26 Search Results for "Crochemore, Maxime"

Document
DOI: 10.4230/LIPIcs.ESA.2024.16
Longest Common Substring with Gaps and Related Problems

Authors: Aranya Banerjee, Daniel Gibney, and Sharma V. Thankachan

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

Abstract
The longest common substring (also known as longest common factor) and longest common subsequence problems are two well-studied classical string problems. The former is solvable in optimal 𝒪(n) time for two strings of length m and n with m ≤ n, and the latter is solvable in 𝒪(nm) time, which is conditionally optimal under the Strong Exponential Time Hypothesis. In this work, we study the problem of longest common factor with gaps, that is, finding a set of at most k matching substrings obeying precedence conditions with maximum total length. For k = 1, this is equivalent to the longest common factor problem, and for k = m, this is equivalent to the longest common subsequence problem. Our work demonstrates that, for constant k, this problem can be solved in strongly subquadratic time, i.e., nm^{1 - Θ(1)}. Motivated by co-linear chaining applications in Computational Biology, we further demonstrate that the longest common factor with gaps results can be extended to the case where the matches are restricted to maximal exact matches (MEMs). To further demonstrate the applicability of our techniques, we show that a similar approach can be used for a restricted version of the episode matching problem where one seeks an ordered set of at most k matches whose concatenation equals a query pattern P and the length of the substring of T containing the matches is minimized. These solutions all run in strongly subquadratic time for constant k.
Cite as

Aranya Banerjee, Daniel Gibney, and Sharma V. Thankachan. Longest Common Substring with Gaps and Related Problems. In 32nd Annual European Symposium on Algorithms (ESA 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 308, pp. 16:1-16:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{banerjee_et_al:LIPIcs.ESA.2024.16,
  author =	{Banerjee, Aranya and Gibney, Daniel and Thankachan, Sharma V.},
  title =	{{Longest Common Substring with Gaps and Related Problems}},
  booktitle =	{32nd Annual European Symposium on Algorithms (ESA 2024)},
  pages =	{16:1--16:18},
  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.2024.16},
  URN =		{urn:nbn:de:0030-drops-210877},
  doi =		{10.4230/LIPIcs.ESA.2024.16},
  annote =	{Keywords: Pattern Matching, Longest Common Subsequence, Episode Matching}
}
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)

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@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.ESA.2024.19
Longest Common Extensions with Wildcards: Trade-Off and Applications

Authors: Gabriel Bathie, Panagiotis Charalampopoulos, and Tatiana Starikovskaya

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

Abstract
We study the Longest Common Extension (LCE) problem in a string containing wildcards. Wildcards (also called "don't cares" or "holes") are special characters that match any other character in the alphabet, similar to the character "?" in Unix commands or "." in regular expression engines. We consider the problem parametrized by G, the number of maximal contiguous groups of wildcards in the input string. Our main contribution is a simple data structure for this problem that can be built in O(n (G/t) log n) time, occupies O(nG/t) space, and answers queries in O(t) time, for any t ∈ [1 .. G]. Up to the O(log n) factor, this interpolates smoothly between the data structure of Crochemore et al. [JDA 2015], which has O(nG) preprocessing time and space, and O(1) query time, and a simple solution based on the "kangaroo jumping" technique [Landau and Vishkin, STOC 1986], which has O(n) preprocessing time and space, and O(G) query time. By establishing a connection between this problem and Boolean matrix multiplication, we show that our solution is optimal up to subpolynomial factors when G = Ω(n) under a widely believed hypothesis. In addition, we develop a new simple, deterministic and combinatorial algorithm for sparse Boolean matrix multiplication. Finally, we show that our data structure can be used to obtain efficient algorithms for approximate pattern matching and structural analysis of strings with wildcards. First, we consider the problem of pattern matching with k errors (i.e., edit operations) in the setting where both the pattern and the text may contain wildcards. The "kangaroo jumping" technique can be adapted to yield an algorithm for this problem with runtime O(n(k+G)), where G is the total number of maximal contiguous groups of wildcards in the text and the pattern and n is the length of the text. By combining "kangaroo jumping" with a tailor-made data structure for LCE queries, Akutsu [IPL 1995] devised an O(n√{km} polylog m)-time algorithm. We improve on both algorithms when k ≪ G ≪ m by giving an algorithm with runtime O(n(k + √{Gk log n})). Secondly, we give O(n√G log n)-time and O(n)-space algorithms for computing the prefix array, as well as the quantum/deterministic border and period arrays of a string with wildcards. This is an improvement over the O(n√{nlog n})-time algorithms of Iliopoulos and Radoszewski [CPM 2016] when G = O(n / log n).
Cite as

