/{log log log n}) bits of additional space. Moving to the encoding model (where access to the input array is not allowed), we begin by proving an information-theoretic lower bound for the space usage of 2n-O(log n) bits, and then design a matching encoding with O(1) time queries. We then consider the case in which the alphabet size σ is constant. In this setting, the lower bound can be refined to n log(r_σ) - 3 log(σ+2) + O(1) bits, where r_σ = 4cos²(π/(σ+2)). This lower bound is matched by an encoding with O(1) time queries.
Cite as

Johannes Fischer and Filippo Lari. Indexing and Encoding Arrays for Element Distinctness Queries. In 37th Annual Symposium on Combinatorial Pattern Matching (CPM 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 369, pp. 9:1-9:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{fischer_et_al:LIPIcs.CPM.2026.9,
  author =	{Fischer, Johannes and Lari, Filippo},
  title =	{{Indexing and Encoding Arrays for Element Distinctness Queries}},
  booktitle =	{37th Annual Symposium on Combinatorial Pattern Matching (CPM 2026)},
  pages =	{9:1--9:17},
  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.2026.9},
  URN =		{urn:nbn:de:0030-drops-259350},
  doi =		{10.4230/LIPIcs.CPM.2026.9},
  annote =	{Keywords: element distinctness, range queries, lower bounds, succinct data structures}
}
Document
DOI: 10.4230/LIPIcs.CPM.2026.10
R-Enum Revisited: Speedup and Extension for Context-Sensitive Repeats and Net Frequencies

Authors: Kotaro Kimura and Tomohiro I

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

Abstract
A repeat is a substring that occurs at least twice in a string, and is called a maximal repeat if it cannot be extended outwards without reducing its frequency. Nishimoto and Tabei [CPM, 2021] proposed r-enum, an algorithm to enumerate various characteristic substrings, including maximal repeats, in a string T of length n in O(r) words of compressed working space, where r ≤ n is the number of runs in the Burrows-Wheeler transform (BWT) of T. Given the run-length encoded BWT (RLBWT) of T, r-enum runs in O(n log log_w (n/r)) time in addition to the time linear to the number of output strings, where w = Θ(log n) is the word size. In this paper, we first improve the O(n log log_w (n/r)) term to O(n). We next extend r-enum to compute other context-sensitive repeats such as near-supermaximal repeats (NSMRs) and supermaximal repeats, as well as the context diversity for every maximal repeat in the same complexities. Furthermore, we study net occurrences: An occurrence of a repeat is called a net occurrence if it is not covered by another repeat, and the net frequency of a repeat is the number of its net occurrences. With this terminology, an NSMR is a repeat with a positive net frequency. Given the RLBWT of T, we show how to compute the set 𝒮^{nsmr} of all NSMRs in T together with their net frequency/occurrences in O(n) time and O(r) space. We also show that an O(r)-space data structure can be built from the RLBWT to compute the net frequency/occurrences of any pattern in optimal time. The data structure is built in O(r) space and in O(n) time with high probability or deterministic O(n + |𝒮^{nsmr}| log log min(σ, |𝒮^{nsmr}|)) time, where σ ≤ r is the alphabet size of T. To achieve this, we prove that the total number of net occurrences is less than 2r. With the duality between net occurrences and minimal unique substrings (MUSs), we get a new upper bound 2r of the number of MUSs in T, which may be of independent interest.
Cite as

Kotaro Kimura and Tomohiro I. R-Enum Revisited: Speedup and Extension for Context-Sensitive Repeats and Net Frequencies. In 37th Annual Symposium on Combinatorial Pattern Matching (CPM 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 369, pp. 10:1-10:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{kimura_et_al:LIPIcs.CPM.2026.10,
  author =	{Kimura, Kotaro and I, Tomohiro},
  title =	{{R-Enum Revisited: Speedup and Extension for Context-Sensitive Repeats and Net Frequencies}},
  booktitle =	{37th Annual Symposium on Combinatorial Pattern Matching (CPM 2026)},
  pages =	{10:1--10:14},
  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.2026.10},
  URN =		{urn:nbn:de:0030-drops-259361},
  doi =		{10.4230/LIPIcs.CPM.2026.10},
  annote =	{Keywords: Supermaximal repeats, Largest maximal repeats, Net frequencies, Run-length Burrows-Wheeler transform, Compressed data mining}
}
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