23 Search Results for "Kucherov, Gregory"

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.ITCS.2026.7
An Unholy Trinity: TFNP, Polynomial Systems, and the Quantum Satisfiability Problem

Authors: Marco Aldi, Sevag Gharibian, and Dorian Rudolph

Published in: LIPIcs, Volume 362, 17th Innovations in Theoretical Computer Science Conference (ITCS 2026)

Abstract
The theory of Total Function NP (TFNP) and its subclasses says that, even if one is promised an efficiently verifiable proof exists for a problem, finding this proof can be intractable. Despite the success of the theory at showing intractability of problems such as computing Brouwer fixed points and Nash equilibria, subclasses of TFNP remain arguably few and far between. In this work, we define two new subclasses of TFNP borne of the study of complex polynomial systems: Multi-homogeneous Systems (MHS) and Sparse Fundamental Theorem of Algebra (SFTA). The first of these is based on Bézout’s theorem from algebraic geometry, marking the first TFNP subclass based on an algebraic geometric principle. At the heart of our study is the computational problem known as Quantum SAT (QSAT) with a System of Distinct Representatives (SDR), first studied by [Laumann, Läuchli, Moessner, Scardicchio, and Sondhi 2010]. Among other results, we show that QSAT with SDR is MHS-complete, thus giving not only the first link between quantum complexity theory and TFNP, but also the first TFNP problem whose classical variant (SAT with SDR) is easy but whose quantum variant is hard. We also show how to embed the roots of a sparse, high-degree, univariate polynomial into QSAT with SDR, obtaining that SFTA is contained in a zero-error version of MHS. We conjecture this construction also works in the low-error setting, which would imply SFTA ⊆ MHS.
Cite as

Marco Aldi, Sevag Gharibian, and Dorian Rudolph. An Unholy Trinity: TFNP, Polynomial Systems, and the Quantum Satisfiability Problem. In 17th Innovations in Theoretical Computer Science Conference (ITCS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 362, pp. 7:1-7:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{aldi_et_al:LIPIcs.ITCS.2026.7,
  author =	{Aldi, Marco and Gharibian, Sevag and Rudolph, Dorian},
  title =	{{An Unholy Trinity: TFNP, Polynomial Systems, and the Quantum Satisfiability Problem}},
  booktitle =	{17th Innovations in Theoretical Computer Science Conference (ITCS 2026)},
  pages =	{7:1--7:24},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-410-9},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{362},
  editor =	{Saraf, Shubhangi},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2026.7},
  URN =		{urn:nbn:de:0030-drops-252946},
  doi =		{10.4230/LIPIcs.ITCS.2026.7},
  annote =	{Keywords: quantum complexity theory, Quantum Merlin Arthur (QMA), Quantum Satisfiability Problem (QSAT), total function NP (TFNP)}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2026.4
Pseudodeterministic Algorithms for Minimum Cut Problems

Authors: Aryan Agarwala and Nithin Varma

Published in: LIPIcs, Volume 362, 17th Innovations in Theoretical Computer Science Conference (ITCS 2026)

Abstract
In this paper we present efficient pseudodeterministic algorithms for both the global minimum cut and minimum s-t cut problems. The running time of our algorithm for the global minimum cut problem is asymptotically better than the fastest sequential deterministic global minimum cut algorithm (Henzinger, Li, Rao, Wang; SODA 2024). Furthermore, we implement our algorithm in streaming, PRAM, and cut-query models, where no efficient deterministic global minimum cut algorithms are known.
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Aryan Agarwala and Nithin Varma. Pseudodeterministic Algorithms for Minimum Cut Problems. In 17th Innovations in Theoretical Computer Science Conference (ITCS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 362, pp. 4:1-4:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{agarwala_et_al:LIPIcs.ITCS.2026.4,
  author =	{Agarwala, Aryan and Varma, Nithin},
  title =	{{Pseudodeterministic Algorithms for Minimum Cut Problems}},
  booktitle =	{17th Innovations in Theoretical Computer Science Conference (ITCS 2026)},
  pages =	{4:1--4:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-410-9},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{362},
  editor =	{Saraf, Shubhangi},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2026.4},
  URN =		{urn:nbn:de:0030-drops-252917},
  doi =		{10.4230/LIPIcs.ITCS.2026.4},
  annote =	{Keywords: Minimum Cut, Pseudodeterministic Algorithms}
}
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/LIPIcs.WABI.2025.17
An Efficient Data Structure and Algorithm for Long-Match Query in Run-Length Compressed BWT