Gabriel Bathie, Panagiotis Charalampopoulos, and Tatiana Starikovskaya. Longest Common Extensions with Wildcards: Trade-Off and Applications. In 32nd Annual European Symposium on Algorithms (ESA 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 308, pp. 19:1-19:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{bathie_et_al:LIPIcs.ESA.2024.19,
  author =	{Bathie, Gabriel and Charalampopoulos, Panagiotis and Starikovskaya, Tatiana},
  title =	{{Longest Common Extensions with Wildcards: Trade-Off and Applications}},
  booktitle =	{32nd Annual European Symposium on Algorithms (ESA 2024)},
  pages =	{19:1--19:17},
  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.2024.19},
  URN =		{urn:nbn:de:0030-drops-210904},
  doi =		{10.4230/LIPIcs.ESA.2024.19},
  annote =	{Keywords: Longest common prefix, longest common extension, wildcards, Boolean matrix multiplication, approximate pattern matching, periodicity arrays}
}
Document
DOI: 10.4230/LIPIcs.ESA.2024.20
Pattern Matching with Mismatches and Wildcards

Authors: Gabriel Bathie, Panagiotis Charalampopoulos, and Tatiana Starikovskaya

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

Abstract
In this work, we address the problem of approximate pattern matching with wildcards. Given a pattern P of length m containing D wildcards, a text T of length n, and an integer k, our objective is to identify all fragments of T within Hamming distance k from P. Our primary contribution is an algorithm with runtime 𝒪(n + (D+k)(G+k)⋅ n/m) for this problem. Here, G ≤ D represents the number of maximal wildcard fragments in P. We derive this algorithm by elaborating in a non-trivial way on the ideas presented by [Charalampopoulos, Kociumaka, and Wellnitz, FOCS'20] for pattern matching with mismatches (without wildcards). Our algorithm improves over the state of the art when D, G, and k are small relative to n. For instance, if m = n/2, k = G = n^{2/5}, and D = n^{3/5}, our algorithm operates in 𝒪(n) time, surpassing the Ω(n^{6/5}) time requirement of all previously known algorithms. In the case of exact pattern matching with wildcards (k = 0), we present a much simpler algorithm with runtime 𝒪(n + DG ⋅ n/m) that clearly illustrates our main technical innovation: the utilisation of positions of P that do not belong to any fragment of P with a density of wildcards much larger than D/m as anchors for the sought (approximate) occurrences. Notably, our algorithm outperforms the best-known 𝒪(n log m)-time FFT-based algorithms of [Cole and Hariharan, STOC'02] and [Clifford and Clifford, IPL'04] if DG = o(m log m). We complement our algorithmic results with a structural characterization of the k-mismatch occurrences of P. We demonstrate that in a text of length 𝒪(m), these occurrences can be partitioned into 𝒪((D+k)(G+k)) arithmetic progressions. Additionally, we construct an infinite family of examples with Ω((D+k)k) arithmetic progressions of occurrences, leveraging a combinatorial result on progression-free sets [Elkin, SODA'10].
Cite as

Gabriel Bathie, Panagiotis Charalampopoulos, and Tatiana Starikovskaya. Pattern Matching with Mismatches and Wildcards. In 32nd Annual European Symposium on Algorithms (ESA 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 308, pp. 20:1-20:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{bathie_et_al:LIPIcs.ESA.2024.20,
  author =	{Bathie, Gabriel and Charalampopoulos, Panagiotis and Starikovskaya, Tatiana},
  title =	{{Pattern Matching with Mismatches and Wildcards}},
  booktitle =	{32nd Annual European Symposium on Algorithms (ESA 2024)},
  pages =	{20:1--20:15},
  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.2024.20},
  URN =		{urn:nbn:de:0030-drops-210910},
  doi =		{10.4230/LIPIcs.ESA.2024.20},
  annote =	{Keywords: pattern matching, wildcards, mismatches, Hamming distance}
}
Document
DOI: 10.4230/LIPIcs.ESA.2024.35
On Finding Longest Palindromic Subsequences Using Longest Common Subsequences

