31 Search Results for "Walen, Tomasz"

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.FSTTCS.2025.24
Languages of Words of Low Automatic Complexity Are Hard to Compute

Authors: Joey Chen, Bjørn Kjos-Hanssen, Ivan Koswara, Linus Richter, and Frank Stephan

Published in: LIPIcs, Volume 360, 45th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2025)

Abstract
The automatic complexity of a finite word (string) is an analogue for finite automata of Sipser’s distinguishing complexity (1983) and was introduced by Shallit and Wang (2001). For a finite alphabet Σ of at least two elements, we consider the non-deterministic automatic complexity given by exactly - yet not necessarily uniquely - accepting automata: a word x ∈ Σ^* has exact non-deterministic automatic complexity k ∈ ℕ if there exists a non-deterministic automaton of k states which accepts x while rejecting every other word of the same length as x, and no automaton of fewer states has this property. Importantly, and in contrast to the classical notion, the witnessing automaton may have multiple paths of computation accepting x. We denote this measure of complexity by A_{Ne}, and study a class of languages of low A_{Ne}-complexity defined as L_q = {x ∈ Σ^* : A_{Ne}(x) < q|x|}, which is parameterised by rationals q ∈ (0,1/2) (generalising a class of sets first studied by Kjos-Hanssen). We show that for every q ∈ (0,1/2), this class is neither context-free nor recognisable by certain Boolean circuits. In the process, we answer an open question of Kjos-Hanssen quantifying the complexity of L_{1/3} in terms of Boolean circuits, and also prove the Shannon effect for A_{Ne}.
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Joey Chen, Bjørn Kjos-Hanssen, Ivan Koswara, Linus Richter, and Frank Stephan. Languages of Words of Low Automatic Complexity Are Hard to Compute. In 45th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 360, pp. 24:1-24:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{chen_et_al:LIPIcs.FSTTCS.2025.24,
  author =	{Chen, Joey and Kjos-Hanssen, Bj{\o}rn and Koswara, Ivan and Richter, Linus and Stephan, Frank},
  title =	{{Languages of Words of Low Automatic Complexity Are Hard to Compute}},
  booktitle =	{45th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2025)},
  pages =	{24:1--24:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-406-2},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{360},
  editor =	{Aiswarya, C. and Mehta, Ruta and Roy, Subhajit},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2025.24},
  URN =		{urn:nbn:de:0030-drops-251055},
  doi =		{10.4230/LIPIcs.FSTTCS.2025.24},
  annote =	{Keywords: Automatic complexity, automata theory, formal languages, Boolean circuits, Shannon effect}
}
Document
DOI: 10.4230/LIPIcs.ESA.2025.72
Color Distance Oracles and Snippets: Separation Between Exact and Approximate Solutions

Authors: Noam Horowicz and Tsvi Kopelowitz

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

Abstract
In the snippets problem, the goal is to preprocess a text T so that given two pattern queries, P₁ and P₂, one can quickly locate the occurrences of the two patterns in T that are closest to each other, or report the distance between these occurrences. Kopelowitz and Krauthgamer [CPM2016] showed upper bound tradeoffs and conditional lower bounds tradeoffs for the snippets problem, by utilizing connections between the snippets problem and the problem of constructing a color distance oracle (CDO), which is a data structure that preprocess a set of points with associated colors so that given two colors c and c' one can quickly find the (distance between the) closest pair of points where one has color c and the other has color c'. However, the existing upper bound and lower bound curves are not tight. Inspired by recent advances by Kopelowitz and Vassilevska-Williams [ICALP2020] regarding tradeoff curves for Set-disjointness data structures, in this paper we introduce new conditionally optimal algorithms for a (1+ε) approximation version of the snippets problem and a (1+ε) approximation version of the CDO problem, by applying fast matrix multiplication. For example, for CDO on n points in an array, if the preprocessing time is Õ(n^a) and the query time is Õ(n^b) then, assuming that ω = 2 (where ω is the exponent of n in the runtime of the fastest matrix multiplication algorithm on two squared matrices of size n× n), we show that approximate CDO can be solved with the following tradeoff a + 2b = 2 (if 0 ≤ b ≤ 1/3) 2a + b = 3 (if 1/3 ≤ b ≤ 1). Moreover, we prove that for exact CDO on points in an array, the algorithm of Kopelowitz and Krauthgamer [CPM2016], which obtains a tradeoff of a+b = 2, is essentially optimal assuming that the strong all-pairs shortest paths hypothesis holds for randomized algorithms. Thus, we demonstrate that the exact version of CDO is strictly harder than the approximate version. Moreover, this separation carries over to the snippets problem.
Cite as

