DROPS

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)

Copy BibTex To Clipboard

@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.MFCS.2025.49

Morphisms and BWT-Run Sensitivity

Authors: Gabriele Fici, Giuseppe Romana, Marinella Sciortino, and Cristian Urbina

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

Abstract

We study how the application of morphisms affects the number r of equal-letter runs in the Burrows–Wheeler Transform (BWT). This parameter has emerged as a key repetitiveness measure in compressed indexing. We focus on the notion of BWT-run sensitivity after application of morphisms. For binary alphabets, we characterize the class of injective morphisms that preserve the number of BWT-runs up to a bounded additive increase by showing that it coincides with the known class of primitivity-preserving morphisms, which are those that map primitive words to primitive words. We further prove that deciding whether a given binary morphism has bounded BWT-run sensitivity is possible in polynomial time with respect to the total length of the images of the two letters. Additionally, we explore new structural and combinatorial properties of synchronizing and recognizable morphisms. These results establish new connections between BWT-based compressibility, code theory, and symbolic dynamics.

Cite as

Gabriele Fici, Giuseppe Romana, Marinella Sciortino, and Cristian Urbina. Morphisms and BWT-Run Sensitivity. In 50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 345, pp. 49:1-49:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

Copy BibTex To Clipboard

@InProceedings{fici_et_al:LIPIcs.MFCS.2025.49,
  author =	{Fici, Gabriele and Romana, Giuseppe and Sciortino, Marinella and Urbina, Cristian},
  title =	{{Morphisms and BWT-Run Sensitivity}},
  booktitle =	{50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025)},
  pages =	{49:1--49:18},
  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.2025.49},
  URN =		{urn:nbn:de:0030-drops-241567},
  doi =		{10.4230/LIPIcs.MFCS.2025.49},
  annote =	{Keywords: Burrows-Wheeler transform, BWT-runs, morphism, pure code, repetitiveness}
}

Document

DOI: 10.4230/OASIcs.Manzini.1

BWT and Combinatorics on Words

Authors: Gabriele Fici, Sabrina Mantaci, Antonio Restivo, Giuseppe Romana, Giovanna Rosone, and Marinella Sciortino

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

Abstract

The Burrows-Wheeler Transform (BWT) is a reversible transformation on words (strings) introduced in 1994 in the context of data compression, which is a permutation of the characters in the word. Its clustering effect, i.e., the remarkable property of grouping identical characters (BWT runs) when they share common contexts, has made it a powerful tool for boosting compression performances and enabling efficient pattern searching in highly repetitive string collections. In this chapter, we analyze the Burrows-Wheeler transform under the combinatorial point of view, and we survey known properties and connections with different aspects of combinatorics on words. In particular, we focus on the properties of words in relation to the number of their BWT runs. The value r, which counts the number of BWT runs, impacts both compression performance and indexing efficiency, and is considered a measure to evaluate the above-mentioned clustering effect and, consequently, the repetitiveness of a word. We give an overview of the results relating r to other combinatorial repetitiveness measures related to the factor complexity. The chapter also explores extremal cases of the clustering effect. Finally, some results on the sensitivity of the measure r are considered, where the effects of combinatorial operations are studied, such as reversal, edits, and the application of morphisms.

Cite as

Gabriele Fici, Sabrina Mantaci, Antonio Restivo, Giuseppe Romana, Giovanna Rosone, and Marinella Sciortino. BWT and Combinatorics on Words. In The Expanding World of Compressed Data: A Festschrift for Giovanni Manzini's 60th Birthday. Open Access Series in Informatics (OASIcs), Volume 131, pp. 1:1-1:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

Copy BibTex To Clipboard

@InProceedings{fici_et_al:OASIcs.Manzini.1,
  author =	{Fici, Gabriele and Mantaci, Sabrina and Restivo, Antonio and Romana, Giuseppe and Rosone, Giovanna and Sciortino, Marinella},
  title =	{{BWT and Combinatorics on Words}},
  booktitle =	{The Expanding World of Compressed Data: A Festschrift for Giovanni Manzini's 60th Birthday},
  pages =	{1:1--1:23},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-95977-390-4},
  ISSN =	{2190-6807},
  year =	{2025},
  volume =	{131},
  editor =	{Ferragina, Paolo and Gagie, Travis and Navarro, Gonzalo},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.Manzini.1},
  URN =		{urn:nbn:de:0030-drops-239090},
  doi =		{10.4230/OASIcs.Manzini.1},
  annote =	{Keywords: Burrows-Wheeler Transform, Combinatorics on Words, Clustering Effect, BWT Runs}
}