Authors: Gerth Stølting Brodal, Rolf Fagerberg, and Casper Moldrup Rysgaard

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

Abstract
Two standard textbook problems illustrating dynamic programming are to find the longest common subsequence (LCS) between two strings and to find the longest palindromic subsequence (LPS) of a single string. A popular claim is that the longest palindromic subsequence in a string can be computed as the longest common subsequence between the string and the reversed string. We prove that the correctness of this claim depends on how the longest common subsequence is computed. In particular, we prove that the classical dynamic programming solution by Wagner and Fischer [JACM 1974] for finding an LCS in fact does find an LPS, while a slightly different LCS backtracking strategy makes the algorithm fail to always report a palindrome.
Cite as

Gerth Stølting Brodal, Rolf Fagerberg, and Casper Moldrup Rysgaard. On Finding Longest Palindromic Subsequences Using Longest Common Subsequences. In 32nd Annual European Symposium on Algorithms (ESA 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 308, pp. 35:1-35:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{brodal_et_al:LIPIcs.ESA.2024.35,
  author =	{Brodal, Gerth St{\o}lting and Fagerberg, Rolf and Rysgaard, Casper Moldrup},
  title =	{{On Finding Longest Palindromic Subsequences Using Longest Common Subsequences}},
  booktitle =	{32nd Annual European Symposium on Algorithms (ESA 2024)},
  pages =	{35:1--35:16},
  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.2024.35},
  URN =		{urn:nbn:de:0030-drops-211068},
  doi =		{10.4230/LIPIcs.ESA.2024.35},
  annote =	{Keywords: Palindromic subsequence, longest common subsequence, dynamic programming}
}
Document
DOI: 10.4230/LIPIcs.WABI.2024.14
A Unifying Taxonomy of Pattern Matching in Degenerate Strings and Founder Graphs

Authors: Rocco Ascone, Giulia Bernardini, Alessio Conte, Massimo Equi, Esteban Gabory, Roberto Grossi, and Nadia Pisanti

Published in: LIPIcs, Volume 312, 24th International Workshop on Algorithms in Bioinformatics (WABI 2024)

Abstract
Elastic Degenerate (ED) strings and Elastic Founder (EF) graphs are two versions of acyclic components of pangenomes. Both ED strings and EF graphs (which we collectively name variable strings) extend the well-known notion of indeterminate string. Recent work has extensively investigated algorithmic tasks over these structures, and over several other variable strings notions that they generalise. Among such tasks, the basic operation of matching a pattern into a text, which can serve as a toolkit for many pangenomic data analyses using these data structures, deserves special attention. In this paper we: (1) highlight a clear taxonomy within both ED strings and EF graphs ranging through variable strings of all types, from the linear string up to the most general one; (2) investigate the problem PvarT(X,Y) of matching a solid or variable pattern of type X into a variable text of type Y; (3) using as a reference the quadratic conditional lower bounds that are known for PvarT(solid,ED) and PvarT(solid,EF), for all possible types of variable strings X and Y we either prove the quadratic conditional lower bound for PvarT(X,Y), or provide non-trivial, often sub-quadratic, upper bounds, also exploiting the above-mentioned taxonomy.
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Rocco Ascone, Giulia Bernardini, Alessio Conte, Massimo Equi, Esteban Gabory, Roberto Grossi, and Nadia Pisanti. A Unifying Taxonomy of Pattern Matching in Degenerate Strings and Founder Graphs. In 24th International Workshop on Algorithms in Bioinformatics (WABI 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 312, pp. 14:1-14:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{ascone_et_al:LIPIcs.WABI.2024.14,
  author =	{Ascone, Rocco and Bernardini, Giulia and Conte, Alessio and Equi, Massimo and Gabory, Esteban and Grossi, Roberto and Pisanti, Nadia},
  title =	{{A Unifying Taxonomy of Pattern Matching in Degenerate Strings and Founder Graphs}},
  booktitle =	{24th International Workshop on Algorithms in Bioinformatics (WABI 2024)},
  pages =	{14:1--14:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-340-9},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{312},
  editor =	{Pissis, Solon P. and Sung, Wing-Kin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.WABI.2024.14},
  URN =		{urn:nbn:de:0030-drops-206586},
  doi =		{10.4230/LIPIcs.WABI.2024.14},
  annote =	{Keywords: Pangenomics, pattern matching, degenerate string, founder graph, fine-grained complexity}
}
Document
DOI: 10.4230/LIPIcs.WABI.2024.21
McDag: Indexing Maximal Common Subsequences in Practice