Noam Horowicz and Tsvi Kopelowitz. Color Distance Oracles and Snippets: Separation Between Exact and Approximate Solutions. In 33rd Annual European Symposium on Algorithms (ESA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 351, pp. 72:1-72:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{horowicz_et_al:LIPIcs.ESA.2025.72,
  author =	{Horowicz, Noam and Kopelowitz, Tsvi},
  title =	{{Color Distance Oracles and Snippets: Separation Between Exact and Approximate Solutions}},
  booktitle =	{33rd Annual European Symposium on Algorithms (ESA 2025)},
  pages =	{72:1--72:17},
  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.2025.72},
  URN =		{urn:nbn:de:0030-drops-245403},
  doi =		{10.4230/LIPIcs.ESA.2025.72},
  annote =	{Keywords: data structures, fast matrix multiplication, fine-grained complexity, pattern matching, distance oracles}
}
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.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.11
Circular Dictionary Matching Using Extended BWT

Authors: Wing-Kai Hon, Rahul Shah, and Sharma V. Thankachan

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

Abstract
The dictionary matching problem involves preprocessing a set of strings (patterns) into a data structure that efficiently identifies all occurrences of these patterns within a query string (text). In this work, we investigate a variation of this problem, termed circular dictionary matching, where the patterns are circular, meaning their cyclic shifts are also considered valid patterns. Such patterns naturally occur in areas such as bioinformatics and computational geometry. Based on the extended Burrows-Wheeler Transformation (eBWT), we design a space-efficient solution for this problem. Specifically, we show that a dictionary of d circular patterns of total length n can be indexed in nlog σ + O(n+dlog n+σ log n) bits of space and support circular dictionary matching on a query text T in O((|T|+occ)log n) time, where σ represents the size of the underlying alphabet and occ represents the output size.
Cite as

Wing-Kai Hon, Rahul Shah, and Sharma V. Thankachan. Circular Dictionary Matching Using Extended BWT. In The Expanding World of Compressed Data: A Festschrift for Giovanni Manzini's 60th Birthday. Open Access Series in Informatics (OASIcs), Volume 131, pp. 11:1-11:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{hon_et_al:OASIcs.Manzini.11,
  author =	{Hon, Wing-Kai and Shah, Rahul and Thankachan, Sharma V.},
  title =	{{Circular Dictionary Matching Using Extended BWT}},
  booktitle =	{The Expanding World of Compressed Data: A Festschrift for Giovanni Manzini's 60th Birthday},
  pages =	{11:1--11:14},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-95977-390-4},
  ISSN =	{2190-6807},
  year =	{2025},
  volume =	{131},
  editor =	{Ferragina, Paolo and Gagie, Travis and Navarro, Gonzalo},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.Manzini.11},
  URN =		{urn:nbn:de:0030-drops-239195},
  doi =		{10.4230/OASIcs.Manzini.11},
  annote =	{Keywords: String algorithms, Burrows-Wheeler transformation, suffix trees, succinct data structures}
}
Document
DOI: 10.4230/LIPIcs.CPM.2025.7
FL-RMQ: A Learned Approach to Range Minimum Queries