Document

DOI: 10.4230/OASIcs.Manzini.2

A Survey of the Bijective Burrows-Wheeler Transform

Authors: Hideo Bannai, Dominik Köppl, and Zsuzsanna Lipták

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

Abstract

The Bijective BWT (BBWT), conceived by Scott in 2007, later summarized in a preprint by Gil and Scott in 2009 (arXiv 2012), is a variant of the Burrows-Wheeler Transform which is bijective: every string is the BBWT of some string. Indeed, the BBWT of a string is the extended BWT [Mantaci et al., 2007] of the factors of its Lyndon factorization. The BBWT has been receiving increasing interest in recent years. In this paper, we survey existing research on the BBWT, starting with its history and motivation. We then present algorithmic topics including construction algorithms with various complexities and an index on top of the BBWT for pattern matching. We subsequently address some properties of the BBWT as a compressor, discussing robustness to operations such as reversal, edits, rotation, as well as compression power. We close with listing other bijective variants of the BWT and open problems concerning the BBWT.

Cite as

Hideo Bannai, Dominik Köppl, and Zsuzsanna Lipták. A Survey of the Bijective Burrows-Wheeler Transform. In The Expanding World of Compressed Data: A Festschrift for Giovanni Manzini's 60th Birthday. Open Access Series in Informatics (OASIcs), Volume 131, pp. 2:1-2:26, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

Copy BibTex To Clipboard

@InProceedings{bannai_et_al:OASIcs.Manzini.2,
  author =	{Bannai, Hideo and K\"{o}ppl, Dominik and Lipt\'{a}k, Zsuzsanna},
  title =	{{A Survey of the Bijective Burrows-Wheeler Transform}},
  booktitle =	{The Expanding World of Compressed Data: A Festschrift for Giovanni Manzini's 60th Birthday},
  pages =	{2:1--2:26},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-95977-390-4},
  ISSN =	{2190-6807},
  year =	{2025},
  volume =	{131},
  editor =	{Ferragina, Paolo and Gagie, Travis and Navarro, Gonzalo},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.Manzini.2},
  URN =		{urn:nbn:de:0030-drops-239100},
  doi =		{10.4230/OASIcs.Manzini.2},
  annote =	{Keywords: Burrows-Wheeler Transform, compression, text indexing, repetitiveness measure, Lyndon words, index construction algorithms, bijective string transformation}
}

Document

DOI: 10.4230/LIPIcs.CPM.2025.14

Minimal Generators in Optimal Time

Authors: Jonas Ellert, Paweł Gawrychowski, and Tatiana Starikovskaya

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

Abstract

A walk of length n on a string S of length m is a function f : {1, … , n} → {1, … , m} such that ∀ i ∈ {2, … , n} : |f(i) - f(i - 1)| ≤ 1. The walk generates the string T of length n defined by {∀ i ∈ {1, … , n} : T[i] = S[f(i)]}. Intuitively, this can be seen as walking n steps in S and outputting the encountered symbols, where in each step we either remain at the same position, or move one position to the left or to the right. The minimal generator of a string T is the shortest string S such that a walk on S generates T. Recently, it was shown that each string admits exactly one (up to reversal) minimal generator (Pratt-Hartmann, CPM 2024). However, no efficient algorithm for computing the minimal generator was known. We provide an optimal algorithm for this task, taking {O}(n) time for a string of length n over general unordered alphabet, i.e., accessing the string only by equality comparisons of symbols. The main challenge is to detect substrings of the form axbx̃axb and replace them with axb, where a,b are symbols and x is a string with reversal x̃. We solve this problem with a non-trivial adaptation of Manacher’s classic algorithm for computing maximal palindromic substrings (Manacher, J. ACM 1975). To obtain the final algorithm, we solve small subinstances of the problem in optimal time by adapting the "Four Russians" technique to strings over general unordered alphabet, which may be of independent interest.

