25 Search Results for "Ellert, Jonas"

Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2026.55
Suffix Random Access via Function Inversion: A Key for Asymmetric Streaming String Algorithms

Authors: Panagiotis Charalampopoulos, Taha El Ghazi, Jonas Ellert, Paweł Gawrychowski, and Tatiana Starikovskaya

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

Abstract
Many string processing problems can be phrased in the streaming setting, where the input arrives symbol by symbol and we have sublinear working space. The area of streaming algorithms for string processing has flourished since the seminal work of Porat and Porat [FOCS 2009]. Unfortunately, problems with efficient solutions in the classical setting often do not admit efficient solutions in the streaming setting. As a bridge between these two settings, Saks and Seshadhri [SODA 2013] introduced the asymmetric streaming model (see also [Andoni, Krauthgamer, and Onak; FOCS 2010]). Here, one is given read-only access to a (typically short) reference string R of length m, while a (typically long) text T arrives as a stream. We provide a generic technique to reduce fundamental string problems in the asymmetric streaming model to the online read-only model, lifting several existing algorithms and generally improving upon the state of the art. Most notably, we obtain asymmetric streaming algorithms for exact and approximate pattern matching (under both the Hamming and edit distances), and for relative Lempel-Ziv compression, a popular scheme for measuring and exploiting redundancy in repetitive text collections. At the heart of our approach lies a novel tool that facilitates efficient computation in the asymmetric streaming model: the suffix random access data structure. In its simplest variant, it maintains constant-time random access to the longest suffix of (the seen prefix of) T that occurs in R. Let τ be a parameter that denotes the size of the data structure. A straightforward approach maintains the data structure in {O}(m/τ) time per arriving symbol of T. We drastically improve this tradeoff and reveal fundamental barriers via a bidirectional reduction between suffix random access and function inversion, a central problem in cryptography: - By leveraging Fiat and Naor’s function inversion data structure [SIAM J. Comput. 2000], we achieve Õ(1+m³/τ⁶) update time. In particular, for τ = √m, we obtain Õ(1) update time, improving over the Ω(√m) bound of the straightforward solution. - We establish an unconditional Ω̃(m/τ³) lower bound on the update time. Additionally, we show that achieving update time o(m³/τ⁷) would imply a breakthrough in function inversion. On the way to our upper bound, we propose a variant of the string synchronizing sets ([Kempa and Kociumaka; STOC 2019]) with a local sparsity condition that, as we show, admits an efficient streaming construction algorithm. We believe that our framework and techniques will find broad applications in the development of small-space string algorithms.
Cite as

Panagiotis Charalampopoulos, Taha El Ghazi, Jonas Ellert, Paweł Gawrychowski, and Tatiana Starikovskaya. Suffix Random Access via Function Inversion: A Key for Asymmetric Streaming String Algorithms. In 53rd International Colloquium on Automata, Languages, and Programming (ICALP 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 374, pp. 55:1-55:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{charalampopoulos_et_al:LIPIcs.ICALP.2026.55,
  author =	{Charalampopoulos, Panagiotis and El Ghazi, Taha and Ellert, Jonas and Gawrychowski, Pawe{\l} and Starikovskaya, Tatiana},
  title =	{{Suffix Random Access via Function Inversion: A Key for Asymmetric Streaming String Algorithms}},
  booktitle =	{53rd International Colloquium on Automata, Languages, and Programming (ICALP 2026)},
  pages =	{55:1--55:20},
  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.2026.55},
  URN =		{urn:nbn:de:0030-drops-264440},
  doi =		{10.4230/LIPIcs.ICALP.2026.55},
  annote =	{Keywords: streaming algorithms, function inversion, string algorithms}
}
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.
Cite as

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.
Cite as

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.2026.16
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.2026.4
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.
Cite as

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.SWAT.2026.13
Faster Algorithms for Shortest Unique or Absent Substrings

Authors: Panagiotis Charalampopoulos, Manal Mohamed, Solon P. Pissis, Hilde Verbeek, and Wiktor Zuba

Published in: LIPIcs, Volume 370, 20th Scandinavian Symposium on Algorithm Theory (SWAT 2026)