Authors: Ahsan Sanaullah, Degui Zhi, and Shaojie Zhang

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

Abstract
String matching problems in bioinformatics are typically for finding exact substring matches between a query and a reference text. Previous formulations often focus on maximum exact matches (MEMs). However, multiple occurrences of substrings of the query in the text that are long enough but not maximal may not be captured by MEMs. Such long matches can be informative, especially when the text is a collection of similar sequences such as genomes. In this paper, we describe a new type of match between a pattern and a text that aren't necessarily maximal in the query, but still contain useful matching information: locally maximal exact matches (LEMs). There are usually a large amount of LEMs, so we only consider those above some length threshold ℒ. These are referred to as long LEMs. The purpose of long LEMs is to capture substring matches between a query and a text that are not necessarily maximal in the pattern but still long enough to be important. Therefore efficient long LEMs finding algorithms are desired for these datasets. However, these datasets are too large to query on traditional string indexes. Fortunately, these datasets are very repetitive. Recently, compressed string indexes that take advantage of the redundancy in the data but retain efficient querying capability have been proposed as a solution. We therefore give an efficient algorithm for computing all the long LEMs of a query and a text in a BWT runs compressed string index. We describe an O(m+occ) expected time algorithm that relies on an O(r) words space string index for outputting all long LEMs of a pattern with respect to a text given the matching statistics of the pattern with respect to the text. Here m is the length of the query, occ is the number of long LEMs outputted, and r is the number of runs in the BWT of the text. The O(r) space string index we describe relies on an adaptation of the move data structure by Nishimoto and Tabei. We are able to support LCP[i] queries in constant time given SA[i]. In other words, we answer PLCP[i] queries in constant time. These PLCP queries enable the efficient long LEM query. Long LEMs may provide useful similarity information between a pattern and a text that MEMs may ignore. This information is particularly useful in pangenome and biobank scale haplotype panel contexts.
Cite as

Ahsan Sanaullah, Degui Zhi, and Shaojie Zhang. An Efficient Data Structure and Algorithm for Long-Match Query in Run-Length Compressed BWT. In 25th International Conference on Algorithms for Bioinformatics (WABI 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 344, pp. 17:1-17:25, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{sanaullah_et_al:LIPIcs.WABI.2025.17,
  author =	{Sanaullah, Ahsan and Zhi, Degui and Zhang, Shaojie},
  title =	{{An Efficient Data Structure and Algorithm for Long-Match Query in Run-Length Compressed BWT}},
  booktitle =	{25th International Conference on Algorithms for Bioinformatics (WABI 2025)},
  pages =	{17:1--17:25},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-386-7},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{344},
  editor =	{Brejov\'{a}, Bro\v{n}a and Patro, Rob},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.WABI.2025.17},
  URN =		{urn:nbn:de:0030-drops-239433},
  doi =		{10.4230/LIPIcs.WABI.2025.17},
  annote =	{Keywords: BWT, LEM, Long LEM, MEM, Run Length Compressed BWT, Move Data Structure, Pangenome}
}
Document
DOI: 10.4230/LIPIcs.WABI.2025.22
Design of Worst-Case-Optimal Spaced Seeds