Authors: Giovanni Buzzega, Alessio Conte, Roberto Grossi, and Giulia Punzi

Published in: LIPIcs, Volume 312, 24th International Workshop on Algorithms in Bioinformatics (WABI 2024)

Abstract
Analyzing and comparing sequences of symbols is among the most fundamental problems in computer science, possibly even more so in bioinformatics. Maximal Common Subsequences (MCSs), i.e., inclusion-maximal sequences of non-contiguous symbols common to two or more strings, have only recently received attention in this area, despite being a basic notion and a natural generalization of more common tools like Longest Common Substrings/Subsequences. In this paper we simplify and engineer recent advancements on MCSs into a practical tool called McDag, the first publicly available tool that can index MCSs of real genomic data. We demonstrate that our tool can index sequences exceeding 10,000 base pairs within minutes, utilizing only 4-7% more than the minimum required nodes, while also extracting relevant insights.
Cite as

Giovanni Buzzega, Alessio Conte, Roberto Grossi, and Giulia Punzi. McDag: Indexing Maximal Common Subsequences in Practice. In 24th International Workshop on Algorithms in Bioinformatics (WABI 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 312, pp. 21:1-21:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{buzzega_et_al:LIPIcs.WABI.2024.21,
  author =	{Buzzega, Giovanni and Conte, Alessio and Grossi, Roberto and Punzi, Giulia},
  title =	{{McDag: Indexing Maximal Common Subsequences in Practice}},
  booktitle =	{24th International Workshop on Algorithms in Bioinformatics (WABI 2024)},
  pages =	{21:1--21:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-340-9},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{312},
  editor =	{Pissis, Solon P. and Sung, Wing-Kin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.WABI.2024.21},
  URN =		{urn:nbn:de:0030-drops-206650},
  doi =		{10.4230/LIPIcs.WABI.2024.21},
  annote =	{Keywords: Index data structure, DAG, Common subsequence, Inclusion-wise maximality, LCS}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2024.12
Generalizing Roberts' Characterization of Unit Interval Graphs

Authors: Virginia Ardévol Martínez, Romeo Rizzi, Abdallah Saffidine, Florian Sikora, and Stéphane Vialette

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

Abstract
For any natural number d, a graph G is a (disjoint) d-interval graph if it is the intersection graph of (disjoint) d-intervals, the union of d (disjoint) intervals on the real line. Two important subclasses of d-interval graphs are unit and balanced d-interval graphs (where every interval has unit length or all the intervals associated to a same vertex have the same length, respectively). A celebrated result by Roberts gives a simple characterization of unit interval graphs being exactly claw-free interval graphs. Here, we study the generalization of this characterization for d-interval graphs. In particular, we prove that for any d ⩾ 2, if G is a K_{1,2d+1}-free interval graph, then G is a unit d-interval graph. However, somehow surprisingly, under the same assumptions, G is not always a disjoint unit d-interval graph. This implies that the class of disjoint unit d-interval graphs is strictly included in the class of unit d-interval graphs. Finally, we study the relationships between the classes obtained under disjoint and non-disjoint d-intervals in the balanced case and show that the classes of disjoint balanced 2-intervals and balanced 2-intervals coincide, but this is no longer true for d > 2.
Cite as

