46 Search Results for "Nakashima, Yuto"

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.2026.2
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.2026.8
Constant Multiplicative Sensitivity on the CDAWGs

Authors: Rikuya Hamai, Hiroto Fujimaru, and Shunsuke Inenaga

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

Abstract
Compact directed acyclic word graphs (CDAWGs) [Blumer et al. 1987] are a fundamental data structure on strings with applications in text pattern searching, data compression, and pattern discovery. Intuitively, the CDAWG of a string T is obtained by merging isomorphic subtrees of the suffix tree [Weiner 1973] of the same string T, and thus CDAWGs are a compact indexing structure. Indeed, the CDAWG size 𝖾 can be sublinear in n for some highly repetitive strings. Of its various applications, the CDAWG allows for computing pattern occurrences, maximal exact matches (MEMs), minimal absent words (MAWs), and minimal unique substrings (MUSs) in optimal time using O(𝖾) space. For designing space-efficient data storage, it is crucial that the underlying data structure is robust against data edits and errors. As a mathematical measure for this, the notion of compression sensitivity [Akagi et al. 2023] was introduced as the maximum of the size increase in the compressed data structures after edits operations. In this paper, we investigate the sensitivity of CDAWGs when a single character edit operation is performed at an arbitrary position in the input string T. We show that the size of the CDAWG after an edit operation on T is asymptotically at most 8 times larger than the original CDAWG before the edit. This O(1) upper bound significantly improves on the only known upper bound O(n/log n) for the problem.
Cite as

Rikuya Hamai, Hiroto Fujimaru, and Shunsuke Inenaga. Constant Multiplicative Sensitivity on the CDAWGs. In 37th Annual Symposium on Combinatorial Pattern Matching (CPM 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 369, pp. 8:1-8:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{hamai_et_al:LIPIcs.CPM.2026.8,
  author =	{Hamai, Rikuya and Fujimaru, Hiroto and Inenaga, Shunsuke},
  title =	{{Constant Multiplicative Sensitivity on the CDAWGs}},
  booktitle =	{37th Annual Symposium on Combinatorial Pattern Matching (CPM 2026)},
  pages =	{8:1--8:17},
  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.2026.8},
  URN =		{urn:nbn:de:0030-drops-259345},
  doi =		{10.4230/LIPIcs.CPM.2026.8},
  annote =	{Keywords: string data structures, maximal repeats, data compression, compression sensitivity, CDAWGs}
}
Document
DOI: 10.4230/LIPIcs.CPM.2026.14
Hardness Results on Characteristics for Elastic-Degenerate Strings

Authors: Dominik Köppl and Jannik Olbrich

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

Abstract
Generalizations of plain strings have been proposed as a compact way to represent a collection of nearly identical sequences or to express uncertainty at specific text positions by enumerating all possibilities. While a plain string stores a character at each of its positions, generalizations consider a set of characters (indeterminate strings), a set of strings of equal length (generalized degenerate strings, or shortly GD strings), or a set of strings of arbitrary lengths (elastic-degenerate strings, or shortly ED strings). These generalizations are of importance to compactly represent such type of data, and find applications in bioinformatics for representing and maintaining a set of genetic sequences of the same taxonomy or a multiple sequence alignment. To be of use, attention has been drawn to answering various query types such as pattern matching or measuring similarity of ED strings by generalizing techniques known to plain strings. However, for some types of queries, it has been shown that a generalization of a polynomial-time solvable query on classic strings becomes NP-hard on ED strings, e.g. [Russo et al., 2022]. In that light, we wonder about other types of queries that are of particular interest to bioinformatics: unique substrings, absent words, anti-powers, longest previous factors, and Lempel-Ziv-like compression schemes. While we obtain a polynomial time algorithm for a variation of longest previous factors, we show that all other problems are NP-hard to compute, some of them even under the restriction that the input can be modeled as an indeterminate or GD string.
Cite as

Dominik Köppl and Jannik Olbrich. Hardness Results on Characteristics for Elastic-Degenerate Strings. In 37th Annual Symposium on Combinatorial Pattern Matching (CPM 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 369, pp. 14:1-14:25, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{koppl_et_al:LIPIcs.CPM.2026.14,
  author =	{K\"{o}ppl, Dominik and Olbrich, Jannik},
  title =	{{Hardness Results on Characteristics for Elastic-Degenerate Strings}},
  booktitle =	{37th Annual Symposium on Combinatorial Pattern Matching (CPM 2026)},
  pages =	{14:1--14:25},
  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.2026.14},
  URN =		{urn:nbn:de:0030-drops-259409},
  doi =		{10.4230/LIPIcs.CPM.2026.14},
  annote =	{Keywords: Elastic-degenerate strings, NP-hardness, longest common factor, minimal unique substring, minimal absent word, anti-power, longest previous factor}
}
Document
DOI: 10.4230/LIPIcs.CPM.2026.17
Sensitivity of Repetitiveness Measures to String Reversal