Abstract
We revisit two well-known algorithmic problems on strings: computing a shortest unique substring (SUS) and a shortest absent substring (SAS) in a string S of length n. Both problems admit folklore 𝒪(n)-time solutions using the suffix tree of S. However, for small alphabets, this complexity is not necessarily optimal in the word RAM model, where a string of length n over alphabet [0,σ) can be stored in 𝒪(n log σ/log n) space and read in 𝒪(n log σ/log n) time. We present an 𝒪(n log σ/√{log n})-time algorithm for computing a SUS in S. This algorithm decomposes the problem according to the length and the period of the sought substring and uses several tools and techniques, such as synchronizing sets, the analysis of runs, and wavelet trees, to reduce the computation of a SUS to a simple geometric problem. Further, we adapt this algorithm and combine it with an efficient construction of de Bruijn sequences in order to obtain an 𝒪(n log σ/√{log n})-time algorithm for computing a SAS in S.
Cite as

Panagiotis Charalampopoulos, Manal Mohamed, Solon P. Pissis, Hilde Verbeek, and Wiktor Zuba. Faster Algorithms for Shortest Unique or Absent Substrings. In 20th Scandinavian Symposium on Algorithm Theory (SWAT 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 370, pp. 13:1-13:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{charalampopoulos_et_al:LIPIcs.SWAT.2026.13,
  author =	{Charalampopoulos, Panagiotis and Mohamed, Manal and Pissis, Solon P. and Verbeek, Hilde and Zuba, Wiktor},
  title =	{{Faster Algorithms for Shortest Unique or Absent Substrings}},
  booktitle =	{20th Scandinavian Symposium on Algorithm Theory (SWAT 2026)},
  pages =	{13:1--13:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-421-5},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{370},
  editor =	{Fraigniaud, Pierre},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SWAT.2026.13},
  URN =		{urn:nbn:de:0030-drops-260493},
  doi =		{10.4230/LIPIcs.SWAT.2026.13},
  annote =	{Keywords: string algorithms, unique substrings, absent substrings, absent words}
}
Document
DOI: 10.4230/LIPIcs.CPM.2026.28
Periodicity Property Testing on Strings with Wildcards

Authors: Carl Barton, Panagiotis Charalampopoulos, Taha El Ghazi, Jonas Ellert, Oded Lachish, and Tatiana Starikovskaya

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

Abstract
In this work, we study periodicity in strings with wildcards. A string T with at most k wildcards is called strongly (p,k)-periodic if the wildcards in T can be replaced with alphabet symbols to obtain a string with period p, and weakly (p,k)-periodic if T[i] matches T[i+p] for all i. Intuitively, both generalize to (≤ g, k)-periodicity, which is the property of being (p,k)-periodic for some p ∈ [1..g]. An ε-tester for a property 𝒫 is an algorithm that distinguishes between strings that satisfy 𝒫 and strings where one needs to change at least an ε-fraction of the symbols to obtain a string that satisfies 𝒫. We study one-sided error testers, where strings satisfying 𝒫 must always be accepted, while strings that are ε-far must be rejected with probability at least 2/3. The complexity of a tester is the worst-case number of symbols of an input of length n it must read to make the decision. We design the following testers for p,g ≤ n/2: 1) An ε-tester for strong (p,k)-periodicity with complexity Õ_ε(1) . 2) An ε-tester for strong (≤ g,k)-periodicity with complexity Õ_ε(√g). 3) An ε-tester for weak (p,k)-periodicity with complexity Õ_ε(min(k, n /(k+p))). 4) An ε-tester for weak (≤ g,k)-periodicity with complexity Õ_ε(min(k+ √{gk}, n/√k)). Additionally, we show a lower bound on the complexity of ε-testers for weak (≤ g,k)-periodicity, implying that our tester for weak (≤ g,k)-periodicity is optimal up to a multiplicative (ε^{-1} ln(gk))^O(1) factor for a wide range of g and k. Finally, our tester for strong (≤ g,k)-periodicity generalizes the one of [Lachish and Newman; Algorithmica 2011] for strings without wildcards, matching (up to polylogarithmic factors) the unconditional lower bound of ̃Ω(√g) in said work for constant ε.
Cite as