Authors: Jens Zentgraf and Sven Rahmann

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

Abstract
Read mapping (and alignment) is a fundamental problem in biological sequence analysis. For speed and computational efficiency, many popular read mappers tolerate only a few differences between the read and the corresponding part of the reference genome, which leads to reference bias: Reads with too many differences are not guaranteed to be mapped correctly or at all, because to even consider a genomic position, a sufficiently long exact match (seed) must exist. While pangenomes and their graph-based representations provide one way to avoid reference bias by enlarging the reference, we explore an orthogonal approach and consider stronger substitution-tolerant primitives, namely spaced seeds or gapped k-mers. Given two integers k ≤ w, one considers k selected positions, described by a mask, from each length-w window in a sequence. In the existing literature, masks with certain probabilistic guarantees have been designed for small values of k. Here, for the first time, we take a combinatorial approach from a worst-case perspective. For any mask, using integer linear programs, we find least favorable distributions of sequence changes in two different senses: (1) minimizing the number of unchanged windows; (2) minimizing the number of positions covered by unchanged windows. Then, among all masks or all symmetric masks of a given shape (k,w), we find the set of best masks that maximize these minima. As a result, we obtain robust masks, even for large numbers of changes. We illustrate the properties of these masks by constructing a challenging set of reads that contain many approximately equidistributed substitutions (but no indels) that many existing tools cannot map, even though they are in principle easily mappable (apart from the large number of changes) because they originate from selected non-repetitive regions of the human reference genome. We observe that the majority of these reads can be mapped with a simple alignment-free approach using chosen spaced masks, where seeding approaches based on contiguous k-mers fail.
Cite as

Jens Zentgraf and Sven Rahmann. Design of Worst-Case-Optimal Spaced Seeds. In 25th International Conference on Algorithms for Bioinformatics (WABI 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 344, pp. 22:1-22:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{zentgraf_et_al:LIPIcs.WABI.2025.22,
  author =	{Zentgraf, Jens and Rahmann, Sven},
  title =	{{Design of Worst-Case-Optimal Spaced Seeds}},
  booktitle =	{25th International Conference on Algorithms for Bioinformatics (WABI 2025)},
  pages =	{22:1--22:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-386-7},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{344},
  editor =	{Brejov\'{a}, Bro\v{n}a and Patro, Rob},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.WABI.2025.22},
  URN =		{urn:nbn:de:0030-drops-239488},
  doi =		{10.4230/LIPIcs.WABI.2025.22},
  annote =	{Keywords: Spaced seed, Gapped k-mer, Integer linear program (ILP), Worst-case design, Reference bias}
}
Document
Research
DOI: 10.4230/OASIcs.Grossi.14
Specific Patterns Against Reference Sequences

Authors: Marie-Pierre Béal and Maxime Crochemore

Published in: OASIcs, Volume 132, From Strings to Graphs, and Back Again: A Festschrift for Roberto Grossi's 60th Birthday (2025)

Abstract
We design alignment-free techniques for comparing a set of sequences or just a word, called a target, against another set of words, called a reference. This is done with the detection of factor patterns that distinguish the target from the reference. A target-specific factor of a target T against a reference R is then a factor w of a word in T that is not a factor of a word in R but whose proper factors of w are factors of a word in R. The strategy is based on the notion of minimal absent/forbidden words. We first address the computation of the set of target-specific factors of a target T against a reference R, where T and R are finite sets of sequences. The result is the construction of an automaton accepting the set of all considered target-specific factors. The construction algorithm runs in linear time according to the size of T ∪ R. The second result is the design of an algorithm to compute all the occurrences in a single sequence T of its target-specific factors against a reference R. The algorithm runs in real-time on the target sequence, independently of the number of occurrences of target-specific factors.
Cite as

