3 Search Results for "Hyyrö, Heikki"

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/OASIcs.Manzini.4
Wavelet Tree, Part II: Text Indexing

Authors: Paolo Ferragina, Raffaele Giancarlo, Roberto Grossi, Giovanna Rosone, Rossano Venturini, and Jeffrey Scott Vitter

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

Abstract
The Wavelet Tree data structure introduced in Grossi, Gupta, and Vitter [Grossi et al., 2003] is a space-efficient technique for rank and select queries that generalizes from binary symbols to an arbitrary multisymbol alphabet. Over the last two decades, it has become a pivotal tool in modern full-text indexing and data compression because of its properties and capabilities in compressing and indexing data, with many applications to information retrieval, genome analysis, data mining, and web search. In this paper, we survey the fascinating history and impact of Wavelet Trees; no doubt many more developments are yet to come. Our survey borrows some content from the authors' earlier works. This paper is divided into two parts: The first part gives a brief history of Wavelet Trees, including its varieties and practical implementations, which appears in the Festschrift dedicated to Roberto Grossi; the second part (this one) deals with Wavelet Tree-based text indexing and is included in the Festschrift dedicated to Giovanni Manzini.
Cite as

Paolo Ferragina, Raffaele Giancarlo, Roberto Grossi, Giovanna Rosone, Rossano Venturini, and Jeffrey Scott Vitter. Wavelet Tree, Part II: Text Indexing. In The Expanding World of Compressed Data: A Festschrift for Giovanni Manzini's 60th Birthday. Open Access Series in Informatics (OASIcs), Volume 131, pp. 4:1-4:10, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{ferragina_et_al:OASIcs.Manzini.4,
  author =	{Ferragina, Paolo and Giancarlo, Raffaele and Grossi, Roberto and Rosone, Giovanna and Venturini, Rossano and Vitter, Jeffrey Scott},
  title =	{{Wavelet Tree, Part II: Text Indexing}},
  booktitle =	{The Expanding World of Compressed Data: A Festschrift for Giovanni Manzini's 60th Birthday},
  pages =	{4:1--4:10},
  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.4},
  URN =		{urn:nbn:de:0030-drops-239127},
  doi =		{10.4230/OASIcs.Manzini.4},
  annote =	{Keywords: Wavelet tree, data compression, text indexing, compressed suffix array, Burrows-Wheeler transform, rank and select}
}
Document
DOI: 10.4230/LIPIcs.CPM.2018.15
Computing longest common square subsequences

Authors: Takafumi Inoue, Shunsuke Inenaga, Heikki Hyyrö, Hideo Bannai, and Masayuki Takeda

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

Abstract
A square is a non-empty string of form YY. The longest common square subsequence (LCSqS) problem is to compute a longest square occurring as a subsequence in two given strings A and B. We show that the problem can easily be solved in O(n^6) time or O(|M|n^4) time with O(n^4) space, where n is the length of the strings and M is the set of matching points between A and B. Then, we show that the problem can also be solved in O(sigma |M|^3 + n) time and O(|M|^2 + n) space, or in O(|M|^3 log^2 n log log n + n) time with O(|M|^3 + n) space, where sigma is the number of distinct characters occurring in A and B. We also study lower bounds for the LCSqS problem for two or more strings.
Cite as

Takafumi Inoue, Shunsuke Inenaga, Heikki Hyyrö, Hideo Bannai, and Masayuki Takeda. Computing longest common square subsequences. In 29th Annual Symposium on Combinatorial Pattern Matching (CPM 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 105, pp. 15:1-15:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{inoue_et_al:LIPIcs.CPM.2018.15,
  author =	{Inoue, Takafumi and Inenaga, Shunsuke and Hyyr\"{o}, Heikki and Bannai, Hideo and Takeda, Masayuki},
  title =	{{Computing longest common square subsequences}},
  booktitle =	{29th Annual Symposium on Combinatorial Pattern Matching (CPM 2018)},
  pages =	{15:1--15:13},
  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.2018.15},
  URN =		{urn:nbn:de:0030-drops-86946},
  doi =		{10.4230/LIPIcs.CPM.2018.15},
  annote =	{Keywords: squares, subsequences, matching rectangles, dynamic programming}
}
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