30 Search Results for "Jez, Artur"

Document
DOI: 10.4230/LIPIcs.STACS.2026.77
An Improved Version of Hmelevskii’s Theorem on Three-Variable Word Equations

Authors: Aleksi Saarela

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

Abstract
Hmelevskii proved in 1971 that every constant-free three-variable word equation has a parametric solution. We prove an improved version of this result by showing that every such equation has a parametric solution using only three numerical parameters and with only two levels of nesting. This means that the structure of the solution sets of these equations is considerably simpler than has been known before.
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Aleksi Saarela. An Improved Version of Hmelevskii’s Theorem on Three-Variable Word Equations. In 43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 364, pp. 77:1-77:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{saarela:LIPIcs.STACS.2026.77,
  author =	{Saarela, Aleksi},
  title =	{{An Improved Version of Hmelevskii’s Theorem on Three-Variable Word Equations}},
  booktitle =	{43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026)},
  pages =	{77:1--77:14},
  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.2026.77},
  URN =		{urn:nbn:de:0030-drops-255664},
  doi =		{10.4230/LIPIcs.STACS.2026.77},
  annote =	{Keywords: Combinatorics on words, word equation, parametric word}
}
Document
DOI: 10.4230/LIPIcs.STACS.2026.36
Time-Optimal Construction of String Synchronizing Sets

Authors: Jonas Ellert and Tomasz Kociumaka

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

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

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

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@InProceedings{ellert_et_al:LIPIcs.STACS.2026.36,
  author =	{Ellert, Jonas and Kociumaka, Tomasz},
  title =	{{Time-Optimal Construction of String Synchronizing Sets}},
  booktitle =	{43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026)},
  pages =	{36:1--36:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-412-3},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{364},
  editor =	{Mahajan, Meena and Manea, Florin and McIver, Annabelle and Thắng, Nguy\~{ê}n Kim},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2026.36},
  URN =		{urn:nbn:de:0030-drops-255258},
  doi =		{10.4230/LIPIcs.STACS.2026.36},
  annote =	{Keywords: synchronizing sets, local consistency, packed strings}
}
Document
DOI: 10.4230/LIPIcs.ISAAC.2025.9
Small Space Encoding and Recognition of k-Palindromic Prefixes

Authors: Gabriel Bathie, Jonas Ellert, and Tatiana Starikovskaya

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

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

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

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@InProceedings{bathie_et_al:LIPIcs.ISAAC.2025.9,
  author =	{Bathie, Gabriel and Ellert, Jonas and Starikovskaya, Tatiana},
  title =	{{Small Space Encoding and Recognition of k-Palindromic Prefixes}},
  booktitle =	{36th International Symposium on Algorithms and Computation (ISAAC 2025)},
  pages =	{9:1--9:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-408-6},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{359},
  editor =	{Chen, Ho-Lin and Hon, Wing-Kai and Tsai, Meng-Tsung},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2025.9},
  URN =		{urn:nbn:de:0030-drops-249178},
  doi =		{10.4230/LIPIcs.ISAAC.2025.9},
  annote =	{Keywords: palindromic length, read-only algorithms, palindromes}
}
Document
DOI: 10.4230/LIPIcs.ESA.2025.32
Linear-Time Multilevel Graph Partitioning via Edge Sparsification

Authors: Lars Gottesbüren, Nikolai Maas, Dominik Rosch, Peter Sanders, and Daniel Seemaier

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

Abstract
The current landscape of balanced graph partitioning is divided into high-quality but expensive multilevel algorithms and cheaper approaches with linear running time, such as single-level algorithms and streaming algorithms. We demonstrate how to achieve the best of both worlds with a linear time multilevel algorithm. Multilevel algorithms construct a hierarchy of increasingly smaller graphs by repeatedly contracting clusters of nodes. Our approach preserves their distinct advantage, allowing refinement of the partition over multiple levels with increasing detail. At the same time, we use edge sparsification to guarantee geometric size reduction between the levels and thus linear running time. We provide a proof of the linear running time as well as additional insights into the behavior of multilevel algorithms, showing that graphs with low modularity are most likely to trigger worst-case running time. We evaluate multiple approaches for edge sparsification and integrate our algorithm into the state-of-the-art multilevel partitioner KaMinPar, maintaining its excellent parallel scalability. As demonstrated in detailed experiments, this results in a 1.49× average speedup (up to 4× for some instances) with only 1% loss in solution quality. Moreover, our algorithm clearly outperforms state-of-the-art single-level and streaming approaches.
Cite as