Cite as

Jonas Ellert, Paweł Gawrychowski, and Tatiana Starikovskaya. Minimal Generators in Optimal Time. In 36th Annual Symposium on Combinatorial Pattern Matching (CPM 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 331, pp. 14:1-14:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

Copy BibTex To Clipboard

@InProceedings{ellert_et_al:LIPIcs.CPM.2025.14,
  author =	{Ellert, Jonas and Gawrychowski, Pawe{\l} and Starikovskaya, Tatiana},
  title =	{{Minimal Generators in Optimal Time}},
  booktitle =	{36th Annual Symposium on Combinatorial Pattern Matching (CPM 2025)},
  pages =	{14:1--14:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-369-0},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{331},
  editor =	{Bonizzoni, Paola and M\"{a}kinen, Veli},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CPM.2025.14},
  URN =		{urn:nbn:de:0030-drops-231082},
  doi =		{10.4230/LIPIcs.CPM.2025.14},
  annote =	{Keywords: string algorithms, walking on words, minimal generator, palindromic substrings, general unordered alphabet, decision tree complexity}
}

Document

DOI: 10.4230/LIPIcs.CPM.2025.16

Net Occurrences in Fibonacci and Thue-Morse Words

Authors: Peaker Guo and Kaisei Kishi

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

Abstract

A net occurrence of a repeated string in a text is an occurrence with unique left and right extensions, and the net frequency of the string is the number of its net occurrences in the text. Originally introduced for applications in Natural Language Processing, net frequency has recently gained attention for its algorithmic aspects. Guo et al. [CPM 2024] and Ohlebusch et al. [SPIRE 2024] focus on its computation in the offline setting, while Guo et al. [SPIRE 2024], Inenaga [arXiv 2024], and Mieno and Inenaga [CPM 2025] tackle the online counterpart. Mieno and Inenaga also characterize net occurrences in terms of the minimal unique substrings of the text. Additionally, Guo et al. [CPM 2024] initiate the study of net occurrences in Fibonacci words to establish a lower bound on the asymptotic running time of algorithms. Although there has been notable progress in algorithmic developments and some initial combinatorial insights, the combinatorial aspects of net occurrences have yet to be thoroughly examined. In this work, we make two key contributions. First, we confirm the conjecture that each Fibonacci word contains exactly three net occurrences. Second, we show that each Thue-Morse word contains exactly nine net occurrences. To achieve these results, we introduce the notion of overlapping net occurrence cover, which narrows down the candidate net occurrences in any text. Furthermore, we provide a precise characterization of occurrences of Fibonacci and Thue-Morse words of smaller order, offering structural insights that may have independent interest and potential applications in algorithm analysis and combinatorial properties of these words.

Cite as

Peaker Guo and Kaisei Kishi. Net Occurrences in Fibonacci and Thue-Morse Words. In 36th Annual Symposium on Combinatorial Pattern Matching (CPM 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 331, pp. 16:1-16:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

Copy BibTex To Clipboard

@InProceedings{guo_et_al:LIPIcs.CPM.2025.16,
  author =	{Guo, Peaker and Kishi, Kaisei},
  title =	{{Net Occurrences in Fibonacci and Thue-Morse Words}},
  booktitle =	{36th Annual Symposium on Combinatorial Pattern Matching (CPM 2025)},
  pages =	{16:1--16:22},
  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.2025.16},
  URN =		{urn:nbn:de:0030-drops-231107},
  doi =		{10.4230/LIPIcs.CPM.2025.16},
  annote =	{Keywords: Fibonacci words, Thue-Morse words, net occurrence, net frequency, factorization}
}

Document

DOI: 10.4230/LIPIcs.CPM.2025.26

Extending the Burrows-Wheeler Transform for Cartesian Tree Matching and Constructing It

Authors: Eric M. Osterkamp and Dominik Köppl

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

Abstract

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

Cite as

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

Copy BibTex To Clipboard

@InProceedings{osterkamp_et_al:LIPIcs.CPM.2025.26,
  author =	{Osterkamp, Eric M. and K\"{o}ppl, Dominik},
  title =	{{Extending the Burrows-Wheeler Transform for Cartesian Tree Matching and Constructing It}},
  booktitle =	{36th Annual Symposium on Combinatorial Pattern Matching (CPM 2025)},
  pages =	{26:1--26:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-369-0},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{331},
  editor =	{Bonizzoni, Paola and M\"{a}kinen, Veli},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CPM.2025.26},
  URN =		{urn:nbn:de:0030-drops-231201},
  doi =		{10.4230/LIPIcs.CPM.2025.26},
  annote =	{Keywords: Cartesian tree matching, extended Burrows-Wheeler transform, construction algorithm, generalized pattern matching}
}

