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Documents authored by Mohamed, Manal

Document
DOI: 10.4230/LIPIcs.MFCS.2025.36
Counting Distinct Square Substrings in Sublinear Time

Authors: Panagiotis Charalampopoulos, Manal Mohamed, Jakub Radoszewski, Wojciech Rytter, Tomasz Waleń, and Wiktor Zuba

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

Abstract
We show that the number of distinct squares in a packed string of length n over an alphabet of size σ can be computed in 𝒪(n/log_{σ}n) time in the word-RAM model of computation. This paper is the first to introduce a sublinear time algorithm for the packed version of squares counting. The packed representation of a string of length n over an alphabet of size σ is given as a sequence of 𝒪(n/ log_{σ} n) machine words in the word-RAM model (a machine word consists of ω ≥ log₂ n bits). Previously it was known how to count distinct squares in 𝒪(n) time [Gusfield and Stoye, JCSS 2004], even for a string over an integer alphabet, see [Crochemore et al., TCS 2014; Bannai et al., CPM 2017; Charalampopoulos et al., SPIRE 2020]. We use techniques of squares extraction from runs described by Crochemore et al. [TCS 2014]. However, the packed model requires novel approaches. In particular, we need an 𝒪(n/log_{σ}n) sized representation of all long-period runs (runs with periods that are Ω(log_{σ}n)) which guarantees sublinear time counting of potentially linearly-many implied squares. The long-period runs with a string period that is periodic itself (called layer runs) are an obstacle, since their number can be Ω(n). Fortunately, the number of all other long-period runs is 𝒪(n/log_{σ}n) and we can construct an implicit representation of all long-period runs in 𝒪(n/log_{σ}n) time by adopting the insights of Amir et al. [ESA 2019], combined with sublinear time tools provided by the PILLAR model of computations in case of packed strings. We count squares in layer runs in sublinear time by exploiting combinatorial properties of types of pyramidally-shaped groups of layer runs. As a by-product, we discover several new structural properties of runs. Another difficulty is to compute, in sublinear time, locations of Lyndon roots of runs in packed strings, which is needed for grouping of runs that can generate equal squares. To overcome this difficulty, we introduce sparse-Lyndon roots which are based on the notion of string synchronizers proposed by Kempa and Kociumaka [STOC 2019].
Cite as

Panagiotis Charalampopoulos, Manal Mohamed, Jakub Radoszewski, Wojciech Rytter, Tomasz Waleń, and Wiktor Zuba. Counting Distinct Square Substrings in Sublinear Time. In 50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 345, pp. 36:1-36:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{charalampopoulos_et_al:LIPIcs.MFCS.2025.36,
  author =	{Charalampopoulos, Panagiotis and Mohamed, Manal and Radoszewski, Jakub and Rytter, Wojciech and Wale\'{n}, Tomasz and Zuba, Wiktor},
  title =	{{Counting Distinct Square Substrings in Sublinear Time}},
  booktitle =	{50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025)},
  pages =	{36:1--36:19},
  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.2025.36},
  URN =		{urn:nbn:de:0030-drops-241439},
  doi =		{10.4230/LIPIcs.MFCS.2025.36},
  annote =	{Keywords: square in a string, packed model, run (maximal repetition), Lyndon word}
}
Document
DOI: 10.4230/LIPIcs.CPM.2020.8
Counting Distinct Patterns in Internal Dictionary Matching

Authors: Panagiotis Charalampopoulos, Tomasz Kociumaka, Manal Mohamed, Jakub Radoszewski, Wojciech Rytter, Juliusz Straszyński, Tomasz Waleń, and Wiktor Zuba

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

Abstract
We consider the problem of preprocessing a text T of length n and a dictionary 𝒟 in order to be able to efficiently answer queries CountDistinct(i,j), that is, given i and j return the number of patterns from 𝒟 that occur in the fragment T[i..j]. The dictionary is internal in the sense that each pattern in 𝒟 is given as a fragment of T. This way, the dictionary takes space proportional to the number of patterns d=|𝒟| rather than their total length, which could be Θ(n⋅ d). An 𝒪̃(n+d)-size data structure that answers CountDistinct(i,j) queries 𝒪(log n)-approximately in 𝒪̃(1) time was recently proposed in a work that introduced internal dictionary matching [ISAAC 2019]. Here we present an 𝒪̃(n+d)-size data structure that answers CountDistinct(i,j) queries 2-approximately in 𝒪̃(1) time. Using range queries, for any m, we give an 𝒪̃(min(nd/m,n²/m²)+d)-size data structure that answers CountDistinct(i,j) queries exactly in 𝒪̃(m) time. We also consider the special case when the dictionary consists of all square factors of the string. We design an 𝒪(n log² n)-size data structure that allows us to count distinct squares in a text fragment T[i..j] in 𝒪(log n) time.
Cite as

