175 Search Results for "Gawrychowski, Paweł"

Volume

LIPIcs, Volume 345

50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025)

MFCS 2025, August 25-29, 2025, Warsaw, Poland

Editors: Paweł Gawrychowski, Filip Mazowiecki, and Michał Skrzypczak

Volume

LIPIcs, Volume 191

32nd Annual Symposium on Combinatorial Pattern Matching (CPM 2021)

CPM 2021, July 5-7, 2021, Wrocław, Poland

Editors: Paweł Gawrychowski and Tatiana Starikovskaya

Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2026.25
Permutation Patterns in Streams

Authors: Benjamin Aram Berendsohn

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

Abstract
Permutation patterns and pattern avoidance are central, well-studied concepts in combinatorics and computer science. Given two permutations τ and π, the pattern matching problem (PPM) asks whether τ contains π. This problem arises in various contexts in computer science and statistics and has been studied extensively in exact-, parameterized-, approximate-, property-testing- and other formulations. In this paper, we study pattern matching in a streaming setting, when the input τ is revealed sequentially, one element at a time. There is extensive work on the space complexity of various statistics in streams of integers. The novelty of our setting is that the input stream is a permutation, which allows inferring some information about future inputs. Our algorithms crucially take advantage of this fact, while existing lower bound techniques become difficult to apply. We show that the complexity of the problem changes dramatically depending on the pattern π. The space requirement is: - Θ(klog{n}) for the monotone patterns π = 12…k, or π = k…21, - 𝒪(√{nlog{n}}) for π ∈ {312,132}, - 𝒪(√n log n) for π ∈ {231,213}, - Θ̃_π(n) for all other π. If τ is an arbitrary sequence of integers (not necessary a permutation), we show that the complexity is Θ̃_π(n) in all except the first (monotone) cases.
Cite as

Benjamin Aram Berendsohn. Permutation Patterns in Streams. In 53rd International Colloquium on Automata, Languages, and Programming (ICALP 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 374, pp. 25:1-25:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{berendsohn:LIPIcs.ICALP.2026.25,
  author =	{Berendsohn, Benjamin Aram},
  title =	{{Permutation Patterns in Streams}},
  booktitle =	{53rd International Colloquium on Automata, Languages, and Programming (ICALP 2026)},
  pages =	{25:1--25:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-428-4},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{374},
  editor =	{Bhattacharya, Sayan and Nanongkai, Danupon and Benedikt, Michael and Puppis, Gabriele},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2026.25},
  URN =		{urn:nbn:de:0030-drops-264144},
  doi =		{10.4230/LIPIcs.ICALP.2026.25},
  annote =	{Keywords: permutations, pattern matching, streaming}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2026.55
Suffix Random Access via Function Inversion: A Key for Asymmetric Streaming String Algorithms

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

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

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

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

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@InProceedings{charalampopoulos_et_al:LIPIcs.ICALP.2026.55,
  author =	{Charalampopoulos, Panagiotis and El Ghazi, Taha and Ellert, Jonas and Gawrychowski, Pawe{\l} and Starikovskaya, Tatiana},
  title =	{{Suffix Random Access via Function Inversion: A Key for Asymmetric Streaming String Algorithms}},
  booktitle =	{53rd International Colloquium on Automata, Languages, and Programming (ICALP 2026)},
  pages =	{55:1--55:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-428-4},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{374},
  editor =	{Bhattacharya, Sayan and Nanongkai, Danupon and Benedikt, Michael and Puppis, Gabriele},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2026.55},
  URN =		{urn:nbn:de:0030-drops-264440},
  doi =		{10.4230/LIPIcs.ICALP.2026.55},
  annote =	{Keywords: streaming algorithms, function inversion, string algorithms}
}
Document
DOI: 10.4230/LIPIcs.SEA.2026.13
Practical Parallel Block Tree Construction

Authors: Robert Clausecker, Florian Kurpicz, and Etienne Palanga

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

Abstract
The block tree [Belazzougui et al., J. Comput. Syst. Sci. '21] is a compressed representation of a length-n text that supports access, rank, and select queries while requiring only O(z log n/z) words of space, where z is the number of Lempel-Ziv factors of the text. In other words, its space requirements are asymptotically comparable to those of the compressed text itself. In practice, block trees offer query performance comparable to that of state-of-the-art compressed rank and select indices. However, their construction is significantly slower, and the fastest known construction algorithms additionally require a significant amount of working memory. To address these limitations, we propose fast and lightweight parallel algorithms for the efficient construction of block trees. Our algorithm achieves similar construction speed than the currently fastest block tree construction algorithm on a single core and is up to eight times faster using 64 cores, while requiring an order of magnitude less memory. Overall, we achieve a speedup of up to 15.5 on 64 cores, which is in line with the parallel construction of the Lempel-Ziv compression.
Cite as