Document

DOI: 10.4230/LIPIcs.CPM.2025.23

Space-Efficient Online Computation of String Net Occurrences

Authors: Takuya Mieno and Shunsuke Inenaga

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

Abstract

A substring u of a string T is said to be a repeat if u occurs at least twice in T. An occurrence [i..j] of a repeat u in T is said to be a net occurrence if each of the substrings aub = T[i-1..j+1], au = T[i-1..j], and ub = T[i..j+1] occurs exactly once in T. The occurrence [i-1..j+1] of aub is said to be an extended net occurrence of u. Let T be an input string of length n over an alphabet of size σ, and let ENO(T) denote the set of extended net occurrences of repeats in T. Guo et al. [SPIRE 2024] presented an online algorithm which can report ENO(T[1..i]) in T[1..i] in O(nσ²) time, for each prefix T[1..i] of T. Very recently, Inenaga [arXiv 2024] gave a faster online algorithm that can report ENO(T[1..i]) in optimal O(#ENO(T[1..i])) time for each prefix T[1..i] of T, where #S denotes the cardinality of a set S. Both of the aforementioned data structures can be maintained in O(n log σ) time and occupy O(n) space, where the O(n)-space requirement comes from the suffix tree data structure. In particular, Inenaga’s recent algorithm is based on Weiner’s right-to-left online suffix tree construction. In this paper, we show that one can modify Ukkonen’s left-to-right online suffix tree construction algorithm in O(n) space, so that ENO(T[1..i]) can be reported in optimal O(#ENO(T[1..i])) time for each prefix T[1..i] of T. This is an improvement over Guo et al.’s method that is also based on Ukkonen’s algorithm. Further, this leads us to the two following space-efficient alternatives: - A sliding-window algorithm of O(d) working space that can report ENO(T[i-d+1..i]) in optimal O(#ENO(T[i-d+1..i])) time for each sliding window T[i-d+1..i] of size d in T. - A CDAWG-based online algorithm of O(𝖾) working space that can report ENO(T[1..i]) in optimal O(#ENO(T[1..i])) time for each prefix T[1..i] of T, where 𝖾 < 2n is the number of edges in the CDAWG for T. All of our proposed data structures can be maintained in O(n log σ) time for the input online string T. We also discuss that the extended net occurrences of repeats in T can be fully characterized in terms of the minimal unique substrings (MUSs) in T.

Cite as

Takuya Mieno and Shunsuke Inenaga. Space-Efficient Online Computation of String Net Occurrences. In 36th Annual Symposium on Combinatorial Pattern Matching (CPM 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 331, pp. 23:1-23:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

Copy BibTex To Clipboard

@InProceedings{mieno_et_al:LIPIcs.CPM.2025.23,
  author =	{Mieno, Takuya and Inenaga, Shunsuke},
  title =	{{Space-Efficient Online Computation of String Net Occurrences}},
  booktitle =	{36th Annual Symposium on Combinatorial Pattern Matching (CPM 2025)},
  pages =	{23:1--23:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-369-0},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{331},
  editor =	{Bonizzoni, Paola and M\"{a}kinen, Veli},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CPM.2025.23},
  URN =		{urn:nbn:de:0030-drops-231175},
  doi =		{10.4230/LIPIcs.CPM.2025.23},
  annote =	{Keywords: string net occurrences, suffix trees, CDAWGs, maximal repeats, minimal unique substrings (MUSs)}
}

Document

DOI: 10.4230/LIPIcs.ESA.2024.18

Height-Bounded Lempel-Ziv Encodings

Authors: Hideo Bannai, Mitsuru Funakoshi, Diptarama Hendrian, Myuji Matsuda, and Simon J. Puglisi

Published in: LIPIcs, Volume 308, 32nd Annual European Symposium on Algorithms (ESA 2024)