Authors: Hideo Bannai, Yuto Fujie, Peaker Guo, Shunsuke Inenaga, Yuto Nakashima, Simon J. Puglisi, and Cristian Urbina

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

Abstract
We study the impact that string reversal can have on several repetitiveness measures. First, we exhibit an infinite family of strings where the number, r, of runs in the run-length encoding of the Burrows-Wheeler transform (BWT) can increase additively by Θ(n) when reversing the string. This substantially improves the known Ω(log n) lower-bound for the additive sensitivity of r and it is asymptotically tight. We generalize our result to other variants of the BWT, including the variant with an appended end-of-string symbol and the bijective BWT. We show that an analogous result holds for the size z of the Lempel-Ziv 77 (LZ) parsing of the text, and also for some of its variants, including the non-overlapping LZ parsing, and the LZ-end parsing. Moreover, we describe a family of strings for which the ratio z(w^R)/z(w) approaches 3 from below as |w| → ∞. We also show an asymptotically tight lower-bound of Θ(n) for the additive sensitivity of the size v of the smallest lexicographic parsing to string reversal. Finally, we show that the multiplicative sensitivity of v to reversing the string is Θ(log n), and this lower-bound is also tight. Overall, our results expose the limitations of repetitiveness measures that are widely used in practice, against string reversal - a simple and natural data transformation.
Cite as

Hideo Bannai, Yuto Fujie, Peaker Guo, Shunsuke Inenaga, Yuto Nakashima, Simon J. Puglisi, and Cristian Urbina. Sensitivity of Repetitiveness Measures to String Reversal. In 37th Annual Symposium on Combinatorial Pattern Matching (CPM 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 369, pp. 17:1-17:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{bannai_et_al:LIPIcs.CPM.2026.17,
  author =	{Bannai, Hideo and Fujie, Yuto and Guo, Peaker and Inenaga, Shunsuke and Nakashima, Yuto and Puglisi, Simon J. and Urbina, Cristian},
  title =	{{Sensitivity of Repetitiveness Measures to String Reversal}},
  booktitle =	{37th Annual Symposium on Combinatorial Pattern Matching (CPM 2026)},
  pages =	{17:1--17:18},
  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.2026.17},
  URN =		{urn:nbn:de:0030-drops-259434},
  doi =		{10.4230/LIPIcs.CPM.2026.17},
  annote =	{Keywords: String reversal, Repetitiveness measures, Burrows-Wheeler transform, Lempel-Ziv parsing, Lexicographic parsings}
}
Document
DOI: 10.4230/LIPIcs.CPM.2026.23
Improved Bounds on the Sum of Exponents of Runs in a String

Authors: Arkadiusz Czarkowski

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

Abstract
A substring of a word is a run if it is at least twice as long as its minimum period and cannot be extended to either side with the same period. The exponent of a run is the quotient of its length and its minimum period. ρ(n) is the maximum number of runs in a string of length n, while σ(n) is the maximum sum of exponents of runs in a string of length n. While quite tight bounds on ρ(n) are known (0.944575712n ≤ ρ(n) ≤ n), the best upper bound on σ(n) is 3n whereas the best lower bound on σ(n) is 2.035n. In this paper, we improve the upper bound on σ(n) to 2.3n and the lower bound on σ(n) to 2.04448n. We also provide an improved upper bound on σ(n) of 2.2n in the case of a binary alphabet. Our results are achieved using a combination of theoretical and computer-based approaches.
Cite as

Arkadiusz Czarkowski. Improved Bounds on the Sum of Exponents of Runs in a String. In 37th Annual Symposium on Combinatorial Pattern Matching (CPM 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 369, pp. 23:1-23:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{czarkowski:LIPIcs.CPM.2026.23,
  author =	{Czarkowski, Arkadiusz},
  title =	{{Improved Bounds on the Sum of Exponents of Runs in a String}},
  booktitle =	{37th Annual Symposium on Combinatorial Pattern Matching (CPM 2026)},
  pages =	{23:1--23:18},
  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.2026.23},
  URN =		{urn:nbn:de:0030-drops-259494},
  doi =		{10.4230/LIPIcs.CPM.2026.23},
  annote =	{Keywords: strings, runs, sum of exponents of runs, Lyndon words, L-roots, maximal repetitions, combinatorics on words}
}
Document
DOI: 10.4230/LIPIcs.CPM.2026.27
Exploring the Gap Between LCS and LCStr