Carl Barton, Panagiotis Charalampopoulos, Taha El Ghazi, Jonas Ellert, Oded Lachish, and Tatiana Starikovskaya. Periodicity Property Testing on Strings with Wildcards. In 37th Annual Symposium on Combinatorial Pattern Matching (CPM 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 369, pp. 28:1-28:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{barton_et_al:LIPIcs.CPM.2026.28,
  author =	{Barton, Carl and Charalampopoulos, Panagiotis and Ghazi, Taha El and Ellert, Jonas and Lachish, Oded and Starikovskaya, Tatiana},
  title =	{{Periodicity Property Testing on Strings with Wildcards}},
  booktitle =	{37th Annual Symposium on Combinatorial Pattern Matching (CPM 2026)},
  pages =	{28:1--28:18},
  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.2026.28},
  URN =		{urn:nbn:de:0030-drops-259543},
  doi =		{10.4230/LIPIcs.CPM.2026.28},
  annote =	{Keywords: periodicity, property testing, wildcards}
}
Document
DOI: 10.4230/LIPIcs.CPM.2026.35
Efficient Index for Square Pattern Matching

Authors: Po-Chun Chen, Che-Wei Tsao, Wing-Kai Hon, and Dominik Köppl

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

Abstract
A string S is called a square if it can be written as the concatenation of two identical strings. Two strings P and Q of the same length are said to square match if, for every substring of P, it is a square if and only if the corresponding substring of Q is also a square. The square pattern matching problem asks for locating all substrings of a given text T of length n that square match a query pattern P of length m. This notion captures similarity in repetition structures and is motivated by applications in areas such as bioinformatics and music structure analysis. In this paper, we introduce a novel technique, called the longest prefix square (LPS) encoding, which represents the square structure of a string as an integer array of the same length. We show that two strings square match if and only if they have identical LPS encodings. Based on this result, we construct an index solving the square pattern matching problem in time O(m lg m + occ) using O(nlg²n) bits of space, where occ denotes the number of occurrences of substrings in T that square match P. If the LPS encoding of P is precomputed, the query time improves to O(m + occ).
Cite as

Po-Chun Chen, Che-Wei Tsao, Wing-Kai Hon, and Dominik Köppl. Efficient Index for Square Pattern Matching. In 37th Annual Symposium on Combinatorial Pattern Matching (CPM 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 369, pp. 35:1-35:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{chen_et_al:LIPIcs.CPM.2026.35,
  author =	{Chen, Po-Chun and Tsao, Che-Wei and Hon, Wing-Kai and K\"{o}ppl, Dominik},
  title =	{{Efficient Index for Square Pattern Matching}},
  booktitle =	{37th Annual Symposium on Combinatorial Pattern Matching (CPM 2026)},
  pages =	{35:1--35:12},
  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.2026.35},
  URN =		{urn:nbn:de:0030-drops-259617},
  doi =		{10.4230/LIPIcs.CPM.2026.35},
  annote =	{Keywords: string algorithms, pattern matching, indexing, squares}
}
Document
DOI: 10.4230/LIPIcs.STACS.2026.26
Approximate Cartesian Tree Matching with Substitutions

Authors: Panagiotis Charalampopoulos, Jonas Ellert, and Manal Mohamed

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

Abstract
The Cartesian tree of a sequence captures the relative order of the sequence’s elements. In recent years, Cartesian tree matching has attracted considerable attention, particularly due to its applications in time series analysis. Consider a text T of length n and a pattern P of length m. In the exact Cartesian tree matching problem, the task is to find all length-m fragments of T whose Cartesian tree coincides with the Cartesian tree CT(P) of the pattern. Although the exact version of the problem can be solved in linear time [Park et al., TCS 2020], it remains rather restrictive; for example, it is not robust to outliers in the pattern. To overcome this limitation, we consider the approximate setting, where the goal is to identify all fragments of T that are close to some string whose Cartesian tree matches CT(P). In this work, we quantify closeness via the widely used Hamming distance metric. For a given integer parameter k > 0, we present an algorithm that computes all fragments of T that are at Hamming distance at most k from a string whose Cartesian tree matches CT(P). Our algorithm runs in time 𝒪(n √m ⋅ k^{2.5}) for k ≤ m^{1/5} and in time 𝒪(nk⁵) for k ≥ m^{1/5}, thereby improving upon the state-of-the-art 𝒪(nmk)-time algorithm of Kim and Han [TCS 2025] in the regime k = o(m^{1/4}). On the way to our solution, we develop a toolbox of independent interest. First, we introduce a new notion of periodicity in Cartesian trees. Then, we lift multiple well-known combinatorial and algorithmic results for string matching and periodicity in strings to Cartesian tree matching and periodicity in Cartesian trees.
Cite as