Marie-Pierre Béal and Maxime Crochemore. Specific Patterns Against Reference Sequences. In From Strings to Graphs, and Back Again: A Festschrift for Roberto Grossi's 60th Birthday. Open Access Series in Informatics (OASIcs), Volume 132, pp. 14:1-14:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{beal_et_al:OASIcs.Grossi.14,
  author =	{B\'{e}al, Marie-Pierre and Crochemore, Maxime},
  title =	{{Specific Patterns Against Reference Sequences}},
  booktitle =	{From Strings to Graphs, and Back Again: A Festschrift for Roberto Grossi's 60th Birthday},
  pages =	{14:1--14:12},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-95977-391-1},
  ISSN =	{2190-6807},
  year =	{2025},
  volume =	{132},
  editor =	{Conte, Alessio and Marino, Andrea and Rosone, Giovanna and Vitter, Jeffrey Scott},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.Grossi.14},
  URN =		{urn:nbn:de:0030-drops-238130},
  doi =		{10.4230/OASIcs.Grossi.14},
  annote =	{Keywords: Specific pattern, Minimal absent word, Minimal forbidden word, Directed Acyclic Word Graph (DAWG), Suffix automaton}
}
Document
DOI: 10.4230/OASIcs.Manzini.9
Search Schemes for Approximate Pattern Matching: An Overview

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

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

Abstract
We provide a brief survey of results on solving the approximate pattern matching problem using search schemes, as introduced by Kucherov et al. (2016). We demonstrate that search schemes constitute a flexible and versatile tool that enable the specification of various search strategies, including several known filtering methods. We present approaches for designing efficient search schemes and for implementing them effectively. Finally, we conclude with experimental results comparing multiple search schemes on DNA sequencing data using the Columba software by Renders et al. (2021).
Cite as

Lore Depuydt, Jan Fostier, Simon Gottlieb, Gregory Kucherov, Knut Reinert, and Luca Renders. Search Schemes for Approximate Pattern Matching: An Overview. In The Expanding World of Compressed Data: A Festschrift for Giovanni Manzini's 60th Birthday. Open Access Series in Informatics (OASIcs), Volume 131, pp. 9:1-9:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{depuydt_et_al:OASIcs.Manzini.9,
  author =	{Depuydt, Lore and Fostier, Jan and Gottlieb, Simon and Kucherov, Gregory and Reinert, Knut and Renders, Luca},
  title =	{{Search Schemes for Approximate Pattern Matching: An Overview}},
  booktitle =	{The Expanding World of Compressed Data: A Festschrift for Giovanni Manzini's 60th Birthday},
  pages =	{9:1--9:16},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-95977-390-4},
  ISSN =	{2190-6807},
  year =	{2025},
  volume =	{131},
  editor =	{Ferragina, Paolo and Gagie, Travis and Navarro, Gonzalo},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.Manzini.9},
  URN =		{urn:nbn:de:0030-drops-239172},
  doi =		{10.4230/OASIcs.Manzini.9},
  annote =	{Keywords: FM-index, bidirectional index, approximate pattern matching, search scheme}
}
Document
DOI: 10.4230/LIPIcs.SEA.2025.4
U-Index: A Universal Indexing Framework for Matching Long Patterns

Authors: Lorraine A. K. Ayad, Gabriele Fici, Ragnar Groot Koerkamp, Grigorios Loukides, Rob Patro, Giulio Ermanno Pibiri, and Solon P. Pissis

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

Abstract
Motivation. Text indexing is a fundamental and well-studied problem. Classic solutions to this problem either replace the original text with a compressed representation, e.g., the FM-index and its variants, or keep it uncompressed but attach some redundancy - an index - to accelerate matching, e.g., the suffix array. The former solutions thus retain excellent compressed space, but are practically slow to construct and query. The latter approaches, instead, sacrifice space efficiency but are typically faster; for example, the suffix array takes much more space than the text itself for commonly used alphabets, like ASCII or DNA, but it is very fast to construct and query. Methods. In this paper, we show that efficient text indexing can be achieved using just a small extra space on top of the original text, provided that the query patterns are sufficiently long. More specifically, we develop a new indexing paradigm in which a sketch of a query pattern is first matched against a sketch of the text. Once candidate matches are retrieved, they are verified using the original text. This paradigm is thus universal in the sense that it allows us to use any solution to index the sketched text, like a suffix array, FM-index, or r-index. Results. We explore both the theory and the practice of this universal framework. With an extensive experimental analysis, we show that, surprisingly, universal indexes can be constructed much faster than their unsketched counterparts and take a fraction of the space, as a direct consequence of (i) having a lower bound on the length of patterns and (ii) working in sketch space. Furthermore, these data structures have the potential of retaining or even improving query time, because matching against the sketched text is faster and verifying candidates can be theoretically done in constant time per occurrence (or, in practice, by short and cache-friendly scans of the text). Finally, we discuss some important applications of this novel indexing paradigm to computational biology. We hypothesize that such indexes will be particularly effective when the queries are sufficiently long, and so we demonstrate applications in long-read mapping.
Cite as