Panagiotis Charalampopoulos, Tomasz Kociumaka, Manal Mohamed, Jakub Radoszewski, Wojciech Rytter, Juliusz Straszyński, Tomasz Waleń, and Wiktor Zuba. Counting Distinct Patterns in Internal Dictionary Matching. In 31st Annual Symposium on Combinatorial Pattern Matching (CPM 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 161, pp. 8:1-8:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{charalampopoulos_et_al:LIPIcs.CPM.2020.8,
  author =	{Charalampopoulos, Panagiotis and Kociumaka, Tomasz and Mohamed, Manal and Radoszewski, Jakub and Rytter, Wojciech and Straszy\'{n}ski, Juliusz and Wale\'{n}, Tomasz and Zuba, Wiktor},
  title =	{{Counting Distinct Patterns in Internal Dictionary Matching}},
  booktitle =	{31st Annual Symposium on Combinatorial Pattern Matching (CPM 2020)},
  pages =	{8:1--8:15},
  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.2020.8},
  URN =		{urn:nbn:de:0030-drops-121336},
  doi =		{10.4230/LIPIcs.CPM.2020.8},
  annote =	{Keywords: dictionary matching, internal pattern matching, squares}
}
Document
DOI: 10.4230/LIPIcs.ISAAC.2019.22
Internal Dictionary Matching

Authors: Panagiotis Charalampopoulos, Tomasz Kociumaka, Manal Mohamed, Jakub Radoszewski, Wojciech Rytter, and Tomasz Waleń

Published in: LIPIcs, Volume 149, 30th International Symposium on Algorithms and Computation (ISAAC 2019)

Abstract
We introduce data structures answering queries concerning the occurrences of patterns from a given dictionary D in fragments of a given string T of length n. The dictionary is internal in the sense that each pattern in D is given as a fragment of T. This way, D takes space proportional to the number of patterns d=|D| rather than their total length, which could be Theta(n * d). In particular, we consider the following types of queries: reporting and counting all occurrences of patterns from D in a fragment T[i..j] (operations Report(i,j) and Count(i,j) below, as well as operation Exists(i,j) that returns true iff Count(i,j)>0) and reporting distinct patterns from D that occur in T[i..j] (operation ReportDistinct(i,j)). We show how to construct, in O((n+d) log^{O(1)} n) time, a data structure that answers each of these queries in time O(log^{O(1)} n+|output|) - see the table below for specific time and space complexities. Query | Preprocessing time | Space | Query time Exists(i,j) | O(n+d) | O(n) | O(1) Report(i,j) | O(n+d) | O(n+d) | O(1+|output|) ReportDistinct(i,j) | O(n log n+d) | O(n+d) | O(log n+|output|) Count(i,j) | O({n log n}/{log log n} + d log^{3/2} n) | O(n+d log n) | O({log^2n}/{log log n}) The case of counting patterns is much more involved and needs a combination of a locally consistent parsing with orthogonal range searching. Reporting distinct patterns, on the other hand, uses the structure of maximal repetitions in strings. Finally, we provide tight - up to subpolynomial factors - upper and lower bounds for the case of a dynamic dictionary.
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Panagiotis Charalampopoulos, Tomasz Kociumaka, Manal Mohamed, Jakub Radoszewski, Wojciech Rytter, and Tomasz Waleń. Internal Dictionary Matching. In 30th International Symposium on Algorithms and Computation (ISAAC 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 149, pp. 22:1-22:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{charalampopoulos_et_al:LIPIcs.ISAAC.2019.22,
  author =	{Charalampopoulos, Panagiotis and Kociumaka, Tomasz and Mohamed, Manal and Radoszewski, Jakub and Rytter, Wojciech and Wale\'{n}, Tomasz},
  title =	{{Internal Dictionary Matching}},
  booktitle =	{30th International Symposium on Algorithms and Computation (ISAAC 2019)},
  pages =	{22:1--22:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-130-6},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{149},
  editor =	{Lu, Pinyan and Zhang, Guochuan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2019.22},
  URN =		{urn:nbn:de:0030-drops-115182},
  doi =		{10.4230/LIPIcs.ISAAC.2019.22},
  annote =	{Keywords: string algorithms, dictionary matching, internal pattern matching}
}
Document
DOI: 10.4230/LIPIcs.ISAAC.2018.70
Longest Unbordered Factor in Quasilinear Time