Virginia Ardévol Martínez, Romeo Rizzi, Abdallah Saffidine, Florian Sikora, and Stéphane Vialette. Generalizing Roberts' Characterization of Unit Interval Graphs. In 49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 306, pp. 12:1-12:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{ardevolmartinez_et_al:LIPIcs.MFCS.2024.12,
  author =	{Ard\'{e}vol Mart{\'\i}nez, Virginia and Rizzi, Romeo and Saffidine, Abdallah and Sikora, Florian and Vialette, St\'{e}phane},
  title =	{{Generalizing Roberts' Characterization of Unit Interval Graphs}},
  booktitle =	{49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024)},
  pages =	{12:1--12:15},
  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.2024.12},
  URN =		{urn:nbn:de:0030-drops-205687},
  doi =		{10.4230/LIPIcs.MFCS.2024.12},
  annote =	{Keywords: Interval graphs, Multiple Interval Graphs, Unit Interval Graphs, Characterization}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2024.31
Unveiling the Connection Between the Lyndon Factorization and the Canonical Inverse Lyndon Factorization via a Border Property

Authors: Paola Bonizzoni, Clelia De Felice, Brian Riccardi, Rocco Zaccagnino, and Rosalba Zizza

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

Abstract
The notion of Lyndon word and Lyndon factorization has shown to have unexpected applications in theory as well as in developing novel algorithms on words. A counterpart to these notions are those of inverse Lyndon word and inverse Lyndon factorization. Differently from the Lyndon words, the inverse Lyndon words may be bordered. The relationship between the two factorizations is related to the inverse lexicographic ordering, and has only been recently explored. More precisely, a main open question is how to get an inverse Lyndon factorization from a classical Lyndon factorization under the inverse lexicographic ordering, named CFL_in. In this paper we reveal a strong connection between these two factorizations where the border plays a relevant role. More precisely, we show two main results. We say that a factorization has the border property if a nonempty border of a factor cannot be a prefix of the next factor. First we show that there exists a unique inverse Lyndon factorization having the border property. Then we show that this unique factorization with the border property is the so-called canonical inverse Lyndon factorization, named ICFL. By showing that ICFL is obtained by compacting factors of the Lyndon factorization over the inverse lexicographic ordering, we provide a linear time algorithm for computing ICFL from CFL_in.
Cite as

Paola Bonizzoni, Clelia De Felice, Brian Riccardi, Rocco Zaccagnino, and Rosalba Zizza. Unveiling the Connection Between the Lyndon Factorization and the Canonical Inverse Lyndon Factorization via a Border Property. In 49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 306, pp. 31:1-31:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{bonizzoni_et_al:LIPIcs.MFCS.2024.31,
  author =	{Bonizzoni, Paola and De Felice, Clelia and Riccardi, Brian and Zaccagnino, Rocco and Zizza, Rosalba},
  title =	{{Unveiling the Connection Between the Lyndon Factorization and the Canonical Inverse Lyndon Factorization via a Border Property}},
  booktitle =	{49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024)},
  pages =	{31:1--31:14},
  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.2024.31},
  URN =		{urn:nbn:de:0030-drops-205879},
  doi =		{10.4230/LIPIcs.MFCS.2024.31},
  annote =	{Keywords: Lyndon words, Lyndon factorization, Combinatorial algorithms on words}
}
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)

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@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.MFCS.2024.85
Approximate Suffix-Prefix Dictionary Queries

Authors: Wiktor Zuba, Grigorios Loukides, Solon P. Pissis, and Sharma V. Thankachan

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

Abstract
In the all-pairs suffix-prefix (APSP) problem [Gusfield et al., Inf. Process. Lett. 1992], we are given a dictionary R of r strings, S₁,…,S_r, of total length n, and we are asked to find the length SPL_{i,j} of the longest string that is both a suffix of S_i and a prefix of S_j, for all i,j ∈ [1..r]. APSP is a classic problem in string algorithms with applications in bioinformatics, especially in sequence assembly. Since r = |R| is typically very large in real-world applications, considering all r² pairs of strings explicitly is prohibitive. This is when the data structure variant of APSP makes sense; in the same spirit as distance oracles computing shortest paths between any two vertices given online. We show how to quickly locate k-approximate matches (under the Hamming or the edit distance) in R using a version of the k-errata tree [Cole et al., STOC 2004] that we introduce. Let SPL^k_{i,j} be the length of the longest suffix of S_i that is at distance at most k from a prefix of S_j. In particular, for any k = 𝒪(1), we show an 𝒪(nlog^k n)-sized data structure to support the following queries: - One-to-One^k(i,j): output SPL^k_{i,j} in 𝒪(log^k nlog log n) time. - Report^k(i,d): output all j ∈ [1..r], such that SPL^k_{i,j} ≥ d, in 𝒪(log^{k}n(log n/log log n+output)) time, where output denotes the size of the output. In fact, our algorithms work for any value of k not just for k = 𝒪(1), but the formulas bounding the complexities get much more complicated for larger values of k.
Cite as