Authors: Paolo Ferragina and Filippo Lari

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

Abstract
We address the problem of designing and implementing a data structure for the Range Minimum Query problem. We show a surprising connection between this classical problem and the geometry of a properly defined set of points in the Cartesian plane. Building on this insight, we hinge upon a well-known result in Computational Geometry to introduce the first RMQ solution that exploits (i.e., learns) the distribution of such 2D-points via proper error-bounded linear approximations. Because of these features, we name the resulting data structure: Fully-Learned RMQ, shortly FL-RMQ. We prove theoretical bounds for its space usage and query time, covering both worst-case scenarios and average-case performance for uniformly distributed inputs. These bounds compare favorably with the ones achievable by the best-known indexing solutions (i.e., the ones that allow access to the indexed array), especially when the input data follow some geometric regularities that we characterize in the paper, thus providing principled evidence of FL-RMQ being a novel data-aware solution to the RMQ problem. We corroborate our theoretical findings with a wide set of experiments showing that FL-RMQ offers more robust space-time trade-offs than the other known practical indexing solutions on both artificial and real-world datasets. We believe that our novel approach to the RMQ problem is noteworthy not only for its interesting space-time trade-offs, but also because it is flexible enough to be applied easily to the encoding variant of RMQ (i.e., the one that does not allow access to the indexed array), and moreover, because it paves the way to research opportunities on possibly other problems.
Cite as

Paolo Ferragina and Filippo Lari. FL-RMQ: A Learned Approach to Range Minimum Queries. In 36th Annual Symposium on Combinatorial Pattern Matching (CPM 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 331, pp. 7:1-7:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{ferragina_et_al:LIPIcs.CPM.2025.7,
  author =	{Ferragina, Paolo and Lari, Filippo},
  title =	{{FL-RMQ: A Learned Approach to Range Minimum Queries}},
  booktitle =	{36th Annual Symposium on Combinatorial Pattern Matching (CPM 2025)},
  pages =	{7:1--7:23},
  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.2025.7},
  URN =		{urn:nbn:de:0030-drops-231014},
  doi =		{10.4230/LIPIcs.CPM.2025.7},
  annote =	{Keywords: Range-Minimum query, Learned data structures, Compact data structures, Experimental results}
}
Document
DOI: 10.4230/LIPIcs.CPM.2025.9
Pattern Matching on Run-Length Grammar-Compressed Strings in Linear Time

Authors: Yuto Iguchi, Ryo Yoshinaka, and Ayumi Shinohara

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

Abstract
Run-length straight-line programs (RLSLPs) are a technique for grammar-based compression, allowing any string to be represented with optimal space for δ, the substring complexity of the string. We address the compressed pattern matching problem for RLSLPs: Given a compressed text in RLSLP format and an uncompressed pattern, determine if the pattern appears in the text. This paper proposes an algorithm that solves this problem in linear time with respect to the size of the grammar and the length of the pattern.
Cite as

Yuto Iguchi, Ryo Yoshinaka, and Ayumi Shinohara. Pattern Matching on Run-Length Grammar-Compressed Strings in Linear Time. In 36th Annual Symposium on Combinatorial Pattern Matching (CPM 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 331, pp. 9:1-9:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{iguchi_et_al:LIPIcs.CPM.2025.9,
  author =	{Iguchi, Yuto and Yoshinaka, Ryo and Shinohara, Ayumi},
  title =	{{Pattern Matching on Run-Length Grammar-Compressed Strings in Linear Time}},
  booktitle =	{36th Annual Symposium on Combinatorial Pattern Matching (CPM 2025)},
  pages =	{9:1--9:16},
  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.2025.9},
  URN =		{urn:nbn:de:0030-drops-231034},
  doi =		{10.4230/LIPIcs.CPM.2025.9},
  annote =	{Keywords: pattern matching, run-length straight-line programs, compression, suffix tree}
}
Document
DOI: 10.4230/LIPIcs.CPM.2025.24
Sorted Consecutive Occurrence Queries in Substrings