Abstract

We introduce height-bounded LZ encodings (LZHB), a new family of compressed representations that are variants of Lempel-Ziv parsings with a focus on bounding the worst-case access time to arbitrary positions in the text directly via the compressed representation. An LZ-like encoding is a partitioning of the string into phrases of length 1 which can be encoded literally, or phrases of length at least 2 which have a previous occurrence in the string and can be encoded by its position and length. An LZ-like encoding induces an implicit referencing forest on the set of positions of the string. An LZHB encoding is an LZ-like encoding where the height of the implicit referencing forest is bounded. An LZHB encoding with height constraint h allows access to an arbitrary position of the underlying text using O(h) predecessor queries. While computing the optimal (i.e., smallest) LZHB encoding efficiently seems to be difficult [Cicalese & Ugazio 2024, arXiv, to appear at DLT 2024], we give the first linear time algorithm for strings over a constant size alphabet that computes the greedy LZHB encoding, i.e., the string is processed from beginning to end, and the longest prefix of the remaining string that can satisfy the height constraint is taken as the next phrase. Our algorithms significantly improve both theoretically and practically, the very recently and independently proposed algorithms by Lipták et al. (CPM 2024). We also analyze the size of height bounded LZ encodings in the context of repetitiveness measures, and show that there exists a constant c such that the size ẑ_{HB(clog n)} of the optimal LZHB encoding whose height is bounded by clog n for any string of length n is O(ĝ_{rl}), where ĝ_{rl} is the size of the smallest run-length grammar. Furthermore, we show that there exists a family of strings such that ẑ_{HB(clog n)} = o(ĝ_{rl}), thus making ẑ_{HB(clog n)} one of the smallest known repetitiveness measures for which O(polylog n) time access is possible using linear (O(ẑ_{HB(clog n)})) space.

Cite as

Hideo Bannai, Mitsuru Funakoshi, Diptarama Hendrian, Myuji Matsuda, and Simon J. Puglisi. Height-Bounded Lempel-Ziv Encodings. In 32nd Annual European Symposium on Algorithms (ESA 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 308, pp. 18:1-18:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

Copy BibTex To Clipboard

@InProceedings{bannai_et_al:LIPIcs.ESA.2024.18,
  author =	{Bannai, Hideo and Funakoshi, Mitsuru and Hendrian, Diptarama and Matsuda, Myuji and Puglisi, Simon J.},
  title =	{{Height-Bounded Lempel-Ziv Encodings}},
  booktitle =	{32nd Annual European Symposium on Algorithms (ESA 2024)},
  pages =	{18:1--18:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-338-6},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{308},
  editor =	{Chan, Timothy and Fischer, Johannes and Iacono, John 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.2024.18},
  URN =		{urn:nbn:de:0030-drops-210899},
  doi =		{10.4230/LIPIcs.ESA.2024.18},
  annote =	{Keywords: Lempel-Ziv parsing, data compression}
}

Document

DOI: 10.4230/LIPIcs.MFCS.2024.75

Edit and Alphabet-Ordering Sensitivity of Lex-Parse

Authors: Yuto Nakashima, Dominik Köppl, Mitsuru Funakoshi, Shunsuke Inenaga, and Hideo Bannai

Published in: LIPIcs, Volume 306, 49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024)

Abstract

We investigate the compression sensitivity [Akagi et al., 2023] of lex-parse [Navarro et al., 2021] for two operations: (1) single character edit and (2) modification of the alphabet ordering, and give tight upper and lower bounds for both operations (i.e., we show Θ(log n) bounds for strings of length n). For both lower bounds, we use the family of Fibonacci words. For the bounds on edit operations, our analysis makes heavy use of properties of the Lyndon factorization of Fibonacci words to characterize the structure of lex-parse.