Robert Clausecker, Florian Kurpicz, and Etienne Palanga. Practical Parallel Block Tree Construction. In 24th International Symposium on Experimental Algorithms (SEA 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 371, pp. 13:1-13:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{clausecker_et_al:LIPIcs.SEA.2026.13,
  author =	{Clausecker, Robert and Kurpicz, Florian and Palanga, Etienne},
  title =	{{Practical Parallel Block Tree Construction}},
  booktitle =	{24th International Symposium on Experimental Algorithms (SEA 2026)},
  pages =	{13:1--13:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-422-2},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{371},
  editor =	{Aum\"{u}ller, Martin and Finocchi, Irene},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SEA.2026.13},
  URN =		{urn:nbn:de:0030-drops-260175},
  doi =		{10.4230/LIPIcs.SEA.2026.13},
  annote =	{Keywords: block tree, shared memory, compression, SIMD, Karp-Rabin fingerprints}
}
Document
DOI: 10.4230/LIPIcs.SEA.2026.7
From Relative Compression to Hierarchical Compression

Authors: Philip Bille, Inge Li Gørtz, and Máximo Pérez-López

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

Abstract
We introduce a framework to use any relative compression algorithm as a subroutine for hierarchical relative compression. In a dataset consisting of n sequences, it consists of constructing a rooted tree on the sequences, using hashing and similarity techniques, and compressing the children of a node relative to their parent. We build up on previous techniques [Bille et al., 2023], and optimize them further for computational efficiency. We test our framework with three existing relative compression algorithms on six genomic datasets, and we show that in datasets that contain heterogeneous data, hierarchical relative compression improves the compression ratio by a factor 2 or more, when compared to relative compression to a single sequence. Apart from compression ratio, we also explore the trade-offs with respect to compression speed, dataset decompression speed, and average sequence decompression speed. With two of the surveyed algorithms, dataset decompression becomes faster and sequence decompression remains practical, at the cost of compression time, which remains competitive for the datasets with highest variability.
Cite as

Philip Bille, Inge Li Gørtz, and Máximo Pérez-López. From Relative Compression to Hierarchical Compression. In 24th International Symposium on Experimental Algorithms (SEA 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 371, pp. 7:1-7:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{bille_et_al:LIPIcs.SEA.2026.7,
  author =	{Bille, Philip and G{\o}rtz, Inge Li and P\'{e}rez-L\'{o}pez, M\'{a}ximo},
  title =	{{From Relative Compression to Hierarchical Compression}},
  booktitle =	{24th International Symposium on Experimental Algorithms (SEA 2026)},
  pages =	{7:1--7:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-422-2},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{371},
  editor =	{Aum\"{u}ller, Martin and Finocchi, Irene},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SEA.2026.7},
  URN =		{urn:nbn:de:0030-drops-260117},
  doi =		{10.4230/LIPIcs.SEA.2026.7},
  annote =	{Keywords: Relative compression, RLZ, string collections, compressed representation, data structures, efficient algorithms}
}
Document
DOI: 10.4230/LIPIcs.SEA.2026.10
Compressing Highly Repetitive Binary Trees with an Application to Range Minimum Queries

Authors: Gabriel Carmona and Filippo Lari

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

Abstract
Tree compression is a well-studied area that aims at reducing the size of tree representations by exploiting different forms of repetition. While the underlying theory is well understood, there is still significant room for experimental investigation, particularly in the design of compressed representations that efficiently support navigational queries. In this work, we address the problem of designing, engineering, and experimentally evaluating a compression technique for unlabeled binary trees based on repeated subtrees, yielding the minimal Directed Acyclic Graph (DAG) of the input tree. We show how this representation can be computed in linear time and space directly from a succinct encoding of the tree, and how it can be augmented with compact auxiliary data structures to support Lowest Common Ancestor (LCA) queries. When the input tree is the Cartesian tree of an array, LCA queries can be used to answer Range Minimum Queries (RMQs) on the underlying array. This is particularly relevant in the encoding model, where the array is not accessible at query time, and a space lower bound of 2n-O(log n) bits is known. Given the numerous applications of RMQs, we use this problem as a case study for our experimental evaluation, testing our implementation on 11 real-world datasets. Our experiments show that, on almost every dataset, our implementation is the most space-efficient, using as few as 0.11n bits, while still delivering practical query times.
Cite as