Authors: Waseem Akram and Takuya Mieno

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

Abstract
The string indexing problem is a fundamental computational problem with numerous applications, including information retrieval and bioinformatics. It aims to efficiently solve the pattern matching problem: given a text T of length n for preprocessing and a pattern P of length m as a query, the goal is to report all occurrences of P as substrings of T. Navarro and Thankachan [CPM 2015, Theor. Comput. Sci. 2016] introduced a variant of this problem called the gap-bounded consecutive occurrence query, which reports pairs of consecutive occurrences of P in T such that their gaps (i.e., the distances between them) lie within a query-specified range [g₁, g₂]. Recently, Bille et al. [FSTTCS 2020, Theor. Comput. Sci. 2022] proposed the top-k close consecutive occurrence query, which reports the k closest consecutive occurrences of P in T, sorted in non-decreasing order of distance. Both problems are optimally solved in query time with O(n log n)-space data structures. In this paper, we generalize these problems to the range query model, which focuses only on occurrences of P in a specified substring T[a.. b] of T. Our contributions are as follows: - We propose an O(n log² n)-space data structure that answers the range top-k consecutive occurrence query in O(|P| + log log n + k) time. - We propose an O(n log^{2+ε} n)-space data structure that answers the range gap-bounded consecutive occurrence query in O(|P| + log log n + output) time, where ε is a positive constant and output denotes the number of outputs. Additionally, as by-products, we present algorithms for geometric problems involving weighted horizontal segments in a 2D plane, which are of independent interest.
Cite as

Waseem Akram and Takuya Mieno. Sorted Consecutive Occurrence Queries in Substrings. In 36th Annual Symposium on Combinatorial Pattern Matching (CPM 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 331, pp. 24:1-24:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{akram_et_al:LIPIcs.CPM.2025.24,
  author =	{Akram, Waseem and Mieno, Takuya},
  title =	{{Sorted Consecutive Occurrence Queries in Substrings}},
  booktitle =	{36th Annual Symposium on Combinatorial Pattern Matching (CPM 2025)},
  pages =	{24:1--24:15},
  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.2025.24},
  URN =		{urn:nbn:de:0030-drops-231187},
  doi =		{10.4230/LIPIcs.CPM.2025.24},
  annote =	{Keywords: string algorithm, consecutive occurrences, suffix tree}
}
Document
DOI: 10.4230/LIPIcs.CPM.2025.18
Improved Circular Dictionary Matching

Authors: Nicola Cotumaccio

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

Abstract
The circular dictionary matching problem is an extension of the classical dictionary matching problem where every string in the dictionary is interpreted as a circular string: after reading the last character of a string, we can move back to its first character. The circular dictionary matching problem is motivated by applications in bioinformatics and computational geometry. In 2011, Hon et al. [ISAAC 2011] showed how to efficiently solve circular dictionary matching queries within compressed space by building on Mantaci et al.’s eBWT and Sadakane’s compressed suffix tree. The proposed solution is based on the assumption that the strings in the dictionary are all distinct and non-periodic, no string is a circular rotation of some other string, and the strings in the dictionary have similar lengths. In this paper, we consider arbitrary dictionaries, and we show how to solve circular dictionary matching queries in O((m + occ) log n) time within compressed space using n log σ (1 + o(1)) + O(n) + O(d log n) bits, where n is the total length of the dictionary, m is the length of the pattern, occ is the number of occurrences, d is the number of strings in the dictionary and σ is the size of the alphabet. Our solution is based on an extension of the suffix array to arbitrary dictionaries and a sampling mechanism for the LCP array of a dictionary inspired by recent results in graph indexing and compression.
Cite as

