6 Search Results for "Takagi, Takuya"

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.2026.14
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.SWAT.2026.13
Faster Algorithms for Shortest Unique or Absent Substrings

Authors: Panagiotis Charalampopoulos, Manal Mohamed, Solon P. Pissis, Hilde Verbeek, and Wiktor Zuba

Published in: LIPIcs, Volume 370, 20th Scandinavian Symposium on Algorithm Theory (SWAT 2026)

Abstract
We revisit two well-known algorithmic problems on strings: computing a shortest unique substring (SUS) and a shortest absent substring (SAS) in a string S of length n. Both problems admit folklore 𝒪(n)-time solutions using the suffix tree of S. However, for small alphabets, this complexity is not necessarily optimal in the word RAM model, where a string of length n over alphabet [0,σ) can be stored in 𝒪(n log σ/log n) space and read in 𝒪(n log σ/log n) time. We present an 𝒪(n log σ/√{log n})-time algorithm for computing a SUS in S. This algorithm decomposes the problem according to the length and the period of the sought substring and uses several tools and techniques, such as synchronizing sets, the analysis of runs, and wavelet trees, to reduce the computation of a SUS to a simple geometric problem. Further, we adapt this algorithm and combine it with an efficient construction of de Bruijn sequences in order to obtain an 𝒪(n log σ/√{log n})-time algorithm for computing a SAS in S.
Cite as

Panagiotis Charalampopoulos, Manal Mohamed, Solon P. Pissis, Hilde Verbeek, and Wiktor Zuba. Faster Algorithms for Shortest Unique or Absent Substrings. In 20th Scandinavian Symposium on Algorithm Theory (SWAT 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 370, pp. 13:1-13:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{charalampopoulos_et_al:LIPIcs.SWAT.2026.13,
  author =	{Charalampopoulos, Panagiotis and Mohamed, Manal and Pissis, Solon P. and Verbeek, Hilde and Zuba, Wiktor},
  title =	{{Faster Algorithms for Shortest Unique or Absent Substrings}},
  booktitle =	{20th Scandinavian Symposium on Algorithm Theory (SWAT 2026)},
  pages =	{13:1--13:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-421-5},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{370},
  editor =	{Fraigniaud, Pierre},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SWAT.2026.13},
  URN =		{urn:nbn:de:0030-drops-260493},
  doi =		{10.4230/LIPIcs.SWAT.2026.13},
  annote =	{Keywords: string algorithms, unique substrings, absent substrings, absent words}
}
Document
DOI: 10.4230/LIPIcs.SEA.2025.12
Bit Packed Encodings for Grammar-Compressed Strings Supporting Fast Random Access

Authors: Alan M. Cleary, Joseph Winjum, Jordan Dood, Hiroki Shibata, and Shunsuke Inenaga

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

Abstract
Grammar-based compression is a powerful compression technique that allows for computation over the compressed data. While there has been extensive theoretical work on grammar and encoding size, there has been little work on practical grammar encodings. In this work, we consider the canonical array-of-arrays grammar representation and present a general bit packing approach for reducing its space requirements in practice. We then present three bit packing strategies based on this approach - one online and two offline - with different space-time trade-offs. This technique can be used to encode any grammar-compressed string while preserving the virtues of the array-of-arrays representation. We show that our encodings are Nlog₂ N away from the information-theoretic bound, where N is the number of symbols in the grammar, and that they are much smaller than methods that meet the information-theoretic bound in practice. Moreover, our experiments show that by using bit packed encodings we can achieve state-of-the-art performance both in grammar encoding size and run-time performance of random-access queries.
Cite as

Alan M. Cleary, Joseph Winjum, Jordan Dood, Hiroki Shibata, and Shunsuke Inenaga. Bit Packed Encodings for Grammar-Compressed Strings Supporting Fast Random Access. In 23rd International Symposium on Experimental Algorithms (SEA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 338, pp. 12:1-12:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{cleary_et_al:LIPIcs.SEA.2025.12,
  author =	{Cleary, Alan M. and Winjum, Joseph and Dood, Jordan and Shibata, Hiroki and Inenaga, Shunsuke},
  title =	{{Bit Packed Encodings for Grammar-Compressed Strings Supporting Fast Random Access}},
  booktitle =	{23rd International Symposium on Experimental Algorithms (SEA 2025)},
  pages =	{12:1--12:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-375-1},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{338},
  editor =	{Mutzel, Petra and Prezza, Nicola},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SEA.2025.12},
  URN =		{urn:nbn:de:0030-drops-232506},
  doi =		{10.4230/LIPIcs.SEA.2025.12},
  annote =	{Keywords: String algorithms, data compression, random access, grammar-based compression}
}
Document
DOI: 10.4230/LIPIcs.CPM.2019.30
Online Algorithms for Constructing Linear-Size Suffix Trie