Panagiotis Charalampopoulos, Jonas Ellert, and Manal Mohamed. Approximate Cartesian Tree Matching with Substitutions. In 43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 364, pp. 26:1-26:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{charalampopoulos_et_al:LIPIcs.STACS.2026.26,
  author =	{Charalampopoulos, Panagiotis and Ellert, Jonas and Mohamed, Manal},
  title =	{{Approximate Cartesian Tree Matching with Substitutions}},
  booktitle =	{43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026)},
  pages =	{26:1--26:21},
  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.2026.26},
  URN =		{urn:nbn:de:0030-drops-255151},
  doi =		{10.4230/LIPIcs.STACS.2026.26},
  annote =	{Keywords: Cartesian tree, Hamming distance, approximate pattern matching}
}
Document
DOI: 10.4230/LIPIcs.STACS.2026.36
Time-Optimal Construction of String Synchronizing Sets

Authors: Jonas Ellert and Tomasz Kociumaka

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

Abstract
A powerful design principle behind many modern string algorithms is local consistency: breaking the symmetry between string positions based on their small contexts so that matching fragments are handled consistently. Among the most influential instantiations of this principle are string synchronizing sets [Kempa & Kociumaka; STOC 2019]. A τ-synchronizing set of a string of length n is a set of O(n/τ) string positions, chosen using their length-2τ contexts, such that (outside of highly periodic regions) every block of τ consecutive positions contains at least one element of the set. Synchronizing sets have found dozens of applications in diverse settings, from quantum and dynamic algorithms to fully compressed computation. In the classic word RAM model, particularly for strings over small alphabets, they enabled faster solutions to core problems in data compression, text indexing, and string similarity. In this work, we show that any string T ∈ [0 .. σ)ⁿ can be preprocessed in O(n log σ / log n) time so that, for any given integer τ ∈ [1 .. n], a τ-synchronizing set of T can be constructed in O((n log τ)/(τ log n)) time. Both bounds are optimal in the word RAM model with machine word size w = Θ(log n), matching the information-theoretic minimum for the input and output sizes, respectively. Previously, constructing a τ-synchronizing set required O(n/τ) time after an O(n)-time preprocessing [Kociumaka, Radoszewski, Rytter, and Waleń; SICOMP 2024], or, in the restricted regime of τ < 0.2 log_σ n, without any preprocessing needed [Kempa & Kociumaka; STOC 2019]. A simple instantiation of our method outputs the synchronizing set as a sorted list in O(n/τ) time, or as a bitmask in O(n/log n) time. Our optimal construction produces a compact fully indexable dictionary, supporting select queries in O(1) time and rank queries in O(log ((log τ)/(log log n))) time. The latter complexity matches known unconditional cell-probe lower bounds for τ ≤ n^{1-Ω(1)}. To achieve this, we introduce a general framework for efficiently processing sparse integer sequences via a custom variable-length encoding. We also augment the optimal variant of van Emde Boas trees [Pătraşcu & Thorup; STOC 2006] with a deterministic linear-time construction. When the set is represented as a bitmask under our sparse encoding, the same guarantees for select and rank queries hold after preprocessing in time proportional to the size of our encoding (in words).
Cite as

Jonas Ellert and Tomasz Kociumaka. Time-Optimal Construction of String Synchronizing Sets. In 43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 364, pp. 36:1-36:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{ellert_et_al:LIPIcs.STACS.2026.36,
  author =	{Ellert, Jonas and Kociumaka, Tomasz},
  title =	{{Time-Optimal Construction of String Synchronizing Sets}},
  booktitle =	{43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026)},
  pages =	{36:1--36:22},
  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.2026.36},
  URN =		{urn:nbn:de:0030-drops-255258},
  doi =		{10.4230/LIPIcs.STACS.2026.36},
  annote =	{Keywords: synchronizing sets, local consistency, packed strings}
}
Document
DOI: 10.4230/LIPIcs.ISAAC.2025.9
Small Space Encoding and Recognition of k-Palindromic Prefixes

Authors: Gabriel Bathie, Jonas Ellert, and Tatiana Starikovskaya

Published in: LIPIcs, Volume 359, 36th International Symposium on Algorithms and Computation (ISAAC 2025)