Lars Gottesbüren, Nikolai Maas, Dominik Rosch, Peter Sanders, and Daniel Seemaier. Linear-Time Multilevel Graph Partitioning via Edge Sparsification. In 33rd Annual European Symposium on Algorithms (ESA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 351, pp. 32:1-32:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{gottesburen_et_al:LIPIcs.ESA.2025.32,
  author =	{Gottesb\"{u}ren, Lars and Maas, Nikolai and Rosch, Dominik and Sanders, Peter and Seemaier, Daniel},
  title =	{{Linear-Time Multilevel Graph Partitioning via Edge Sparsification}},
  booktitle =	{33rd Annual European Symposium on Algorithms (ESA 2025)},
  pages =	{32:1--32:20},
  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.2025.32},
  URN =		{urn:nbn:de:0030-drops-245007},
  doi =		{10.4230/LIPIcs.ESA.2025.32},
  annote =	{Keywords: Graph Partitioning, Graph Algorithms, Linear Time Algorithms, Graph Sparsification}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2025.77
Minimization of Deterministic Finite Automata Modulo the Edit Distance

Authors: Jakub Michaliszyn and Jan Otop

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

Abstract
We propose a novel approach to minimization of deterministic finite automata (DFA), in which the DFA is further minimized at the expense of relaxing equality of languages to merely a similarity. As the notion of similarity of languages, we consider the edit distance between languages ℒ, ℒ', i.e., the minimal number of edits necessary to transform any word from ℒ to some word from ℒ' and vice versa. In this paper we address two problems: minimization up to a predetermined edit distance given in the input, and minimization up to a bounded edit distance, in which there has to be an upper bound on the number of edits, but it is not specified. We show the first problem to be PSpace {}-complete and that the second problem is in Σ₂^p, and both NP-hard and coNP-hard. We show that if we limit how many strongly connected components can be visited by a single run (i.e., bounded SCC-depth), the problem becomes NP-complete. We also establish maximal subclasses of DFA over which minimization up to a bounded edit distance can be performed in polynomial time. Additionally, we provide a succinct overview of alternative metrics for assessing language similarity.
Cite as

Jakub Michaliszyn and Jan Otop. Minimization of Deterministic Finite Automata Modulo the Edit Distance. In 50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 345, pp. 77:1-77:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{michaliszyn_et_al:LIPIcs.MFCS.2025.77,
  author =	{Michaliszyn, Jakub and Otop, Jan},
  title =	{{Minimization of Deterministic Finite Automata Modulo the Edit Distance}},
  booktitle =	{50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025)},
  pages =	{77:1--77:17},
  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.2025.77},
  URN =		{urn:nbn:de:0030-drops-241843},
  doi =		{10.4230/LIPIcs.MFCS.2025.77},
  annote =	{Keywords: automata theory, automata minimization, edit distance}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2025.69
FO-Query Enumeration over SLP-Compressed Structures of Bounded Degree