Lorraine A. K. Ayad, Gabriele Fici, Ragnar Groot Koerkamp, Grigorios Loukides, Rob Patro, Giulio Ermanno Pibiri, and Solon P. Pissis. U-Index: A Universal Indexing Framework for Matching Long Patterns. In 23rd International Symposium on Experimental Algorithms (SEA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 338, pp. 4:1-4:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{ayad_et_al:LIPIcs.SEA.2025.4,
  author =	{Ayad, Lorraine A. K. and Fici, Gabriele and Groot Koerkamp, Ragnar and Loukides, Grigorios and Patro, Rob and Pibiri, Giulio Ermanno and Pissis, Solon P.},
  title =	{{U-Index: A Universal Indexing Framework for Matching Long Patterns}},
  booktitle =	{23rd International Symposium on Experimental Algorithms (SEA 2025)},
  pages =	{4:1--4:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-375-1},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{338},
  editor =	{Mutzel, Petra and Prezza, Nicola},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SEA.2025.4},
  URN =		{urn:nbn:de:0030-drops-232420},
  doi =		{10.4230/LIPIcs.SEA.2025.4},
  annote =	{Keywords: Text Indexing, Sketching, Minimizers, Hashing}
}
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.2025.20
Text Indexing for Simple Regular Expressions

Authors: Hideo Bannai, Philip Bille, Inge Li Gørtz, Gad M. Landau, Gonzalo Navarro, Nicola Prezza, Teresa Anna Steiner, and Simon Rumle Tarnow

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

Abstract
We study the problem of indexing a text T[1..n] ∈ Σⁿ so that, later, given a query regular expression pattern R of size m = |R|, we can report all the occ substrings T[i..j] of T matching R. The problem is known to be hard for arbitrary patterns R, so in this paper, we consider the following two types of patterns. (1) Character-class Kleene-star patterns of the form P₁ D^* P₂, where P₁ and P₂ are strings and D = {c₁, …, c_k} ⊂ Σ is a character-class (shorthand for the regular expression (c₁ | c₂ | ⋯ | c_k)) and (2) String Kleene-star patterns of the form P₁ P^* P₂ where P, P₁ and P₂ are strings. In case (1), we describe an index of O(nlog^{1+ε}n) space (for any constant ε > 0) solving queries in time O(m + log n/log log n + occ) on constant-sized alphabets. We also describe a general solution for any alphabet size. This result is conditioned on the existence of an anchor: a character of P₁P₂ that does not belong to D. We justify this assumption by proving that no efficient indexing solution can exist if an anchor is not present unless the Set Disjointness Conjecture fails. In case (2), we describe an index of size O(n) answering queries in time O(m + (occ+1)log^{ε}n) on any alphabet size.
Cite as

Hideo Bannai, Philip Bille, Inge Li Gørtz, Gad M. Landau, Gonzalo Navarro, Nicola Prezza, Teresa Anna Steiner, and Simon Rumle Tarnow. Text Indexing for Simple Regular Expressions. In 36th Annual Symposium on Combinatorial Pattern Matching (CPM 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 331, pp. 20:1-20:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{bannai_et_al:LIPIcs.CPM.2025.20,
  author =	{Bannai, Hideo and Bille, Philip and G{\o}rtz, Inge Li and Landau, Gad M. and Navarro, Gonzalo and Prezza, Nicola and Steiner, Teresa Anna and Tarnow, Simon Rumle},
  title =	{{Text Indexing for Simple Regular Expressions}},
  booktitle =	{36th Annual Symposium on Combinatorial Pattern Matching (CPM 2025)},
  pages =	{20:1--20:16},
  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.2025.20},
  URN =		{urn:nbn:de:0030-drops-231143},
  doi =		{10.4230/LIPIcs.CPM.2025.20},
  annote =	{Keywords: Text indexing, regular expressions, data structures}
}
Document
DOI: 10.4230/LIPIcs.CPM.2025.25
Encodings for Range Minimum Queries over Bounded Alphabets