Wiktor Zuba, Grigorios Loukides, Solon P. Pissis, and Sharma V. Thankachan. Approximate Suffix-Prefix Dictionary Queries. In 49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 306, pp. 85:1-85:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{zuba_et_al:LIPIcs.MFCS.2024.85,
  author =	{Zuba, Wiktor and Loukides, Grigorios and Pissis, Solon P. and Thankachan, Sharma V.},
  title =	{{Approximate Suffix-Prefix Dictionary Queries}},
  booktitle =	{49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024)},
  pages =	{85:1--85:18},
  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.2024.85},
  URN =		{urn:nbn:de:0030-drops-206416},
  doi =		{10.4230/LIPIcs.MFCS.2024.85},
  annote =	{Keywords: all-pairs suffix-prefix, suffix-prefix queries, suffix tree, k-errata tree}
}
Document
DOI: 10.4230/LIPIcs.SEA.2024.24
Efficient Exact Online String Matching Through Linked Weak Factors

Authors: Matthew N. Palmer, Simone Faro, and Stefano Scafiti

Published in: LIPIcs, Volume 301, 22nd International Symposium on Experimental Algorithms (SEA 2024)

Abstract
Online exact string matching is a fundamental computational problem in computer science, involving the sequential search for a pattern within a large text without prior access to the entire text. Its significance is underscored by its diverse applications in data compression, data mining, text editing, and bioinformatics, just to cite a few, where efficient substring matching is crucial. While the problem has been a subject of study for years, recent decades have witnessed a heightened focus on experimental solutions, employing various techniques to achieve superior performance. Notably, approaches centered around weak factor recognition have emerged as leaders in experimental settings, gaining increasing attention. This paper introduces Hash Chain, a novel algorithm founded on a robust weak factor recognition approach that links adjacent factors through hashing. Building upon the efficacy of weak recognition techniques, the proposed algorithm incorporates innovative strategies for organizing data structures and optimizations to enhance performance. Despite its quadratic worst-case time complexity, the new proposed algorithm demonstrates sublinear behavior in practice, outperforming currently known algorithms in the literature.
Cite as

Matthew N. Palmer, Simone Faro, and Stefano Scafiti. Efficient Exact Online String Matching Through Linked Weak Factors. In 22nd International Symposium on Experimental Algorithms (SEA 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 301, pp. 24:1-24:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{palmer_et_al:LIPIcs.SEA.2024.24,
  author =	{Palmer, Matthew N. and Faro, Simone and Scafiti, Stefano},
  title =	{{Efficient Exact Online String Matching Through Linked Weak Factors}},
  booktitle =	{22nd International Symposium on Experimental Algorithms (SEA 2024)},
  pages =	{24:1--24:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-325-6},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{301},
  editor =	{Liberti, Leo},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SEA.2024.24},
  URN =		{urn:nbn:de:0030-drops-203896},
  doi =		{10.4230/LIPIcs.SEA.2024.24},
  annote =	{Keywords: String matching, text processing, weak recognition, hashing, experimental algorithms, design and analysis of algorithms}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2024.39
Optimal Bounds for Distinct Quartics

Authors: Panagiotis Charalampopoulos, Paweł Gawrychowski, and Samah Ghazawi

Published in: LIPIcs, Volume 297, 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)