Authors: Markus Lohrey, Sebastian Maneth, and Markus L. Schmid

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

Abstract
Enumerating the result set of a first-order query over a relational structure of bounded degree can be done with linear preprocessing and constant delay. In this work, we extend this result towards the compressed perspective where the structure is given in a potentially highly compressed form by a straight-line program (SLP). Our main result is an algorithm that enumerates the result set of a first-order query over a structure of bounded degree that is represented by an SLP satisfying the so-called apex condition. For a fixed formula, the enumeration algorithm has constant delay and needs a preprocessing time that is linear in the size of the SLP.
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Markus Lohrey, Sebastian Maneth, and Markus L. Schmid. FO-Query Enumeration over SLP-Compressed Structures of Bounded Degree. In 50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 345, pp. 69:1-69:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{lohrey_et_al:LIPIcs.MFCS.2025.69,
  author =	{Lohrey, Markus and Maneth, Sebastian and Schmid, Markus L.},
  title =	{{FO-Query Enumeration over SLP-Compressed Structures of Bounded Degree}},
  booktitle =	{50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025)},
  pages =	{69:1--69:20},
  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.2025.69},
  URN =		{urn:nbn:de:0030-drops-241760},
  doi =		{10.4230/LIPIcs.MFCS.2025.69},
  annote =	{Keywords: Enumeration algorithms, FO-logic, query evaluation over compressed data}
}
Document
DOI: 10.4230/LIPIcs.SEA.2025.14
Efficient Terabyte-Scale Text Compression via Stable Local Consistency and Parallel Grammar Processing

Authors: Diego Díaz-Domínguez

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

Abstract
We present compression algorithms designed to process terabyte-sized datasets in parallel. Our approach builds on locally consistent grammars, a lightweight form of compression, combined with simple post-processing techniques to achieve further space reductions. Locally consistent grammar algorithms are suitable for scaling as they need minimal satellite information to compact the text, but they are not inherently parallel. To enable parallelisation, we introduce a novel concept that we call stable local consistency. A grammar algorithm ALG is stable if for any pattern P occurring in a collection 𝒯 = {T_1, T_2, …, T_k}, instances ALG(T_1), ALG(T_2), …, ALG(T_k) independently produce cores for P with the same topology. In a locally consistent grammar, the core of P is a subset of nodes and edges in the parse tree of 𝒯 that remains the same in all the occurrences of P. This feature enables compression, but it only holds if ALG defines a common set of nonterminal symbols for the strings. Stability removes this restriction, allowing us to run ALG(T_1), ALG(T_2), …, ALG(T_k) in parallel and subsequently merge their grammars into a single output equivalent to that of ALG(𝒯). We implemented our ideas and tested them on massive datasets. Our experiments showed that our method could process 7.9 TB of bacterial genomes in around nine hours, using 16 threads and 0.43 bits/symbol of working memory, achieving a compression ratio of 85x.
Cite as

Diego Díaz-Domínguez. Efficient Terabyte-Scale Text Compression via Stable Local Consistency and Parallel Grammar Processing. In 23rd International Symposium on Experimental Algorithms (SEA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 338, pp. 14:1-14:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{diazdominguez:LIPIcs.SEA.2025.14,
  author =	{D{\'\i}az-Dom{\'\i}nguez, Diego},
  title =	{{Efficient Terabyte-Scale Text Compression via Stable Local Consistency and Parallel Grammar Processing}},
  booktitle =	{23rd International Symposium on Experimental Algorithms (SEA 2025)},
  pages =	{14:1--14:20},
  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.2025.14},
  URN =		{urn:nbn:de:0030-drops-232525},
  doi =		{10.4230/LIPIcs.SEA.2025.14},
  annote =	{Keywords: Grammar compression, locally consistent parsing, 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.2025.3
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.ICDT.2025.20
A Formal Language Perspective on Factorized Representations

Authors: Benny Kimelfeld, Wim Martens, and Matthias Niewerth

Published in: LIPIcs, Volume 328, 28th International Conference on Database Theory (ICDT 2025)

Abstract
Factorized representations (FRs) are a well-known tool to succinctly represent results of join queries and have been originally defined using the named database perspective. We define FRs in the unnamed database perspective and use them to establish several new connections. First, unnamed FRs can be exponentially more succinct than named FRs, but this difference can be alleviated by imposing a disjointness condition on columns. Conversely, named FRs can also be exponentially more succinct than unnamed FRs. Second, unnamed FRs are the same as (i.e., isomorphic to) context-free grammars for languages in which each word has the same length. This tight connection allows us to transfer a wide range of results on context-free grammars to database factorization; of which we offer a selection in the paper. Third, when we generalize unnamed FRs to arbitrary sets of tuples, they become a generalization of path multiset representations, a formalism that was recently introduced to succinctly represent sets of paths in the context of graph database query evaluation.
Cite as