Authors: Seungbum Jo and Srinivasa Rao Satti

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

Abstract
Range minimum queries (RMQs) are fundamental operations with widespread applications in database management, text indexing and computational biology. While many space-efficient data structures have been designed for RMQs on arrays with arbitrary elements, there has not been any results developed for the case when the alphabet size is small, which is the case in many practical scenarios where RMQ structures are used. In this paper, we investigate the encoding complexity of RMQs on arrays over bounded alphabet. We consider both one-dimensional (1D) and two-dimensional (2D) arrays. For the 1D case, we present a near-optimal space encoding. For constant-sized alphabets, this also supports the queries in constant time. For the 2D case, we systematically analyze the 1-sided, 2-sided, 3-sided and 4-sided queries and derive lower bounds for encoding space, and also matching upper bounds that support efficient queries in most cases. Our results demonstrate that, even with the bounded alphabet restriction, the space requirements remain close to those for the general alphabet case.
Cite as

Seungbum Jo and Srinivasa Rao Satti. Encodings for Range Minimum Queries over Bounded Alphabets. In 36th Annual Symposium on Combinatorial Pattern Matching (CPM 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 331, pp. 25:1-25:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{jo_et_al:LIPIcs.CPM.2025.25,
  author =	{Jo, Seungbum and Satti, Srinivasa Rao},
  title =	{{Encodings for Range Minimum Queries over Bounded Alphabets}},
  booktitle =	{36th Annual Symposium on Combinatorial Pattern Matching (CPM 2025)},
  pages =	{25:1--25:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-369-0},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{331},
  editor =	{Bonizzoni, Paola and M\"{a}kinen, Veli},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CPM.2025.25},
  URN =		{urn:nbn:de:0030-drops-231198},
  doi =		{10.4230/LIPIcs.CPM.2025.25},
  annote =	{Keywords: Range minimum queries, Encoding data structures, Cartesian trees}
}
Document
DOI: 10.4230/LIPIcs.STACS.2025.41
Residue Domination in Bounded-Treewidth Graphs

Authors: Jakob Greilhuber, Philipp Schepper, and Philip Wellnitz

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

Abstract
For the vertex selection problem (σ,ρ)-DomSet one is given two fixed sets σ and ρ of integers and the task is to decide whether we can select vertices of the input graph such that, for every selected vertex, the number of selected neighbors is in σ and, for every unselected vertex, the number of selected neighbors is in ρ [Telle, Nord. J. Comp. 1994]. This framework covers many fundamental graph problems such as Independent Set and Dominating Set. We significantly extend the recent result by Focke et al. [SODA 2023] to investigate the case when σ and ρ are two (potentially different) residue classes modulo m ≥ 2. We study the problem parameterized by treewidth and present an algorithm that solves in time m^tw ⋅ n^O(1) the decision, minimization and maximization version of the problem. This significantly improves upon the known algorithms where for the case m ≥ 3 not even an explicit running time is known. We complement our algorithm by providing matching lower bounds which state that there is no (m-ε)^pw ⋅ n^O(1)-time algorithm parameterized by pathwidth pw, unless SETH fails. For m = 2, we extend these bounds to the minimization version as the decision version is efficiently solvable.
Cite as