Abstract
A fundamental concept related to strings is that of repetitions. It has been extensively studied in many versions, from both purely combinatorial and algorithmic angles. One of the most basic questions is how many distinct squares, i.e., distinct strings of the form UU, a string of length n can contain as fragments. It turns out that this is always 𝒪(n), and the bound cannot be improved to sublinear in n [Fraenkel and Simpson, JCTA 1998]. Several similar questions about repetitions in strings have been considered, and by now we seem to have a good understanding of their repetitive structure. For higher-dimensional strings, the basic concept of periodicity has been successfully extended and applied to design efficient algorithms - it is inherently more complex than for regular strings. Extending the notion of repetitions and understanding the repetitive structure of higher-dimensional strings is however far from complete. Quartics were introduced by Apostolico and Brimkov [TCS 2000] as analogues of squares in two dimensions. Charalampopoulos, Radoszewski, Rytter, Waleń, and Zuba [ESA 2020] proved that the number of distinct quartics in an n×n 2D string is 𝒪(n²log²n) and that they can be computed in 𝒪(n²log²n) time. Gawrychowski, Ghazawi, and Landau [SPIRE 2021] constructed an infinite family of n×n 2D strings with Ω(n²log n) distinct quartics. This brings the challenge of determining asymptotically tight bounds. Here, we settle both the combinatorial and the algorithmic aspects of this question: the number of distinct quartics in an n×n 2D string is 𝒪(n²log n) and they can be computed in the worst-case optimal 𝒪(n²log n) time. As expected, our solution heavily exploits the periodic structure implied by occurrences of quartics. However, the two-dimensional nature of the problem introduces some technical challenges. Somewhat surprisingly, we overcome the final challenge for the combinatorial bound using a result of Marcus and Tardos [JCTA 2004] for permutation avoidance on matrices.
Cite as

Panagiotis Charalampopoulos, Paweł Gawrychowski, and Samah Ghazawi. Optimal Bounds for Distinct Quartics. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 39:1-39:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{charalampopoulos_et_al:LIPIcs.ICALP.2024.39,
  author =	{Charalampopoulos, Panagiotis and Gawrychowski, Pawe{\l} and Ghazawi, Samah},
  title =	{{Optimal Bounds for Distinct Quartics}},
  booktitle =	{51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)},
  pages =	{39:1--39:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-322-5},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{297},
  editor =	{Bringmann, Karl and Grohe, Martin and Puppis, Gabriele and Svensson, Ola},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2024.39},
  URN =		{urn:nbn:de:0030-drops-201823},
  doi =		{10.4230/LIPIcs.ICALP.2024.39},
  annote =	{Keywords: 2D strings, quartics, repetitions, periodicity}
}
Document
Invited Talk
DOI: 10.4230/LIPIcs.CPM.2022.3
Compact Text Indexing for Advanced Pattern Matching Problems: Parameterized, Order-Isomorphic, 2D, etc. (Invited Talk)

Authors: Sharma V. Thankachan

Published in: LIPIcs, Volume 223, 33rd Annual Symposium on Combinatorial Pattern Matching (CPM 2022)

Abstract
In the past two decades, we have witnessed the design of various compact data structures for pattern matching over an indexed text [Navarro, 2016]. Popular indexes like the FM-index [Paolo Ferragina and Giovanni Manzini, 2005], compressed suffix arrays/trees [Roberto Grossi and Jeffrey Scott Vitter, 2005; Kunihiko Sadakane, 2007], the recent r-index [Travis Gagie et al., 2020; Takaaki Nishimoto and Yasuo Tabei, 2021], etc., capture the key functionalities of classic suffix arrays/trees [Udi Manber and Eugene W. Myers, 1993; Peter Weiner, 1973] in compact space. Mostly, they rely on the Burrows-Wheeler Transform (BWT) and its associated operations [Burrows and Wheeler, 1994]. However, compactly encoding some advanced suffix tree (ST) variants, like parameterized ST [Brenda S. Baker, 1993; S. Rao Kosaraju, 1995; Juan Mendivelso et al., 2020], order-isomorphic/preserving ST [Maxime Crochemore et al., 2016], two-dimensional ST [Raffaele Giancarlo, 1995; Dong Kyue Kim et al., 1998], etc. [Sung Gwan Park et al., 2019; Tetsuo Shibuya, 2000]- collectively known as suffix trees with missing suffix links [Richard Cole and Ramesh Hariharan, 2003], has been challenging. The previous techniques are not easily extendable because these variants do not hold some structural properties of the standard ST that enable compression. However, some limited progress has been made in these directions recently [Arnab Ganguly et al., 2017; Travis Gagie et al., 2017; Gianni Decaroli et al., 2017; Dhrumil Patel and Rahul Shah, 2021; Arnab Ganguly et al., 2021; Sung{-}Hwan Kim and Hwan{-}Gue Cho, 2021; Sung{-}Hwan Kim and Hwan{-}Gue Cho, 2021; Arnab Ganguly et al., 2017; Arnab Ganguly et al., 2022; Arnab Ganguly et al., 2021]. This talk will briefly survey them and highlight some interesting open problems.
Cite as