Gabriel Carmona and Filippo Lari. Compressing Highly Repetitive Binary Trees with an Application to Range Minimum Queries. In 24th International Symposium on Experimental Algorithms (SEA 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 371, pp. 10:1-10:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{carmona_et_al:LIPIcs.SEA.2026.10,
  author =	{Carmona, Gabriel and Lari, Filippo},
  title =	{{Compressing Highly Repetitive Binary Trees with an Application to Range Minimum Queries}},
  booktitle =	{24th International Symposium on Experimental Algorithms (SEA 2026)},
  pages =	{10:1--10:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-422-2},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{371},
  editor =	{Aum\"{u}ller, Martin and Finocchi, Irene},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SEA.2026.10},
  URN =		{urn:nbn:de:0030-drops-260140},
  doi =		{10.4230/LIPIcs.SEA.2026.10},
  annote =	{Keywords: tree compression, range minimum query, compact data structures, algorithm engineering, experimental evaluation}
}
Document
DOI: 10.4230/LIPIcs.SEA.2026.11
Wavelet Forests Revisited

Authors: Eric Chiu and Dominik Kempa

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

Abstract
Rank and select queries are basic operations on sequences, with applications in compressed text indexes and other space-efficient data structures. One of the standard data structures supporting these queries is the wavelet tree. In this paper, we study wavelet forests, that is, wavelet-tree structures based on the fixed-block compression boosting technique. Such structures partition the input sequence into fixed-size blocks and build a separate wavelet tree for each block. Previous work showed that this approach yields strong practical performance for rank queries. We extend wavelet forests to support select queries. We show that select support can be added with little additional space overhead and that the resulting structures remain practically efficient. In experiments on a range of non-repetitive and repetitive inputs, wavelet forests are competitive with, and in most cases outperform, standalone wavelet-tree implementations. We also study the effect of internal parameters, including superblock size and navigational data, on select-query performance.
Cite as

Eric Chiu and Dominik Kempa. Wavelet Forests Revisited. In 24th International Symposium on Experimental Algorithms (SEA 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 371, pp. 11:1-11:11, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{chiu_et_al:LIPIcs.SEA.2026.11,
  author =	{Chiu, Eric and Kempa, Dominik},
  title =	{{Wavelet Forests Revisited}},
  booktitle =	{24th International Symposium on Experimental Algorithms (SEA 2026)},
  pages =	{11:1--11:11},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-422-2},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{371},
  editor =	{Aum\"{u}ller, Martin and Finocchi, Irene},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SEA.2026.11},
  URN =		{urn:nbn:de:0030-drops-260152},
  doi =		{10.4230/LIPIcs.SEA.2026.11},
  annote =	{Keywords: wavelet tree, wavelet forest, select queries}
}
Document
DOI: 10.4230/LIPIcs.SEA.2026.16
Efficient Large-Scale Text Precompression via Approximate LZ77 Parsings

Authors: Patrick Dinklage

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

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

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

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@InProceedings{dinklage:LIPIcs.SEA.2026.16,
  author =	{Dinklage, Patrick},
  title =	{{Efficient Large-Scale Text Precompression via Approximate LZ77 Parsings}},
  booktitle =	{24th International Symposium on Experimental Algorithms (SEA 2026)},
  pages =	{16:1--16:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-422-2},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{371},
  editor =	{Aum\"{u}ller, Martin and Finocchi, Irene},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SEA.2026.16},
  URN =		{urn:nbn:de:0030-drops-260204},
  doi =		{10.4230/LIPIcs.SEA.2026.16},
  annote =	{Keywords: compression, algorithm engineering, parallel computation}
}
Document
DOI: 10.4230/LIPIcs.CPM.2026.34
LZBE: An LZ-Style Compressor Supporting O(log n)-Time Random Access

