5 Search Results for "Aoyama, Kotaro"

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/OASIcs.Manzini.3
BWT for String Collections

Authors: Davide Cenzato, Zsuzsanna Lipták, Nadia Pisanti, 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
We survey the different methods used for extending the BWT to collections of strings, following largely [Cenzato and Lipták, CPM 2022, Bioinformatics 2024]. We analyze the specific aspects and combinatorial properties of the resulting BWT variants and give a categorization of publicly available tools for computing the BWT of string collections. We show how the specific method used impacts on the resulting transform, including the number of runs, and on the dynamicity of the transform with respect to adding or removing strings from the collection. We then focus on the number of runs of these BWT variants and present the optimal BWT introduced in [Cenzato et al., DCC 2023], which implements an algorithm originally proposed by [Bentley et al., ESA 2020] to minimize the number of BWT-runs. We also discuss several recent heuristics and study their impact on the compression of biological sequences. We conclude with an overview of the applications and the impact of the BWT of string collections in bioinformatics.
Cite as

Davide Cenzato, Zsuzsanna Lipták, Nadia Pisanti, Giovanna Rosone, and Marinella Sciortino. BWT for String Collections. In The Expanding World of Compressed Data: A Festschrift for Giovanni Manzini's 60th Birthday. Open Access Series in Informatics (OASIcs), Volume 131, pp. 3:1-3:29, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{cenzato_et_al:OASIcs.Manzini.3,
  author =	{Cenzato, Davide and Lipt\'{a}k, Zsuzsanna and Pisanti, Nadia and Rosone, Giovanna and Sciortino, Marinella},
  title =	{{BWT for String Collections}},
  booktitle =	{The Expanding World of Compressed Data: A Festschrift for Giovanni Manzini's 60th Birthday},
  pages =	{3:1--3:29},
  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.3},
  URN =		{urn:nbn:de:0030-drops-239113},
  doi =		{10.4230/OASIcs.Manzini.3},
  annote =	{Keywords: Burrows-Wheeler transform, Extended Burrows-Wheeler transform, compressed text indexes, text compression, string collections, bioinformatics}
}
Document
DOI: 10.4230/LIPIcs.CPM.2025.28
Faster Approximate Elastic-Degenerate String Matching - Part A

Authors: Solon P. Pissis, Jakub Radoszewski, and Wiktor Zuba

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

Abstract
An elastic-degenerate (ED) string 𝐓 is a sequence 𝐓 = 𝐓[1] ⋯ 𝐓[n] of n finite sets of strings. The cardinality m of 𝐓 is the total number of strings in 𝐓[i], for all i ∈ [1..n]. The size N of 𝐓 is the total length of all m strings of 𝐓. ED strings have been introduced to represent a set of closely-related DNA sequences. Let P = P[1..p] be a pattern of length p and k > 0 be an integer. We consider the problem of k-Approximate ED String Matching (EDSM): searching k-approximate occurrences of P in the language of 𝐓. We call k-Approximate EDSM under the Hamming distance, k-Mismatch EDSM; and we call k-Approximate EDSM under edit distance, k-Edit EDSM. Bernardini et al. (Theoretical Computer Science, 2020) showed a simple 𝒪(k m p + kN)-time algorithm for k-Mismatch EDSM and an 𝒪(k² m p + kN)-time algorithm for k-Edit EDSM. We improve the dependency on k in both results, obtaining an Õ(k^{2/3}mp+√kN)-time algorithm for k-Mismatch EDSM and an Õ(kmp+ kN)-time algorithm for k-Edit EDSM. Bernardini et al. (Theory of Computing Systems, 2024) presented several algorithms for 1-Approximate EDSM working in Õ(np²+N) time. They have also left the possibility to generalize these solutions for k > 1 as an open problem. We improve the runtime of their solution for 1-Mismatch and 1-Edit EDSM from Õ(np²+N) to 𝒪(np²+N). We further show algorithms for k-Approximate EDSM for the Hamming and edit distances working in Õ(np² + N) time, for any constant k > 0. Finally, we show how our techniques can be applied to improve upon the complexity of the k-Approximate ED String Intersection and k-Approximate Doubly EDSM problems that were introduced very recently by Gabory et al. (Information and Computation, 2025).
Cite as

Solon P. Pissis, Jakub Radoszewski, and Wiktor Zuba. Faster Approximate Elastic-Degenerate String Matching - Part A. In 36th Annual Symposium on Combinatorial Pattern Matching (CPM 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 331, pp. 28:1-28:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{pissis_et_al:LIPIcs.CPM.2025.28,
  author =	{Pissis, Solon P. and Radoszewski, Jakub and Zuba, Wiktor},
  title =	{{Faster Approximate Elastic-Degenerate String Matching - Part A}},
  booktitle =	{36th Annual Symposium on Combinatorial Pattern Matching (CPM 2025)},
  pages =	{28:1--28:19},
  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.2025.28},
  URN =		{urn:nbn:de:0030-drops-231227},
  doi =		{10.4230/LIPIcs.CPM.2025.28},
  annote =	{Keywords: ED string, approximate string matching, Hamming distance, edit distance}
}
Document
DOI: 10.4230/LIPIcs.CPM.2025.29
Faster Approximate Elastic-Degenerate String Matching - Part B