Sharma V. Thankachan. Compact Text Indexing for Advanced Pattern Matching Problems: Parameterized, Order-Isomorphic, 2D, etc. (Invited Talk). In 33rd Annual Symposium on Combinatorial Pattern Matching (CPM 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 223, pp. 3:1-3:3, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{thankachan:LIPIcs.CPM.2022.3,
  author =	{Thankachan, Sharma V.},
  title =	{{Compact Text Indexing for Advanced Pattern Matching Problems: Parameterized, Order-Isomorphic, 2D, etc.}},
  booktitle =	{33rd Annual Symposium on Combinatorial Pattern Matching (CPM 2022)},
  pages =	{3:1--3:3},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-234-1},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{223},
  editor =	{Bannai, Hideo and Holub, Jan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CPM.2022.3},
  URN =		{urn:nbn:de:0030-drops-161300},
  doi =		{10.4230/LIPIcs.CPM.2022.3},
  annote =	{Keywords: Text Indexing, Suffix Trees, String Matching}
}
Document
DOI: 10.4230/LIPIcs.CPM.2022.13
Back-To-Front Online Lyndon Forest Construction

Authors: Golnaz Badkobeh, Maxime Crochemore, Jonas Ellert, and Cyril Nicaud

Published in: LIPIcs, Volume 223, 33rd Annual Symposium on Combinatorial Pattern Matching (CPM 2022)

Abstract
A Lyndon word is a word that is lexicographically smaller than all of its non-trivial rotations (e.g. ananas is a Lyndon word; banana is not a Lyndon word due to its smaller rotation abanan). The Lyndon forest (or equivalently Lyndon table) identifies maximal Lyndon factors of a word, and is of great combinatoric interest, e.g. when finding maximal repetitions in words. While optimal linear time algorithms for computing the Lyndon forest are known, none of them work in an online manner. We present algorithms that compute the Lyndon forest of a word in a reverse online manner, processing the input word from back to front. We assume a general ordered alphabet, i.e. the only elementary operations on symbols are comparisons of the form less-equal-greater. We start with a naive algorithm and show that, despite its quadratic worst-case behaviour, it already takes expected linear time on words drawn uniformly at random. We then introduce a much more sophisticated algorithm that takes linear time in the worst case. It borrows some ideas from the offline algorithm by Bille et al. (ICALP 2020), combined with new techniques that are necessary for the reverse online setting. While the back-to-front approach for this computation is rather natural (see Franek and Liut, PSC 2019), the steps required to achieve linear time are surprisingly intricate. We envision that our algorithm will be useful for the online computation of maximal repetitions in words.
Cite as

Golnaz Badkobeh, Maxime Crochemore, Jonas Ellert, and Cyril Nicaud. Back-To-Front Online Lyndon Forest Construction. In 33rd Annual Symposium on Combinatorial Pattern Matching (CPM 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 223, pp. 13:1-13:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{badkobeh_et_al:LIPIcs.CPM.2022.13,
  author =	{Badkobeh, Golnaz and Crochemore, Maxime and Ellert, Jonas and Nicaud, Cyril},
  title =	{{Back-To-Front Online Lyndon Forest Construction}},
  booktitle =	{33rd Annual Symposium on Combinatorial Pattern Matching (CPM 2022)},
  pages =	{13:1--13:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-234-1},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{223},
  editor =	{Bannai, Hideo and Holub, Jan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CPM.2022.13},
  URN =		{urn:nbn:de:0030-drops-161404},
  doi =		{10.4230/LIPIcs.CPM.2022.13},
  annote =	{Keywords: Lyndon factorisation, Lyndon forest, Lyndon table, Lyndon array, right Lyndon tree, Cartesian tree, standard factorisation, online algorithms}
}
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