Authors: Shay Golan, Matan Kraus, Ely Porat, and B. Riva Shalom

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

Abstract
The Longest Common Subsequence (LCS) problem and the Longest Common Substring (LCStr) problem are classical string problems with broad theoretical and practical significance. The former has a quadratic conditional lower bound [FOCS, 2015], while the latter admits a linear-time solution. In this paper, we study a natural variation of these problems, the Longest Common Subsequence-Substring (LCSS) problem. The LCSS problem seeks the longest string that is simultaneously a subsequence of one input string and a substring of the other. This variant bridges LCS and LCStr, raising intriguing algorithmic questions: Does the complexity of computing LCSS interpolate between the linear time of LCStr and the quadratic time of LCS? What about approximability? We also examine a natural extension of LCSS to multiple strings, parameterizing the balance between subsequence and substring requirements. Our results reveal several insights. First, under the SETH conjecture, the inherent complexity of LCSS is quadratic, similar to LCS. In contrast, we provide a linear-time approximation for LCSS. Finally, for the multi-string variant, unlike both problems, we design a quadratic-time algorithm, uncovering deeper structural properties of the problem. By studying the complexity of the LCSS problem, we aim to gain some understanding of what influences whether a variant of the LCS problem behaves more like the standard LCS or like LCStr. Our findings suggest that hybrid constraints can create computational "sweet spots," where problems become more tractable than their pure counterparts. This opens a broader research direction in constraint-mediated algorithm design. Beyond LCSS itself, our work highlights unexpected connections between subsequence and substring constraints, advancing the theoretical understanding of string problems and laying the foundation for new algorithmic techniques and complexity-theoretic insights in the rich space between classical string comparison paradigms.
Cite as

Shay Golan, Matan Kraus, Ely Porat, and B. Riva Shalom. Exploring the Gap Between LCS and LCStr. In 37th Annual Symposium on Combinatorial Pattern Matching (CPM 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 369, pp. 27:1-27:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{golan_et_al:LIPIcs.CPM.2026.27,
  author =	{Golan, Shay and Kraus, Matan and Porat, Ely and Shalom, B. Riva},
  title =	{{Exploring the Gap Between LCS and LCStr}},
  booktitle =	{37th Annual Symposium on Combinatorial Pattern Matching (CPM 2026)},
  pages =	{27:1--27:21},
  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.2026.27},
  URN =		{urn:nbn:de:0030-drops-259535},
  doi =		{10.4230/LIPIcs.CPM.2026.27},
  annote =	{Keywords: Longest Common Subsequence, Longest Common Substring, Conditional Lower Bound}
}
Document
DOI: 10.4230/LIPIcs.CPM.2026.24
On Occurrence-Preserving Morphisms

Authors: Kaisei Kishi, Peaker Guo, Cristian Urbina, and Hideo Bannai

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

Abstract
A morphism is a mapping that transforms words through letter-wise substitution, where each symbol is consistently replaced by a fixed word. In the field of combinatorics on words, one topic that has attracted considerable attention is the characterization of morphisms that preserve specific properties, such as overlap-freeness, square-freeness, lexicographic order, and primitivity. Continuing this direction, we initiate the study on occurrence-preserving morphisms, which address the following fundamental question: given a morphism ϕ, two words u and v, and k ≥ 1, under what conditions does the number of occurrences of u in v equal the number of occurrences of ϕ^k(u) in ϕ^k(v)? To answer this question, we introduce the notion of interference-free morphisms, examine their properties, and uncover a connection to recognizable morphisms. We then present a precise characterization of occurrence-preserving morphisms in terms of interference-freeness. As applications of our characterization, we first show that there exists a bijection between the starting positions of the occurrences of u in v and those of ϕ^k(u) in ϕ^k(v). We then apply the characterization to the Fibonacci and Thue-Morse words to identify their minimal unique substrings (MUSs). Finally, we exploit the connection between MUSs and net occurrences to simplify existing proofs on net occurrences in these words.
Cite as

Kaisei Kishi, Peaker Guo, Cristian Urbina, and Hideo Bannai. On Occurrence-Preserving Morphisms. In 37th Annual Symposium on Combinatorial Pattern Matching (CPM 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 369, pp. 24:1-24:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{kishi_et_al:LIPIcs.CPM.2026.24,
  author =	{Kishi, Kaisei and Guo, Peaker and Urbina, Cristian and Bannai, Hideo},
  title =	{{On Occurrence-Preserving Morphisms}},
  booktitle =	{37th Annual Symposium on Combinatorial Pattern Matching (CPM 2026)},
  pages =	{24:1--24:16},
  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.2026.24},
  URN =		{urn:nbn:de:0030-drops-259504},
  doi =		{10.4230/LIPIcs.CPM.2026.24},
  annote =	{Keywords: Property-preserving morphisms, interference-free morphisms, recognizable morphisms, injective morphisms, Fibonacci words, Thue-Morse words, minimal unique substrings (MUSs), net occurrences}
}
Document
DOI: 10.4230/LIPIcs.CPM.2026.33
The Smallest String Attractors of Fibonacci and Period-Doubling Words