Authors: Diptarama Hendrian, Takuya Takagi, and Shunsuke Inenaga

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

Abstract
The suffix trees are fundamental data structures for various kinds of string processing. The suffix tree of a string T of length n has O(n) nodes and edges, and the string label of each edge is encoded by a pair of positions in T. Thus, even after the tree is built, the input text T needs to be kept stored and random access to T is still needed. The linear-size suffix tries (LSTs), proposed by Crochemore et al. [Linear-size suffix tries, TCS 638:171-178, 2016], are a "stand-alone" alternative to the suffix trees. Namely, the LST of a string T of length n occupies O(n) total space, and supports pattern matching and other tasks in the same efficiency as the suffix tree without the need to store the input text T. Crochemore et al. proposed an offline algorithm which transforms the suffix tree of T into the LST of T in O(n log sigma) time and O(n) space, where sigma is the alphabet size. In this paper, we present two types of online algorithms which "directly" construct the LST, from right to left, and from left to right, without constructing the suffix tree as an intermediate structure. Both algorithms construct the LST incrementally when a new symbol is read, and do not access to the previously read symbols. The right-to-left construction algorithm works in O(n log sigma) time and O(n) space and the left-to-right construction algorithm works in O(n (log sigma + log n / log log n)) time and O(n) space. The main feature of our algorithms is that the input text does not need to be stored.
Cite as

Diptarama Hendrian, Takuya Takagi, and Shunsuke Inenaga. Online Algorithms for Constructing Linear-Size Suffix Trie. In 30th Annual Symposium on Combinatorial Pattern Matching (CPM 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 128, pp. 30:1-30:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{hendrian_et_al:LIPIcs.CPM.2019.30,
  author =	{Hendrian, Diptarama and Takagi, Takuya and Inenaga, Shunsuke},
  title =	{{Online Algorithms for Constructing Linear-Size Suffix Trie}},
  booktitle =	{30th Annual Symposium on Combinatorial Pattern Matching (CPM 2019)},
  pages =	{30:1--30:19},
  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.2019.30},
  URN =		{urn:nbn:de:0030-drops-105016},
  doi =		{10.4230/LIPIcs.CPM.2019.30},
  annote =	{Keywords: Indexing structure, Linear-size suffix trie, Online algorithm, Pattern Matching}
}
Document
DOI: 10.4230/LIPIcs.CPM.2016.22
Fully-online Construction of Suffix Trees for Multiple Texts

Authors: Takuya Takagi, Shunsuke Inenaga, and Hiroki Arimura

Published in: LIPIcs, Volume 54, 27th Annual Symposium on Combinatorial Pattern Matching (CPM 2016)

Abstract
We consider fully-online construction of indexing data structures for multiple texts. Let T = {T_1, ..., T_K} be a collection of texts. By fully-online, we mean that a new character can be appended to any text in T at any time. This is a natural generalization of semi-online construction of indexing data structures for multiple texts in which, after a new character is appended to the kth text T_k, then its previous texts T_1, ..., T_k-1 will remain static. Our fully-online scenario arises when we maintain dynamic indexes for multi-sensor data. Let N and sigma denote the total length of texts in T and the alphabet size, respectively. We first show that the algorithm by Blumer et al. [Theoretical Computer Science, 40:31-55, 1985] to construct the directed acyclic word graph (DAWG) for T can readily be extended to our fully-online setting, retaining O(N log sigma)-time and O(N)-space complexities. Then, we give a sophisticated fully-online algorithm which constructs the suffix tree for T in O(N log sigma) time and O(N) space. A key idea of this algorithm is synchronized maintenance of the DAWG and the suffix tree.
Cite as

Takuya Takagi, Shunsuke Inenaga, and Hiroki Arimura. Fully-online Construction of Suffix Trees for Multiple Texts. In 27th Annual Symposium on Combinatorial Pattern Matching (CPM 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 54, pp. 22:1-22:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

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@InProceedings{takagi_et_al:LIPIcs.CPM.2016.22,
  author =	{Takagi, Takuya and Inenaga, Shunsuke and Arimura, Hiroki},
  title =	{{Fully-online Construction of Suffix Trees for Multiple Texts}},
  booktitle =	{27th Annual Symposium on Combinatorial Pattern Matching (CPM 2016)},
  pages =	{22:1--22:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-012-5},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{54},
  editor =	{Grossi, Roberto and Lewenstein, Moshe},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CPM.2016.22},
  URN =		{urn:nbn:de:0030-drops-60719},
  doi =		{10.4230/LIPIcs.CPM.2016.22},
  annote =	{Keywords: suffix trees, DAWGs, multiple texts, online algorithms}
}
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