Jakob Greilhuber, Philipp Schepper, and Philip Wellnitz. Residue Domination in Bounded-Treewidth Graphs. In 42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 327, pp. 41:1-41:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{greilhuber_et_al:LIPIcs.STACS.2025.41,
  author =	{Greilhuber, Jakob and Schepper, Philipp and Wellnitz, Philip},
  title =	{{Residue Domination in Bounded-Treewidth Graphs}},
  booktitle =	{42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025)},
  pages =	{41:1--41:20},
  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.2025.41},
  URN =		{urn:nbn:de:0030-drops-228675},
  doi =		{10.4230/LIPIcs.STACS.2025.41},
  annote =	{Keywords: Parameterized Complexity, Treewidth, Generalized Dominating Set, Strong Exponential Time Hypothesis}
}
Document
DOI: 10.4230/LIPIcs.STACS.2025.44
Independence and Domination on Bounded-Treewidth Graphs: Integer, Rational, and Irrational Distances

Authors: Tim A. Hartmann and Dániel Marx

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

Abstract
The distance-d variants of Independent Set and Dominating Set problems have been extensively studied from different algorithmic viewpoints. In particular, the complexity of these problems are well understood on bounded-treewidth graphs [Katsikarelis, Lampis, and Paschos, Discret. Appl. Math 2022][Borradaile and Le, IPEC 2016]: given a tree decomposition of width t, the two problems can be solved in time d^t⋅ n^O(1) and (2d+1)^t⋅ n^O(1), respectively. Furthermore, assuming the Strong Exponential-Time Hypothesis (SETH), the base constants are best possible in these running times: they cannot be improved to d-ε and 2d+1-ε, respectively, for any ε > 0. We investigate continuous versions of these problems in a setting introduced by Megiddo and Tamir [SICOMP 1983], where every edge is modeled by a unit-length interval of points. In the δ-Dispersion problem, the task is to find a maximum number of points (possibly inside edges) that are pairwise at distance at least δ from each other. Similarly, in the δ-Covering problem, the task is to find a minimum number of points (possibly inside edges) such that every point of the graph (including those inside edges) is at distance at most δ from the selected point set. We provide a comprehensive understanding of these two problems on bounded-treewidth graphs. 1) Let δ = a/b with a and b being coprime. If a ≤ 2, then δ-Dispersion is polynomial-time solvable. For a ≥ 3, given a tree decomposition of width t, the problem can be solved in time (2a)^t⋅ n^O(1), and, assuming SETH, there is no (2a-ε)^t⋅n^{O(1)} time algorithm for any ε > 0. 2) Let δ = a/b with a and b being coprime. If a = 1, then δ-Covering is polynomial-time solvable. For a ≥ 2, given a tree decomposition of width t, the problem can be solved in time ((2+2(bod 2)) a)^t⋅ n^O(1), and, assuming SETH, there is no ((2+2(bod 2))a -ε)^t⋅n^O(1) time algorithm for any ε > 0. 3) For every fixed irrational number δ > 0 satisfying some mild computability condition, both δ-Dispersion and δ-Covering can be solved in time n^O(t) on graphs of treewidth t. We show a very explicitly defined irrational number δ = (4∑_{j=1}^∞ 2^{-2^j})^{-1} ≈ 0.790085 such that δ-Dispersion and δ/2-Covering are W[1]-hard parameterized by the treewidth t of the input graph, and, assuming ETH, cannot be solved in time f(t)⋅n^o(t). As a key step in obtaining these results, we extend earlier results on distance-d versions of Independent Set and Dominating Set: We determine the exact complexity of these problems in the special case when the input graph arises from some graph G' by subdividing every edge exactly b times.
Cite as

Tim A. Hartmann and Dániel Marx. Independence and Domination on Bounded-Treewidth Graphs: Integer, Rational, and Irrational Distances. In 42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 327, pp. 44:1-44:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{hartmann_et_al:LIPIcs.STACS.2025.44,
  author =	{Hartmann, Tim A. and Marx, D\'{a}niel},
  title =	{{Independence and Domination on Bounded-Treewidth Graphs: Integer, Rational, and Irrational Distances}},
  booktitle =	{42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025)},
  pages =	{44:1--44:19},
  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.2025.44},
  URN =		{urn:nbn:de:0030-drops-228700},
  doi =		{10.4230/LIPIcs.STACS.2025.44},
  annote =	{Keywords: Independence, Domination, Irrationals, Treewidth, SETH}
}
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