Cite as

Yuto Nakashima, Dominik Köppl, Mitsuru Funakoshi, Shunsuke Inenaga, and Hideo Bannai. Edit and Alphabet-Ordering Sensitivity of Lex-Parse. In 49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 306, pp. 75:1-75:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

Copy BibTex To Clipboard

@InProceedings{nakashima_et_al:LIPIcs.MFCS.2024.75,
  author =	{Nakashima, Yuto and K\"{o}ppl, Dominik and Funakoshi, Mitsuru and Inenaga, Shunsuke and Bannai, Hideo},
  title =	{{Edit and Alphabet-Ordering Sensitivity of Lex-Parse}},
  booktitle =	{49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024)},
  pages =	{75:1--75:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-335-5},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{306},
  editor =	{Kr\'{a}lovi\v{c}, Rastislav and Ku\v{c}era, Anton{\'\i}n},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2024.75},
  URN =		{urn:nbn:de:0030-drops-206314},
  doi =		{10.4230/LIPIcs.MFCS.2024.75},
  annote =	{Keywords: Compression sensitivity, Lex-parse, Fibonacci words}
}

Document

DOI: 10.4230/LIPIcs.CPM.2023.3

Optimal LZ-End Parsing Is Hard

Authors: Hideo Bannai, Mitsuru Funakoshi, Kazuhiro Kurita, Yuto Nakashima, Kazuhisa Seto, and Takeaki Uno

Published in: LIPIcs, Volume 259, 34th Annual Symposium on Combinatorial Pattern Matching (CPM 2023)

Abstract

LZ-End is a variant of the well-known Lempel-Ziv parsing family such that each phrase of the parsing has a previous occurrence, with the additional constraint that the previous occurrence must end at the end of a previous phrase. LZ-End was initially proposed as a greedy parsing, where each phrase is determined greedily from left to right, as the longest factor that satisfies the above constraint [Kreft & Navarro, 2010]. In this work, we consider an optimal LZ-End parsing that has the minimum number of phrases in such parsings. We show that a decision version of computing the optimal LZ-End parsing is NP-complete by showing a reduction from the vertex cover problem. Moreover, we give a MAX-SAT formulation for the optimal LZ-End parsing adapting an approach for computing various NP-hard repetitiveness measures recently presented by [Bannai et al., 2022]. We also consider the approximation ratio of the size of greedy LZ-End parsing to the size of the optimal LZ-End parsing, and give a lower bound of the ratio which asymptotically approaches 2.

Cite as

Hideo Bannai, Mitsuru Funakoshi, Kazuhiro Kurita, Yuto Nakashima, Kazuhisa Seto, and Takeaki Uno. Optimal LZ-End Parsing Is Hard. In 34th Annual Symposium on Combinatorial Pattern Matching (CPM 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 259, pp. 3:1-3:11, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

Copy BibTex To Clipboard

@InProceedings{bannai_et_al:LIPIcs.CPM.2023.3,
  author =	{Bannai, Hideo and Funakoshi, Mitsuru and Kurita, Kazuhiro and Nakashima, Yuto and Seto, Kazuhisa and Uno, Takeaki},
  title =	{{Optimal LZ-End Parsing Is Hard}},
  booktitle =	{34th Annual Symposium on Combinatorial Pattern Matching (CPM 2023)},
  pages =	{3:1--3:11},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-276-1},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{259},
  editor =	{Bulteau, Laurent and Lipt\'{a}k, Zsuzsanna},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CPM.2023.3},
  URN =		{urn:nbn:de:0030-drops-179571},
  doi =		{10.4230/LIPIcs.CPM.2023.3},
  annote =	{Keywords: Data Compression, LZ-End, Repetitiveness measures}
}

Document

DOI: 10.4230/LIPIcs.ISAAC.2022.15

Computing Palindromes on a Trie in Linear Time

Authors: Takuya Mieno, Mitsuru Funakoshi, and Shunsuke Inenaga

Published in: LIPIcs, Volume 248, 33rd International Symposium on Algorithms and Computation (ISAAC 2022)

Abstract

A trie 𝒯 is a rooted tree such that each edge is labeled by a single character from the alphabet, and the labels of out-going edges from the same node are mutually distinct. Given a trie 𝒯 with n edges, we show how to compute all distinct palindromes and all maximal palindromes on 𝒯 in O(n) time, in the case of integer alphabets of size polynomial in n. This improves the state-of-the-art O(n log h)-time algorithms by Funakoshi et al. [PSC 2019], where h is the height of 𝒯. Using our new algorithms, the eertree with suffix links for a given trie 𝒯 can readily be obtained in O(n) time. Further, our trie-based O(n)-space data structure allows us to report all distinct palindromes and maximal palindromes in a query string represented in the trie 𝒯, in output optimal time. This is an improvement over an existing (naïve) solution that precomputes and stores all distinct palindromes and maximal palindromes for each and every string in the trie 𝒯 separately, using a total O(n²) preprocessing time and space, and reports them in output optimal time upon query.