Nicola Cotumaccio. Improved Circular Dictionary Matching. In 36th Annual Symposium on Combinatorial Pattern Matching (CPM 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 331, pp. 18:1-18:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{cotumaccio:LIPIcs.CPM.2025.18,
  author =	{Cotumaccio, Nicola},
  title =	{{Improved Circular Dictionary Matching}},
  booktitle =	{36th Annual Symposium on Combinatorial Pattern Matching (CPM 2025)},
  pages =	{18:1--18:17},
  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.2025.18},
  URN =		{urn:nbn:de:0030-drops-231122},
  doi =		{10.4230/LIPIcs.CPM.2025.18},
  annote =	{Keywords: Circular pattern matching, dictionary matching, suffix tree, compressed suffix tree, suffix array, LCP array, Burrows-Wheeler Transform, FM-index}
}
Document
DOI: 10.4230/LIPIcs.CPM.2025.26
Extending the Burrows-Wheeler Transform for Cartesian Tree Matching and Constructing It

Authors: Eric M. Osterkamp and Dominik Köppl

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

Abstract
Cartesian tree matching is a form of generalized pattern matching where a substring of the text matches with the pattern if they share the same Cartesian tree. This form of matching finds application for time series of stock prices and can be of interest for melody matching between musical scores. For the indexing problem, the state-of-the-art data structure is a Burrows-Wheeler transform based solution due to [Kim and Cho, CPM'21], which uses nearly succinct space and can count the number of substrings that Cartesian tree match with a pattern in time linear in the pattern length. The authors address the construction of their data structure with a straight-forward solution that, however, requires pointer-based data structures, resulting in O(n lg n) bits of space, where n is the text length [Kim and Cho, CPM'21, Section A.4]. We address this bottleneck by a construction that requires O(n lg σ) bits of space and has a time complexity of O(n (lg σ lg n)/(lg lg n)), where σ is alphabet size. Additionally, we can extend this index for indexing multiple circular texts in the spirit of the extended Burrows-Wheeler transform without sacrificing the time and space complexities. We present this index in a dynamic variant, where we pay a logarithmic slowdown and need space linear in the input texts in bits for the extra functionality that we can incrementally add texts. Our extended setting is of interest for finding repetitive motifs common in the aforementioned applications, independent of offsets and scaling.
Cite as

Eric M. Osterkamp and Dominik Köppl. Extending the Burrows-Wheeler Transform for Cartesian Tree Matching and Constructing It. In 36th Annual Symposium on Combinatorial Pattern Matching (CPM 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 331, pp. 26:1-26:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{osterkamp_et_al:LIPIcs.CPM.2025.26,
  author =	{Osterkamp, Eric M. and K\"{o}ppl, Dominik},
  title =	{{Extending the Burrows-Wheeler Transform for Cartesian Tree Matching and Constructing It}},
  booktitle =	{36th Annual Symposium on Combinatorial Pattern Matching (CPM 2025)},
  pages =	{26:1--26:17},
  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.2025.26},
  URN =		{urn:nbn:de:0030-drops-231201},
  doi =		{10.4230/LIPIcs.CPM.2025.26},
  annote =	{Keywords: Cartesian tree matching, extended Burrows-Wheeler transform, construction algorithm, generalized pattern matching}
}
Document
DOI: 10.4230/LIPIcs.CPM.2025.28
Faster Approximate Elastic-Degenerate String Matching - Part A