Authors: Hiroki Shibata, Yuto Nakashima, Yutaro Yamaguchi, and Shunsuke Inenaga

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

Abstract
An LZ-like factorization of a string divides it into factors, each being either a single character or a copy of a preceding substring. While grammar-based compression schemes support efficient random access with space linear in the compressed size, no comparable guarantees are known for general LZ-like factorizations. This limitation motivated restricted variants such as LZ-End [Kreft and Navarro, 2013] and height-bounded LZ (LZHB) [Bannai et al., 2024], which trade off some compression efficiency for faster access. In this paper, we introduce LZ-Begin-End (LZBE), a new LZ-like variant in which every copy factor must refer to a contiguous sequence of preceding factors. This structural restriction ensures that any context-free grammar can be transformed into an LZBE factorization of the same size. We further study the greedy LZBE factorization, which selects each copy factor to be as long as possible while processing the input from left to right, and show that it can be computed in linear time. Moreover, we exhibit a family of strings for which the greedy LZBE factorization is asymptotically smaller than the smallest grammar. These results demonstrate that the LZBE scheme is strictly more expressive than grammar-based compression in the worst case. To support fast queries, we propose a data structure for LZBE-compressed strings that permits O(log n)-time random access within space linear in the compressed size, where n is the length of the input string.
Cite as

Hiroki Shibata, Yuto Nakashima, Yutaro Yamaguchi, and Shunsuke Inenaga. LZBE: An LZ-Style Compressor Supporting O(log n)-Time Random Access. In 37th Annual Symposium on Combinatorial Pattern Matching (CPM 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 369, pp. 34:1-34:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{shibata_et_al:LIPIcs.CPM.2026.34,
  author =	{Shibata, Hiroki and Nakashima, Yuto and Yamaguchi, Yutaro and Inenaga, Shunsuke},
  title =	{{LZBE: An LZ-Style Compressor Supporting O(log n)-Time Random Access}},
  booktitle =	{37th Annual Symposium on Combinatorial Pattern Matching (CPM 2026)},
  pages =	{34:1--34:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-420-8},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{369},
  editor =	{Bille, Philip and Prezza, Nicola},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CPM.2026.34},
  URN =		{urn:nbn:de:0030-drops-259609},
  doi =		{10.4230/LIPIcs.CPM.2026.34},
  annote =	{Keywords: data compression, Lempel-Ziv parsing, string algorithms, random access}
}
Document
DOI: 10.4230/LIPIcs.CPM.2026.1
Hamming Distance Oracles

Authors: Itai Boneh, Dvir Fried, Shay Golan, Matan Kraus, and Ely Porat

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

Abstract
In this paper, we present and study the Hamming distance oracle problem. In this problem, the task is to preprocess two strings S and T of lengths n and m, respectively, to obtain a data structure that is able to return the Hamming distance between a substring of S and a substring of T. For strings over a constant-size alphabet, we show that for every x ≤ min{n,m} there is a data structure with Õ(nm/x) preprocessing time and O(x) query time. We also provide a conditional lower bound, showing that for every ε > 0 there is no combinatorial data structure with query time O(x) and preprocessing time O((nm/x)^{1-ε}) unless combinatorial fast matrix multiplication is possible. For strings over a general alphabet, we present a data structure with Õ(nm/√x) pre-processing time and O(x) query time for every x ≤ min {n,m}. Moreover, for every ε > 0 we provide a data structure with a preprocessing time of Õ((n+m)/ε³) that returns with high probability a (1±ε) approximation of the Hamming distance of two input substrings. The query time of the approximation data structure is Õ(1/ε²).
Cite as

Itai Boneh, Dvir Fried, Shay Golan, Matan Kraus, and Ely Porat. Hamming Distance Oracles. In 37th Annual Symposium on Combinatorial Pattern Matching (CPM 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 369, pp. 1:1-1:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{boneh_et_al:LIPIcs.CPM.2026.1,
  author =	{Boneh, Itai and Fried, Dvir and Golan, Shay and Kraus, Matan and Porat, Ely},
  title =	{{Hamming Distance Oracles}},
  booktitle =	{37th Annual Symposium on Combinatorial Pattern Matching (CPM 2026)},
  pages =	{1:1--1:12},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-420-8},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{369},
  editor =	{Bille, Philip and Prezza, Nicola},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CPM.2026.1},
  URN =		{urn:nbn:de:0030-drops-259278},
  doi =		{10.4230/LIPIcs.CPM.2026.1},
  annote =	{Keywords: Hamming distance, Fine-grained complexity, Data structure, Oracle}
}
Document
DOI: 10.4230/LIPIcs.CPM.2026.2
Near-Real-Time Solutions for Online String Problems