Cite as

Takuya Mieno, Mitsuru Funakoshi, and Shunsuke Inenaga. Computing Palindromes on a Trie in Linear Time. In 33rd International Symposium on Algorithms and Computation (ISAAC 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 248, pp. 15:1-15:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

Copy BibTex To Clipboard

@InProceedings{mieno_et_al:LIPIcs.ISAAC.2022.15,
  author =	{Mieno, Takuya and Funakoshi, Mitsuru and Inenaga, Shunsuke},
  title =	{{Computing Palindromes on a Trie in Linear Time}},
  booktitle =	{33rd International Symposium on Algorithms and Computation (ISAAC 2022)},
  pages =	{15:1--15:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-258-7},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{248},
  editor =	{Bae, Sang Won and Park, Heejin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2022.15},
  URN =		{urn:nbn:de:0030-drops-173006},
  doi =		{10.4230/LIPIcs.ISAAC.2022.15},
  annote =	{Keywords: palindromes, suffix trees, tries, labeled trees, eertrees}
}

Document

DOI: 10.4230/LIPIcs.CPM.2020.12

Detecting k-(Sub-)Cadences and Equidistant Subsequence Occurrences

Authors: Mitsuru Funakoshi, Yuto Nakashima, Shunsuke Inenaga, Hideo Bannai, Masayuki Takeda, and Ayumi Shinohara

Published in: LIPIcs, Volume 161, 31st Annual Symposium on Combinatorial Pattern Matching (CPM 2020)

Abstract

The equidistant subsequence pattern matching problem is considered. Given a pattern string P and a text string T, we say that P is an equidistant subsequence of T if P is a subsequence of the text such that consecutive symbols of P in the occurrence are equally spaced. We can consider the problem of equidistant subsequences as generalizations of (sub-)cadences. We give bit-parallel algorithms that yield o(n²) time algorithms for finding k-(sub-)cadences and equidistant subsequences. Furthermore, O(nlog² n) and O(nlog n) time algorithms, respectively for equidistant and Abelian equidistant matching for the case |P| = 3, are shown. The algorithms make use of a technique that was recently introduced which can efficiently compute convolutions with linear constraints.

Cite as

Mitsuru Funakoshi, Yuto Nakashima, Shunsuke Inenaga, Hideo Bannai, Masayuki Takeda, and Ayumi Shinohara. Detecting k-(Sub-)Cadences and Equidistant Subsequence Occurrences. In 31st Annual Symposium on Combinatorial Pattern Matching (CPM 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 161, pp. 12:1-12:11, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

Copy BibTex To Clipboard

@InProceedings{funakoshi_et_al:LIPIcs.CPM.2020.12,
  author =	{Funakoshi, Mitsuru and Nakashima, Yuto and Inenaga, Shunsuke and Bannai, Hideo and Takeda, Masayuki and Shinohara, Ayumi},
  title =	{{Detecting k-(Sub-)Cadences and Equidistant Subsequence Occurrences}},
  booktitle =	{31st Annual Symposium on Combinatorial Pattern Matching (CPM 2020)},
  pages =	{12:1--12:11},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-149-8},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{161},
  editor =	{G{\o}rtz, Inge Li and Weimann, Oren},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CPM.2020.12},
  URN =		{urn:nbn:de:0030-drops-121375},
  doi =		{10.4230/LIPIcs.CPM.2020.12},
  annote =	{Keywords: string algorithms, pattern matching, bit parallelism, subsequences, cadences}
}

Document

DOI: 10.4230/LIPIcs.STACS.2020.30

Non-Rectangular Convolutions and (Sub-)Cadences with Three Elements

Authors: Mitsuru Funakoshi and Julian Pape-Lange

Published in: LIPIcs, Volume 154, 37th International Symposium on Theoretical Aspects of Computer Science (STACS 2020)

Abstract

The discrete acyclic convolution computes the 2n+1 sums ∑_{i+j=k|(i,j)∈[0,1,2,… ,n]²} a_i b_j in ?(n log n) time. By using suitable offsets and setting some of the variables to zero, this method provides a tool to calculate all non-zero sums ∑_{i+j=k|(i,j)∈ P∩ℤ²} a_i b_j in a rectangle P with perimeter p in ?(p log p) time. This paper extends this geometric interpretation in order to allow arbitrary convex polygons P with k vertices and perimeter p. Also, this extended algorithm only needs ?(k + p(log p)² log k) time. Additionally, this paper presents fast algorithms for counting sub-cadences and cadences with 3 elements using this extended method.