Authors: Solon P. Pissis, Jakub Radoszewski, and Wiktor Zuba

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

Abstract
An elastic-degenerate (ED) string 𝐓 is a sequence 𝐓 = 𝐓[1] ⋯ 𝐓[n] of n finite sets of strings. The cardinality m of 𝐓 is the total number of strings in 𝐓[i], for all i ∈ [1..n]. The size N of 𝐓 is the total length of all m strings of 𝐓. ED strings have been introduced to represent a set of closely-related DNA sequences. Let P = P[1..p] be a pattern of length p and k > 0 be an integer. We consider the problem of k-Approximate ED String Matching (EDSM): searching k-approximate occurrences of P in the language of 𝐓. We call k-Approximate EDSM under the Hamming distance, k-Mismatch EDSM; and we call k-Approximate EDSM under edit distance, k-Edit EDSM. Bernardini et al. (Theoretical Computer Science, 2020) showed a simple 𝒪(k m p + kN)-time algorithm for k-Mismatch EDSM and an 𝒪(k² m p + kN)-time algorithm for k-Edit EDSM. We improve the dependency on k in both results, obtaining an Õ(k^{2/3}mp+√kN)-time algorithm for k-Mismatch EDSM and an Õ(kmp+ kN)-time algorithm for k-Edit EDSM. Bernardini et al. (Theory of Computing Systems, 2024) presented several algorithms for 1-Approximate EDSM working in Õ(np²+N) time. They have also left the possibility to generalize these solutions for k > 1 as an open problem. We improve the runtime of their solution for 1-Mismatch and 1-Edit EDSM from Õ(np²+N) to 𝒪(np²+N). We further show algorithms for k-Approximate EDSM for the Hamming and edit distances working in Õ(np² + N) time, for any constant k > 0. Finally, we show how our techniques can be applied to improve upon the complexity of the k-Approximate ED String Intersection and k-Approximate Doubly EDSM problems that were introduced very recently by Gabory et al. (Information and Computation, 2025).
Cite as

Solon P. Pissis, Jakub Radoszewski, and Wiktor Zuba. Faster Approximate Elastic-Degenerate String Matching - Part A. In 36th Annual Symposium on Combinatorial Pattern Matching (CPM 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 331, pp. 28:1-28:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{pissis_et_al:LIPIcs.CPM.2025.28,
  author =	{Pissis, Solon P. and Radoszewski, Jakub and Zuba, Wiktor},
  title =	{{Faster Approximate Elastic-Degenerate String Matching - Part A}},
  booktitle =	{36th Annual Symposium on Combinatorial Pattern Matching (CPM 2025)},
  pages =	{28:1--28:19},
  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.2025.28},
  URN =		{urn:nbn:de:0030-drops-231227},
  doi =		{10.4230/LIPIcs.CPM.2025.28},
  annote =	{Keywords: ED string, approximate string matching, Hamming distance, edit distance}
}
Document
DOI: 10.4230/LIPIcs.CPM.2025.5
Covers in Optimal Space

Authors: Itai Boneh and Shay Golan

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

Abstract
A cover of a string S is a string C such that every index of S is contained in some occurrence of C. First introduced by Apostolico and Ehrenfeucht [TCS'93] over 30 years ago, covers have since received significant attention in the string algorithms community. In this work, we present a space-efficient algorithm for computing a compact representation of all covers of a given string. Our algorithm requires only O(log n) additional memory while accessing the input string of length n in a read-only manner. Moreover, it runs in O(n) time, matching the best-known time complexity for this problem while achieving an exponential improvement in space usage.
Cite as

Itai Boneh and Shay Golan. Covers in Optimal Space. In 36th Annual Symposium on Combinatorial Pattern Matching (CPM 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 331, pp. 5:1-5:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{boneh_et_al:LIPIcs.CPM.2025.5,
  author =	{Boneh, Itai and Golan, Shay},
  title =	{{Covers in Optimal Space}},
  booktitle =	{36th Annual Symposium on Combinatorial Pattern Matching (CPM 2025)},
  pages =	{5:1--5:15},
  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.2025.5},
  URN =		{urn:nbn:de:0030-drops-230993},
  doi =		{10.4230/LIPIcs.CPM.2025.5},
  annote =	{Keywords: Cover, Read-only random access, small space}
}
Document
DOI: 10.4230/LIPIcs.CPM.2025.3
Counting on General Run-Length Grammars