Authors: Dominik Köppl and Gregory Kucherov

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

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

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

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@InProceedings{koppl_et_al:LIPIcs.CPM.2026.2,
  author =	{K\"{o}ppl, Dominik and Kucherov, Gregory},
  title =	{{Near-Real-Time Solutions for Online String Problems}},
  booktitle =	{37th Annual Symposium on Combinatorial Pattern Matching (CPM 2026)},
  pages =	{2:1--2:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-420-8},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{369},
  editor =	{Bille, Philip and Prezza, Nicola},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CPM.2026.2},
  URN =		{urn:nbn:de:0030-drops-259287},
  doi =		{10.4230/LIPIcs.CPM.2026.2},
  annote =	{Keywords: online algorithms, string algorithms, suffix tree, real-time computation, Lempel-Ziv factorization, minimal unique substrings}
}
Document
DOI: 10.4230/LIPIcs.CPM.2026.4
Compact Representation of Maximal Palindromes

Authors: Takuya Mieno

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

Abstract
Palindromes are strings that read the same forward and backward. The computation of palindromic structures within strings is a fundamental problem in string algorithms, being motivated by potential applications in formal language theory and bioinformatics. Although the number of palindromic factors in a string of length n can be quadratic, they can be implicitly represented in O(n log n) bits of space by storing the lengths of all maximal palindromes in an integer array, which can be computed in O(n) time [Manacher, 1975]. In this paper, we propose a novel O(n)-bit representation of all maximal palindromes in a string, which enables O(1)-time retrieval of the length of the maximal palindrome centered at any given position. The data structure can be constructed in O(n) time from the input string of length n. Since Manacher’s algorithm and the notion of maximal palindromes are widely utilized for solving numerous problems involving palindromic structures, our compact representation will accelerate the development of more space-efficient solutions to such problems. Indeed, as the first application of our compact representation of maximal palindromes, we present a data structure of size O(n) bits that can compute the longest palindrome appearing in any given factor of a string of length n in O(log n) time.
Cite as

Takuya Mieno. Compact Representation of Maximal Palindromes. In 37th Annual Symposium on Combinatorial Pattern Matching (CPM 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 369, pp. 4:1-4:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{mieno:LIPIcs.CPM.2026.4,
  author =	{Mieno, Takuya},
  title =	{{Compact Representation of Maximal Palindromes}},
  booktitle =	{37th Annual Symposium on Combinatorial Pattern Matching (CPM 2026)},
  pages =	{4:1--4:12},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-420-8},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{369},
  editor =	{Bille, Philip and Prezza, Nicola},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CPM.2026.4},
  URN =		{urn:nbn:de:0030-drops-259304},
  doi =		{10.4230/LIPIcs.CPM.2026.4},
  annote =	{Keywords: palindromes, succinct data structures, internal queries}
}
Document
DOI: 10.4230/LIPIcs.CPM.2026.6
Improved Bounds on the Maximum Number of Distinct Squares in Circular Words

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

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

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

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

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@InProceedings{charalampopoulos_et_al:LIPIcs.CPM.2026.6,
  author =	{Charalampopoulos, Panagiotis and Mohamed, Manal and Radoszewski, Jakub and Rytter, Wojciech and Wale\'{n}, Tomasz and Zuba, Wiktor},
  title =	{{Improved Bounds on the Maximum Number of Distinct Squares in Circular Words}},
  booktitle =	{37th Annual Symposium on Combinatorial Pattern Matching (CPM 2026)},
  pages =	{6:1--6:12},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-420-8},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{369},
  editor =	{Bille, Philip and Prezza, Nicola},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CPM.2026.6},
  URN =		{urn:nbn:de:0030-drops-259325},
  doi =		{10.4230/LIPIcs.CPM.2026.6},
  annote =	{Keywords: circular words, squares, repetitions}
}
Document
DOI: 10.4230/LIPIcs.CPM.2026.9
Indexing and Encoding Arrays for Element Distinctness Queries

Authors: Johannes Fischer and Filippo Lari

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

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

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

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@InProceedings{fischer_et_al:LIPIcs.CPM.2026.9,
  author =	{Fischer, Johannes and Lari, Filippo},
  title =	{{Indexing and Encoding Arrays for Element Distinctness Queries}},
  booktitle =	{37th Annual Symposium on Combinatorial Pattern Matching (CPM 2026)},
  pages =	{9:1--9:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-420-8},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{369},
  editor =	{Bille, Philip and Prezza, Nicola},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CPM.2026.9},
  URN =		{urn:nbn:de:0030-drops-259350},
  doi =		{10.4230/LIPIcs.CPM.2026.9},
  annote =	{Keywords: element distinctness, range queries, lower bounds, succinct data structures}
}
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