Cite as

Mitsuru Funakoshi and Julian Pape-Lange. Non-Rectangular Convolutions and (Sub-)Cadences with Three Elements. In 37th International Symposium on Theoretical Aspects of Computer Science (STACS 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 154, pp. 30:1-30:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

Copy BibTex To Clipboard

@InProceedings{funakoshi_et_al:LIPIcs.STACS.2020.30,
  author =	{Funakoshi, Mitsuru and Pape-Lange, Julian},
  title =	{{Non-Rectangular Convolutions and (Sub-)Cadences with Three Elements}},
  booktitle =	{37th International Symposium on Theoretical Aspects of Computer Science (STACS 2020)},
  pages =	{30:1--30:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-140-5},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{154},
  editor =	{Paul, Christophe and Bl\"{a}ser, Markus},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2020.30},
  URN =		{urn:nbn:de:0030-drops-118911},
  doi =		{10.4230/LIPIcs.STACS.2020.30},
  annote =	{Keywords: discrete acyclic convolutions, string-cadences, geometric algorithms, number theoretic transforms}
}

Document

DOI: 10.4230/LIPIcs.CPM.2019.27

Faster Queries for Longest Substring Palindrome After Block Edit

Authors: Mitsuru Funakoshi, Yuto Nakashima, Shunsuke Inenaga, Hideo Bannai, and Masayuki Takeda

Published in: LIPIcs, Volume 128, 30th Annual Symposium on Combinatorial Pattern Matching (CPM 2019)

Abstract

Palindromes are important objects in strings which have been extensively studied from combinatorial, algorithmic, and bioinformatics points of views. Manacher [J. ACM 1975] proposed a seminal algorithm that computes the longest substring palindromes (LSPals) of a given string in O(n) time, where n is the length of the string. In this paper, we consider the problem of finding the LSPal after the string is edited. We present an algorithm that uses O(n) time and space for preprocessing, and answers the length of the LSPals in O(l + log log n) time, after a substring in T is replaced by a string of arbitrary length l. This outperforms the query algorithm proposed in our previous work [CPM 2018] that uses O(l + log n) time for each query.

Cite as

Mitsuru Funakoshi, Yuto Nakashima, Shunsuke Inenaga, Hideo Bannai, and Masayuki Takeda. Faster Queries for Longest Substring Palindrome After Block Edit. In 30th Annual Symposium on Combinatorial Pattern Matching (CPM 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 128, pp. 27:1-27:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

Copy BibTex To Clipboard

@InProceedings{funakoshi_et_al:LIPIcs.CPM.2019.27,
  author =	{Funakoshi, Mitsuru and Nakashima, Yuto and Inenaga, Shunsuke and Bannai, Hideo and Takeda, Masayuki},
  title =	{{Faster Queries for Longest Substring Palindrome After Block Edit}},
  booktitle =	{30th Annual Symposium on Combinatorial Pattern Matching (CPM 2019)},
  pages =	{27:1--27:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-103-0},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{128},
  editor =	{Pisanti, Nadia and P. Pissis, Solon},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CPM.2019.27},
  URN =		{urn:nbn:de:0030-drops-104989},
  doi =		{10.4230/LIPIcs.CPM.2019.27},
  annote =	{Keywords: palindromes, string algorithm, periodicity}
}

17 Search Results for "Funakoshi, Mitsuru"

Abstract

Cite as

Abstract

Cite as

Abstract

Cite as

Abstract

Cite as

Abstract

Cite as

Abstract

Cite as

Abstract

Cite as

Abstract

Cite as

Abstract

Cite as

Abstract

Cite as

Abstract

Cite as

Abstract

Cite as

Abstract

Cite as

Abstract

Cite as

Abstract

Cite as

Thanks for your feedback!

Could not send message