Authors: Gonzalo Navarro and Alejandro Pacheco

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

Abstract
We introduce a data structure for counting pattern occurrences in texts compressed with any run-length context-free grammar. Our structure uses space proportional to the grammar size and counts the occurrences of a pattern of length m in a text of length n in time O(mlog^{2+ε} n), for any constant ε > 0 chosen at indexing time. This is the first solution to an open problem posed by Christiansen et al. [ACM TALG 2020] and enhances our abilities for computation over compressed data; we give an example application.
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Gonzalo Navarro and Alejandro Pacheco. Counting on General Run-Length Grammars. In 36th Annual Symposium on Combinatorial Pattern Matching (CPM 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 331, pp. 3:1-3:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{navarro_et_al:LIPIcs.CPM.2025.3,
  author =	{Navarro, Gonzalo and Pacheco, Alejandro},
  title =	{{Counting on General Run-Length Grammars}},
  booktitle =	{36th Annual Symposium on Combinatorial Pattern Matching (CPM 2025)},
  pages =	{3:1--3:17},
  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.2025.3},
  URN =		{urn:nbn:de:0030-drops-230977},
  doi =		{10.4230/LIPIcs.CPM.2025.3},
  annote =	{Keywords: Grammar-based indexing, Run-length context-free grammars, Counting pattern occurrences, Periods in strings}
}
Document
DOI: 10.4230/LIPIcs.STACS.2025.38
Two-Dimensional Longest Common Extension Queries in Compact Space

Authors: Arnab Ganguly, Daniel Gibney, Rahul Shah, and Sharma V. Thankachan

Published in: LIPIcs, Volume 327, 42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025)

Abstract
For a length n text over an alphabet of size σ, we can encode the suffix tree data structure in 𝒪(nlog σ) bits of space. It supports suffix array (SA), inverse suffix array (ISA), and longest common extension (LCE) queries in 𝒪(log^ε_σ n) time, which enables efficient pattern matching; here ε > 0 is an arbitrarily small constant. Further improvements are possible for LCE queries, where 𝒪(1) time queries can be achieved using an index of space 𝒪(nlog σ) bits. However, compactly indexing a two-dimensional text (i.e., an n× n matrix) has been a major open problem. We show progress in this direction by first presenting an 𝒪(n²log σ)-bit structure supporting LCE queries in near 𝒪((log_σ n)^{2/3}) time. We then present an 𝒪(n²log σ + n²log log n)-bit structure supporting ISA queries in near 𝒪(log n ⋅ (log_σ n)^{2/3}) time. Within a similar space, achieving SA queries in poly-logarithmic (even strongly sub-linear) time is a significant challenge. However, our 𝒪(n²log σ + n²log log n)-bit structure can support SA queries in 𝒪(n²/(σ log n)^c) time, where c is an arbitrarily large constant, which enables pattern matching in time faster than what is possible without preprocessing. We then design a repetition-aware data structure. The δ_2D compressibility measure for two-dimensional texts was recently introduced by Carfagna and Manzini [SPIRE 2023]. The measure ranges from 1 to n², with smaller δ_2D indicating a highly compressible two-dimensional text. The current data structure utilizing δ_2D allows only element access. We obtain the first structure based on δ_2D for LCE queries. It takes 𝒪^{~}(n^{5/3} + n^{8/5}δ_2D^{1/5}) space and answers queries in 𝒪(log n) time.
Cite as

Arnab Ganguly, Daniel Gibney, Rahul Shah, and Sharma V. Thankachan. Two-Dimensional Longest Common Extension Queries in Compact Space. In 42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 327, pp. 38:1-38:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{ganguly_et_al:LIPIcs.STACS.2025.38,
  author =	{Ganguly, Arnab and Gibney, Daniel and Shah, Rahul and Thankachan, Sharma V.},
  title =	{{Two-Dimensional Longest Common Extension Queries in Compact Space}},
  booktitle =	{42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025)},
  pages =	{38:1--38:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-365-2},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{327},
  editor =	{Beyersdorff, Olaf and Pilipczuk, Micha{\l} and Pimentel, Elaine 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.2025.38},
  URN =		{urn:nbn:de:0030-drops-228649},
  doi =		{10.4230/LIPIcs.STACS.2025.38},
  annote =	{Keywords: String matching, text indexing, two-dimensional text}
}
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