Benny Kimelfeld, Wim Martens, and Matthias Niewerth. A Formal Language Perspective on Factorized Representations. In 28th International Conference on Database Theory (ICDT 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 328, pp. 20:1-20:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{kimelfeld_et_al:LIPIcs.ICDT.2025.20,
  author =	{Kimelfeld, Benny and Martens, Wim and Niewerth, Matthias},
  title =	{{A Formal Language Perspective on Factorized Representations}},
  booktitle =	{28th International Conference on Database Theory (ICDT 2025)},
  pages =	{20:1--20:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-364-5},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{328},
  editor =	{Roy, Sudeepa and Kara, Ahmet},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICDT.2025.20},
  URN =		{urn:nbn:de:0030-drops-229614},
  doi =		{10.4230/LIPIcs.ICDT.2025.20},
  annote =	{Keywords: Databases, relational databases, graph databases, factorized databases, regular path queries, compact representations}
}
Document
DOI: 10.4230/LIPIcs.ICDT.2025.29
FC-Datalog as a Framework for Efficient String Querying

Authors: Owen M. Bell, Joel D. Day, and Dominik D. Freydenberger

Published in: LIPIcs, Volume 328, 28th International Conference on Database Theory (ICDT 2025)

Abstract
Core spanners are a class of document spanners that capture the core functionality of IBM’s AQL. FC is a logic on strings built around word equations that when extended with constraints for regular languages can be seen as a logic for core spanners. The recently introduced FC-Datalog extends FC with recursion, which allows us to define recursive relations for core spanners. Additionally, as FC-Datalog captures 𝖯, it is also a tractable version of Datalog on strings. This presents an opportunity for optimization. We propose a series of FC-Datalog fragments with desirable properties in terms of complexity of model checking, expressive power, and efficiency of checking membership in the fragment. This leads to a range of fragments that all capture LOGSPACE, which we further restrict to obtain linear combined complexity. This gives us a framework to tailor fragments for particular applications. To showcase this, we simulate deterministic regex in a tailored fragment of FC-Datalog.
Cite as

Owen M. Bell, Joel D. Day, and Dominik D. Freydenberger. FC-Datalog as a Framework for Efficient String Querying. In 28th International Conference on Database Theory (ICDT 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 328, pp. 29:1-29:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{bell_et_al:LIPIcs.ICDT.2025.29,
  author =	{Bell, Owen M. and Day, Joel D. and Freydenberger, Dominik D.},
  title =	{{FC-Datalog as a Framework for Efficient String Querying}},
  booktitle =	{28th International Conference on Database Theory (ICDT 2025)},
  pages =	{29:1--29:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-364-5},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{328},
  editor =	{Roy, Sudeepa and Kara, Ahmet},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICDT.2025.29},
  URN =		{urn:nbn:de:0030-drops-229708},
  doi =		{10.4230/LIPIcs.ICDT.2025.29},
  annote =	{Keywords: Information extraction, word equations, datalog, document spanners, regex}
}
Document
DOI: 10.4230/LIPIcs.STACS.2025.74
Nearly-Optimal Algorithm for Non-Clairvoyant Service with Delay

Authors: Noam Touitou

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

Abstract
We consider the online service with delay problem, in which a server traverses a metric space to serve requests that arrive over time. Requests gather individual delay cost while awaiting service, penalizing service latency; an algorithm seeks to minimize both its movement cost and the total delay cost. Algorithms for the problem (on general metric spaces) are only known for the clairvoyant model, where the algorithm knows future delay cost in advance (e.g., Azar et al., STOC'17; Azar and Touitou, FOCS'19; Touitou, STOC'23). However, in the non-clairvoyant setting, only negative results are known: where n is the size of the metric space and m is the number of requests, there are lower bounds of Ω(√n) and Ω(√m) on competitiveness (Azar et al., STOC'17), that hold even for randomized algorithms (Le et al., SODA'23). In this paper, we present the first algorithm for non-clairvoyant online service with delay. Our algorithm is deterministic and O(min{√n log n, √m log m})-competitive; combined with the lower bounds of Azar et al., this settles the correct competitive ratio for the problem up to logarithmic factors, in terms of both n and m.
Cite as