Authors: Mutsunori Banbara, Hideo Bannai, Peaker Guo, Dominik Köppl, Takuya Mieno, and Yoshio Okamoto

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

Abstract
A string attractor of a string T[1..|T|] is a set of positions Γ of T such that any substring w of T has an occurrence that crosses a position in Γ, i.e., there is a position i such that w = T[i..i+|w|-1] and the intersection [i,i+|w|-1]∩ Γ is nonempty. The size of the smallest string attractor of Fibonacci words is known to be 2. We completely characterize the set of all smallest string attractors of Fibonacci words, and show a recursive formula describing the 2^{n-4} + 2^{⌈n/2⌉ - 2} distinct position pairs that are the smallest string attractors of the nth Fibonacci word for n ≥ 7. Similarly, the size of the smallest string attractor of period-doubling words is known to be 2. We also completely characterize the set of all smallest string attractors of period-doubling words, and show a formula describing the two distinct position pairs that are the smallest string attractors of the nth period-doubling word for n ≥ 2. Our results show that strings with the same smallest attractor size can have a drastically different number of distinct smallest attractors.
Cite as

Mutsunori Banbara, Hideo Bannai, Peaker Guo, Dominik Köppl, Takuya Mieno, and Yoshio Okamoto. The Smallest String Attractors of Fibonacci and Period-Doubling Words. In 37th Annual Symposium on Combinatorial Pattern Matching (CPM 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 369, pp. 33:1-33:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{banbara_et_al:LIPIcs.CPM.2026.33,
  author =	{Banbara, Mutsunori and Bannai, Hideo and Guo, Peaker and K\"{o}ppl, Dominik and Mieno, Takuya and Okamoto, Yoshio},
  title =	{{The Smallest String Attractors of Fibonacci and Period-Doubling Words}},
  booktitle =	{37th Annual Symposium on Combinatorial Pattern Matching (CPM 2026)},
  pages =	{33:1--33:21},
  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.2026.33},
  URN =		{urn:nbn:de:0030-drops-259599},
  doi =		{10.4230/LIPIcs.CPM.2026.33},
  annote =	{Keywords: String attractors, Fibonacci words, Period-doubling words, Combinatorics on words}
}
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.2026.35
Efficient Index for Square Pattern Matching

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

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

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

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

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@InProceedings{chen_et_al:LIPIcs.CPM.2026.35,
  author =	{Chen, Po-Chun and Tsao, Che-Wei and Hon, Wing-Kai and K\"{o}ppl, Dominik},
  title =	{{Efficient Index for Square Pattern Matching}},
  booktitle =	{37th Annual Symposium on Combinatorial Pattern Matching (CPM 2026)},
  pages =	{35:1--35:12},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-420-8},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{369},
  editor =	{Bille, Philip and Prezza, Nicola},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CPM.2026.35},
  URN =		{urn:nbn:de:0030-drops-259617},
  doi =		{10.4230/LIPIcs.CPM.2026.35},
  annote =	{Keywords: string algorithms, pattern matching, indexing, squares}
}
Document
DOI: 10.4230/LIPIcs.STACS.2026.26
Approximate Cartesian Tree Matching with Substitutions

Authors: Panagiotis Charalampopoulos, Jonas Ellert, and Manal Mohamed

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

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

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

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@InProceedings{charalampopoulos_et_al:LIPIcs.STACS.2026.26,
  author =	{Charalampopoulos, Panagiotis and Ellert, Jonas and Mohamed, Manal},
  title =	{{Approximate Cartesian Tree Matching with Substitutions}},
  booktitle =	{43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026)},
  pages =	{26:1--26:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-412-3},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{364},
  editor =	{Mahajan, Meena and Manea, Florin and McIver, Annabelle and Thắng, Nguy\~{ê}n Kim},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2026.26},
  URN =		{urn:nbn:de:0030-drops-255151},
  doi =		{10.4230/LIPIcs.STACS.2026.26},
  annote =	{Keywords: Cartesian tree, Hamming distance, approximate pattern matching}
}
Document
DOI: 10.4230/LIPIcs.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}
}
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