Abstract
Palindromes are non-empty strings that read the same forward and backward. We study the problem of recognizing so-called k-palindromic strings, which can be represented as the concatenation of exactly k palindromes. [Rubinchik and Shur, MFCS 2020] showed that the problem is solvable in linear space and time. We present a read-only algorithm that recognizes all k-palindromic prefixes of a string T of length n in O(n ⋅ 6^{k²} ⋅ log^k n) time and O(6^{k²} ⋅ log^k n) space. As a corollary, we also obtain a read-only algorithm for computing the palindromic length of T, i.e., the smallest k such that T is k-palindromic, in O(n ⋅ 6^{k²} ⋅ log^⌈k/2⌉ n) time and O(6^{k²} ⋅ log^⌈k/2⌉ n) space.
Cite as

Gabriel Bathie, Jonas Ellert, and Tatiana Starikovskaya. Small Space Encoding and Recognition of k-Palindromic Prefixes. In 36th International Symposium on Algorithms and Computation (ISAAC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 359, pp. 9:1-9:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{bathie_et_al:LIPIcs.ISAAC.2025.9,
  author =	{Bathie, Gabriel and Ellert, Jonas and Starikovskaya, Tatiana},
  title =	{{Small Space Encoding and Recognition of k-Palindromic Prefixes}},
  booktitle =	{36th International Symposium on Algorithms and Computation (ISAAC 2025)},
  pages =	{9:1--9:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-408-6},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{359},
  editor =	{Chen, Ho-Lin and Hon, Wing-Kai and Tsai, Meng-Tsung},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2025.9},
  URN =		{urn:nbn:de:0030-drops-249178},
  doi =		{10.4230/LIPIcs.ISAAC.2025.9},
  annote =	{Keywords: palindromic length, read-only algorithms, palindromes}
}
Document
DOI: 10.4230/LIPIcs.ESA.2025.8
Fast Computation of k-Runs, Parameterized Squares, and Other Generalised Squares

Authors: Yuto Nakashima, Jakub Radoszewski, and Tomasz Waleń

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

Abstract
A k-mismatch square is a string of the form XY where X and Y are two equal-length strings that have at most k mismatches. Kolpakov and Kucherov [Theor. Comput. Sci., 2003] defined two notions of k-mismatch repeats, called k-repetitions and k-runs, each representing a sequence of consecutive k-mismatch squares of equal length. They proposed algorithms for computing k-repetitions and k-runs working in 𝒪(nklog k+output) time for a string of length n over an integer alphabet, where output is the number of the reported repeats. We show that output = 𝒪(nk log k), both in case of k-repetitions and k-runs, which implies that the complexity of their algorithms is actually 𝒪(nk log k). We apply this result to computing parameterized squares. A parameterized square is a string of the form XY such that X and Y parameterized-match, i.e., there exists a bijection f on the alphabet such that f(X) = Y. Two parameterized squares XY and X'Y' are equivalent if they parameterized match. Recently Hamai et al. [SPIRE 2024] showed that a string of length n over an alphabet of size σ contains less than nσ non-equivalent parameterized squares, improving an earlier bound by Kociumaka et al. [Theor. Comput. Sci., 2016]. We apply our bound for k-mismatch repeats to propose an algorithm that reports all non-equivalent parameterized squares in 𝒪(nσ log σ) time. We also show that the number of non-equivalent parameterized squares can be computed in 𝒪(n log n) time. This last algorithm applies to squares under any substring compatible equivalence relation and also to counting squares that are distinct as strings. In particular, this improves upon the 𝒪(nσ)-time algorithm of Gawrychowski et al. [CPM 2023] for counting order-preserving squares that are distinct as strings if σ = ω(log n).
Cite as

Yuto Nakashima, Jakub Radoszewski, and Tomasz Waleń. Fast Computation of k-Runs, Parameterized Squares, and Other Generalised Squares. In 33rd Annual European Symposium on Algorithms (ESA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 351, pp. 8:1-8:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{nakashima_et_al:LIPIcs.ESA.2025.8,
  author =	{Nakashima, Yuto and Radoszewski, Jakub and Wale\'{n}, Tomasz},
  title =	{{Fast Computation of k-Runs, Parameterized Squares, and Other Generalised Squares}},
  booktitle =	{33rd Annual European Symposium on Algorithms (ESA 2025)},
  pages =	{8:1--8:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-395-9},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{351},
  editor =	{Benoit, Anne and Kaplan, Haim and Wild, Sebastian and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2025.8},
  URN =		{urn:nbn:de:0030-drops-244768},
  doi =		{10.4230/LIPIcs.ESA.2025.8},
  annote =	{Keywords: string algorithm, k-mismatch square, parameterized square, order-preserving square, maximum gapped repeat}
}
Document
DOI: 10.4230/LIPIcs.ESA.2025.60
Fast and Memory-Efficient BWT Construction of Repetitive Texts Using Lyndon Grammars