Noam Touitou. Nearly-Optimal Algorithm for Non-Clairvoyant Service with Delay. In 42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 327, pp. 74:1-74:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{touitou:LIPIcs.STACS.2025.74,
  author =	{Touitou, Noam},
  title =	{{Nearly-Optimal Algorithm for Non-Clairvoyant Service with Delay}},
  booktitle =	{42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025)},
  pages =	{74:1--74:21},
  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.2025.74},
  URN =		{urn:nbn:de:0030-drops-228995},
  doi =		{10.4230/LIPIcs.STACS.2025.74},
  annote =	{Keywords: Online, Delay, Deadlines, k-server, Non-clairvoyant}
}
Document
DOI: 10.4230/LIPIcs.STACS.2025.59
Online Matching with Delays and Size-Based Costs

Authors: Yasushi Kawase and Tomohiro Nakayoshi

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

Abstract
In this paper, we introduce the problem of Online Matching with Delays and Size-based Costs (OMDSC). The OMDSC problem involves m requests arriving online. At any time, a group can be formed by matching any number of requests that have been received but remain unmatched. The cost associated with each group is determined by the waiting time for each request within the group and size-dependent cost. The size-dependent cost is specified by a penalty function. Our goal is to partition all the incoming requests into multiple groups while minimizing the total associated cost. This problem is an extension of the TCP acknowledgment problem proposed by Dooly et al. (J. ACM, 2001). It generalizes the cost model for sending acknowledgments. This study reveals the competitive ratios for a fundamental case, in which the penalty function takes only values of either 0 or 1. We classify such penalty functions into three distinct cases: (i) a fixed penalty of 1 regardless of the group size, (ii) a penalty of 0 if and only if the group size is a multiple of a specific integer k, and (iii) other situations. The problem in case (i) is equivalent to the TCP acknowledgment problem, for which Dooly et al. proposed a 2-competitive algorithm. For case (ii), we first show that natural algorithms that match all remaining requests are Ω(√k)-competitive. We then propose an O(log k / log log k)-competitive deterministic algorithm by carefully managing the match size and timing, and prove its optimality. For any penalty function in case (iii), we demonstrate the non-existence of a competitive online algorithm. Additionally, we discuss competitive ratios for other typical penalty functions that are not restricted to take values of 0 or 1.
Cite as

Yasushi Kawase and Tomohiro Nakayoshi. Online Matching with Delays and Size-Based Costs. In 42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 327, pp. 59:1-59:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{kawase_et_al:LIPIcs.STACS.2025.59,
  author =	{Kawase, Yasushi and Nakayoshi, Tomohiro},
  title =	{{Online Matching with Delays and Size-Based Costs}},
  booktitle =	{42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025)},
  pages =	{59:1--59:18},
  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.2025.59},
  URN =		{urn:nbn:de:0030-drops-228846},
  doi =		{10.4230/LIPIcs.STACS.2025.59},
  annote =	{Keywords: Online matching, competitive analysis, delayed service}
}
Document
DOI: 10.4230/LIPIcs.STACS.2025.18
Online Disjoint Set Covers: Randomization Is Not Necessary

Authors: Marcin Bienkowski, Jarosław Byrka, and Łukasz Jeż

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

Abstract
In the online disjoint set covers problem, the edges of a hypergraph are revealed online, and the goal is to partition them into a maximum number of disjoint set covers. That is, n nodes of a hypergraph are given at the beginning, and then a sequence of hyperedges (subsets of [n]) is presented to an algorithm. For each hyperedge, an online algorithm must assign a color (an integer). Once an input terminates, the gain of the algorithm is the number of colors that correspond to valid set covers (i.e., the union of hyperedges that have that color contains all n nodes). We present a deterministic online algorithm that is O(log² n)-competitive, exponentially improving on the previous bound of O(n) and matching the performance of the best randomized algorithm by Emek et al. [ESA 2019]. For color selection, our algorithm uses a novel potential function, which can be seen as an online counterpart of the derandomization method of conditional probabilities and pessimistic estimators. There are only a few cases where derandomization has been successfully used in the field of online algorithms. In contrast to previous approaches, our result extends to the following new challenges: (i) the potential function derandomizes not only the Chernoff bound, but also the coupon collector’s problem, (ii) the value of Opt of the maximization problem is not bounded a priori, and (iii) we do not produce a fractional solution first, but work directly on the input.
Cite as