Authors: Paweł Gawrychowski, Adam Górkiewicz, Pola Marciniak, Solon P. Pissis, and Karol Pokorski

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

Abstract
We revisit the complexity of approximate pattern matching in an elastic-degenerate string. Such a string is a sequence of n finite sets of strings of total length N, and compactly describes a collection of strings obtained by first choosing exactly one string in every set, and then concatenating them together. This is motivated by the need of storing a collection of highly similar DNA sequences. The basic algorithmic question on elastic-degenerate strings is pattern matching: given such an elastic-degenerate string and a standard pattern of length m, check if the pattern occurs in one of the strings in the described collection. Bernardini et al. [SICOMP 2022] showed how to leverage fast matrix multiplication to obtain an Õ(nm^{ω-1})+𝒪(N)-time complexity for this problem, where ω is the matrix multiplication exponent. However, from the point of view of possible applications, it is more desirable to work with approximate pattern matching, where we seek approximate occurrences of the pattern. This generalization has been considered in a few papers already, but the best result so far for occurrences with k mismatches, where k is a constant, is the Õ(nm²+N)-time algorithm presented in Part A [CPM 2025]. This brings the question whether increasing the dependency on m from m^{ω-1} to quadratic is necessary when moving from k = 0 to larger (but still constant) k. We design an Õ(nm^{1.5}+N)-time algorithm for pattern matching with k mismatches in an elastic-degenerate string, for any constant k. To obtain this time bound, we leverage the structural characterization of occurrences with k mismatches of Charalampopoulos, Kociumaka, and Wellnitz [FOCS 2020] together with fast Fourier transform. We need to work with multiple patterns at the same time, instead of a single pattern, which requires refining the original characterization. This might be of independent interest.
Cite as

Paweł Gawrychowski, Adam Górkiewicz, Pola Marciniak, Solon P. Pissis, and Karol Pokorski. Faster Approximate Elastic-Degenerate String Matching - Part B. In 36th Annual Symposium on Combinatorial Pattern Matching (CPM 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 331, pp. 29:1-29:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{gawrychowski_et_al:LIPIcs.CPM.2025.29,
  author =	{Gawrychowski, Pawe{\l} and G\'{o}rkiewicz, Adam and Marciniak, Pola and Pissis, Solon P. and Pokorski, Karol},
  title =	{{Faster Approximate Elastic-Degenerate String Matching - Part B}},
  booktitle =	{36th Annual Symposium on Combinatorial Pattern Matching (CPM 2025)},
  pages =	{29:1--29:21},
  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.2025.29},
  URN =		{urn:nbn:de:0030-drops-231236},
  doi =		{10.4230/LIPIcs.CPM.2025.29},
  annote =	{Keywords: ED string, approximate pattern matching, Hamming distance, k mismatches}
}
Document
DOI: 10.4230/LIPIcs.CPM.2018.9
Faster Online Elastic Degenerate String Matching

Authors: Kotaro Aoyama, Yuto Nakashima, Tomohiro I, Shunsuke Inenaga, Hideo Bannai, and Masayuki Takeda

Published in: LIPIcs, Volume 105, 29th Annual Symposium on Combinatorial Pattern Matching (CPM 2018)

Abstract
An Elastic-Degenerate String [Iliopoulus et al., LATA 2017] is a sequence of sets of strings, which was recently proposed as a way to model a set of similar sequences. We give an online algorithm for the Elastic-Degenerate String Matching (EDSM) problem that runs in O(nm sqrt{m log m} + N) time and O(m) working space, where n is the number of elastic degenerate segments of the text, N is the total length of all strings in the text, and m is the length of the pattern. This improves the previous algorithm by Grossi et al. [CPM 2017] that runs in O(nm^2 + N) time.
Cite as

Kotaro Aoyama, Yuto Nakashima, Tomohiro I, Shunsuke Inenaga, Hideo Bannai, and Masayuki Takeda. Faster Online Elastic Degenerate String Matching. In 29th Annual Symposium on Combinatorial Pattern Matching (CPM 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 105, pp. 9:1-9:10, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{aoyama_et_al:LIPIcs.CPM.2018.9,
  author =	{Aoyama, Kotaro and Nakashima, Yuto and I, Tomohiro and Inenaga, Shunsuke and Bannai, Hideo and Takeda, Masayuki},
  title =	{{Faster Online Elastic Degenerate String Matching}},
  booktitle =	{29th Annual Symposium on Combinatorial Pattern Matching (CPM 2018)},
  pages =	{9:1--9:10},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-074-3},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{105},
  editor =	{Navarro, Gonzalo and Sankoff, David and Zhu, Binhai},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CPM.2018.9},
  URN =		{urn:nbn:de:0030-drops-87016},
  doi =		{10.4230/LIPIcs.CPM.2018.9},
  annote =	{Keywords: elastic degenerate pattern matching, boolean convolution}
}
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