Authors: Jannik Olbrich

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

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

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

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@InProceedings{olbrich:LIPIcs.ESA.2025.60,
  author =	{Olbrich, Jannik},
  title =	{{Fast and Memory-Efficient BWT Construction of Repetitive Texts Using Lyndon Grammars}},
  booktitle =	{33rd Annual European Symposium on Algorithms (ESA 2025)},
  pages =	{60:1--60:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-395-9},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{351},
  editor =	{Benoit, Anne and Kaplan, Haim and Wild, Sebastian and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2025.60},
  URN =		{urn:nbn:de:0030-drops-245286},
  doi =		{10.4230/LIPIcs.ESA.2025.60},
  annote =	{Keywords: Burrows-Wheeler Transform, Grammar compression}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2025.36
Counting Distinct Square Substrings in Sublinear Time

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

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

Abstract
We show that the number of distinct squares in a packed string of length n over an alphabet of size σ can be computed in 𝒪(n/log_{σ}n) time in the word-RAM model of computation. This paper is the first to introduce a sublinear time algorithm for the packed version of squares counting. The packed representation of a string of length n over an alphabet of size σ is given as a sequence of 𝒪(n/ log_{σ} n) machine words in the word-RAM model (a machine word consists of ω ≥ log₂ n bits). Previously it was known how to count distinct squares in 𝒪(n) time [Gusfield and Stoye, JCSS 2004], even for a string over an integer alphabet, see [Crochemore et al., TCS 2014; Bannai et al., CPM 2017; Charalampopoulos et al., SPIRE 2020]. We use techniques of squares extraction from runs described by Crochemore et al. [TCS 2014]. However, the packed model requires novel approaches. In particular, we need an 𝒪(n/log_{σ}n) sized representation of all long-period runs (runs with periods that are Ω(log_{σ}n)) which guarantees sublinear time counting of potentially linearly-many implied squares. The long-period runs with a string period that is periodic itself (called layer runs) are an obstacle, since their number can be Ω(n). Fortunately, the number of all other long-period runs is 𝒪(n/log_{σ}n) and we can construct an implicit representation of all long-period runs in 𝒪(n/log_{σ}n) time by adopting the insights of Amir et al. [ESA 2019], combined with sublinear time tools provided by the PILLAR model of computations in case of packed strings. We count squares in layer runs in sublinear time by exploiting combinatorial properties of types of pyramidally-shaped groups of layer runs. As a by-product, we discover several new structural properties of runs. Another difficulty is to compute, in sublinear time, locations of Lyndon roots of runs in packed strings, which is needed for grouping of runs that can generate equal squares. To overcome this difficulty, we introduce sparse-Lyndon roots which are based on the notion of string synchronizers proposed by Kempa and Kociumaka [STOC 2019].
Cite as

Panagiotis Charalampopoulos, Manal Mohamed, Jakub Radoszewski, Wojciech Rytter, Tomasz Waleń, and Wiktor Zuba. Counting Distinct Square Substrings in Sublinear Time. In 50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 345, pp. 36:1-36:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{charalampopoulos_et_al:LIPIcs.MFCS.2025.36,
  author =	{Charalampopoulos, Panagiotis and Mohamed, Manal and Radoszewski, Jakub and Rytter, Wojciech and Wale\'{n}, Tomasz and Zuba, Wiktor},
  title =	{{Counting Distinct Square Substrings in Sublinear Time}},
  booktitle =	{50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025)},
  pages =	{36:1--36:19},
  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.2025.36},
  URN =		{urn:nbn:de:0030-drops-241439},
  doi =		{10.4230/LIPIcs.MFCS.2025.36},
  annote =	{Keywords: square in a string, packed model, run (maximal repetition), Lyndon word}
}
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}
}
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