Marcin Bienkowski, Jarosław Byrka, and Łukasz Jeż. Online Disjoint Set Covers: Randomization Is Not Necessary. In 42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 327, pp. 18:1-18:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{bienkowski_et_al:LIPIcs.STACS.2025.18,
  author =	{Bienkowski, Marcin and Byrka, Jaros{\l}aw and Je\.{z}, {\L}ukasz},
  title =	{{Online Disjoint Set Covers: Randomization Is Not Necessary}},
  booktitle =	{42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025)},
  pages =	{18:1--18:16},
  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.2025.18},
  URN =		{urn:nbn:de:0030-drops-228433},
  doi =		{10.4230/LIPIcs.STACS.2025.18},
  annote =	{Keywords: Disjoint Set Covers, Derandomization, pessimistic Estimator, potential Function, online Algorithms, competitive Analysis}
}
Document
DOI: 10.4230/LIPIcs.ESA.2021.45
Compression by Contracting Straight-Line Programs

Authors: Moses Ganardi

Published in: LIPIcs, Volume 204, 29th Annual European Symposium on Algorithms (ESA 2021)

Abstract
In grammar-based compression a string is represented by a context-free grammar, also called a straight-line program (SLP), that generates only that string. We refine a recent balancing result stating that one can transform an SLP of size g in linear time into an equivalent SLP of size 𝒪(g) so that the height of the unique derivation tree is 𝒪(log N) where N is the length of the represented string (FOCS 2019). We introduce a new class of balanced SLPs, called contracting SLPs, where for every rule A → β₁ … β_k the string length of every variable β_i on the right-hand side is smaller by a constant factor than the string length of A. In particular, the derivation tree of a contracting SLP has the property that every subtree has logarithmic height in its leaf size. We show that a given SLP of size g can be transformed in linear time into an equivalent contracting SLP of size 𝒪(g) with rules of constant length. This result is complemented by a lower bound, proving that converting SLPs into so called α-balanced SLPs or AVL-grammars can incur an increase by a factor of Ω(log N). We present an application to the navigation problem in compressed unranked trees, represented by forest straight-line programs (FSLPs). A linear space data structure by Reh and Sieber (2020) supports navigation steps such as going to the parent, left/right sibling, or to the first/last child in constant time. We extend their solution by the operation of moving to the i-th child in time 𝒪(log d) where d is the degree of the current node. Contracting SLPs are also applied to the finger search problem over SLP-compressed strings where one wants to access positions near to a pre-specified finger position, ideally in 𝒪(log d) time where d is the distance between the accessed position and the finger. We give a linear space solution for the dynamic variant where one can set the finger in 𝒪(log N) time, and then access symbols or move the finger in time 𝒪(log d + log^(t) N) for any constant t where log^(t) N is the t-fold logarithm of N. This improves a previous solution by Bille, Christiansen, Cording, and Gørtz (2018) with access/move time 𝒪(log d + log log N).
Cite as

Moses Ganardi. Compression by Contracting Straight-Line Programs. In 29th Annual European Symposium on Algorithms (ESA 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 204, pp. 45:1-45:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{ganardi:LIPIcs.ESA.2021.45,
  author =	{Ganardi, Moses},
  title =	{{Compression by Contracting Straight-Line Programs}},
  booktitle =	{29th Annual European Symposium on Algorithms (ESA 2021)},
  pages =	{45:1--45:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-204-4},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{204},
  editor =	{Mutzel, Petra and Pagh, Rasmus 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.2021.45},
  URN =		{urn:nbn:de:0030-drops-146263},
  doi =		{10.4230/LIPIcs.ESA.2021.45},
  annote =	{Keywords: grammar-based compression, balancing, finger search}
}
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