Authors: Tomasz Kociumaka, Ritu Kundu, Manal Mohamed, and Solon P. Pissis

Published in: LIPIcs, Volume 123, 29th International Symposium on Algorithms and Computation (ISAAC 2018)

Abstract
A border u of a word w is a proper factor of w occurring both as a prefix and as a suffix. The maximal unbordered factor of w is the longest factor of w which does not have a border. Here an O(n log n)-time with high probability (or O(n log n log^2 log n)-time deterministic) algorithm to compute the Longest Unbordered Factor Array of w for general alphabets is presented, where n is the length of w. This array specifies the length of the maximal unbordered factor starting at each position of w. This is a major improvement on the running time of the currently best worst-case algorithm working in O(n^{1.5}) time for integer alphabets [Gawrychowski et al., 2015].
Cite as

Tomasz Kociumaka, Ritu Kundu, Manal Mohamed, and Solon P. Pissis. Longest Unbordered Factor in Quasilinear Time. In 29th International Symposium on Algorithms and Computation (ISAAC 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 123, pp. 70:1-70:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{kociumaka_et_al:LIPIcs.ISAAC.2018.70,
  author =	{Kociumaka, Tomasz and Kundu, Ritu and Mohamed, Manal and Pissis, Solon P.},
  title =	{{Longest Unbordered Factor in Quasilinear Time}},
  booktitle =	{29th International Symposium on Algorithms and Computation (ISAAC 2018)},
  pages =	{70:1--70:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-094-1},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{123},
  editor =	{Hsu, Wen-Lian and Lee, Der-Tsai and Liao, Chung-Shou},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2018.70},
  URN =		{urn:nbn:de:0030-drops-100184},
  doi =		{10.4230/LIPIcs.ISAAC.2018.70},
  annote =	{Keywords: longest unbordered factor, factorisation, period, border, strings}
}
Document
DOI: 10.4230/LIPIcs.WABI.2017.4
Optimal Computation of Overabundant Words

Authors: Yannis Almirantis, Panagiotis Charalampopoulos, Jia Gao, Costas S. Iliopoulos, Manal Mohamed, Solon P. Pissis, and Dimitris Polychronopoulos

Published in: LIPIcs, Volume 88, 17th International Workshop on Algorithms in Bioinformatics (WABI 2017)

Abstract
The observed frequency of the longest proper prefix, the longest proper suffix, and the longest infix of a word w in a given sequence x can be used for classifying w as avoided or overabundant. The definitions used for the expectation and deviation of w in this statistical model were described and biologically justified by Brendel et al. (J Biomol Struct Dyn 1986). We have very recently introduced a time-optimal algorithm for computing all avoided words of a given sequence over an integer alphabet (Algorithms Mol Biol 2017). In this article, we extend this study by presenting an O(n)-time and O(n)-space algorithm for computing all overabundant words in a sequence x of length n over an integer alphabet. Our main result is based on a new non-trivial combinatorial property of the suffix tree T of x: the number of distinct factors of x whose longest infix is the label of an explicit node of T is no more than 3n-4. We further show that the presented algorithm is time-optimal by proving that O(n) is a tight upper bound for the number of overabundant words. Finally, we present experimental results, using both synthetic and real data, which justify the effectiveness and efficiency of our approach in practical terms.
Cite as

Yannis Almirantis, Panagiotis Charalampopoulos, Jia Gao, Costas S. Iliopoulos, Manal Mohamed, Solon P. Pissis, and Dimitris Polychronopoulos. Optimal Computation of Overabundant Words. In 17th International Workshop on Algorithms in Bioinformatics (WABI 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 88, pp. 4:1-4:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{almirantis_et_al:LIPIcs.WABI.2017.4,
  author =	{Almirantis, Yannis and Charalampopoulos, Panagiotis and Gao, Jia and Iliopoulos, Costas S. and Mohamed, Manal and Pissis, Solon P. and Polychronopoulos, Dimitris},
  title =	{{Optimal Computation of Overabundant Words}},
  booktitle =	{17th International Workshop on Algorithms in Bioinformatics (WABI 2017)},
  pages =	{4:1--4:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-050-7},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{88},
  editor =	{Schwartz, Russell and Reinert, Knut},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.WABI.2017.4},
  URN =		{urn:nbn:de:0030-drops-76468},
  doi =		{10.4230/LIPIcs.WABI.2017.4},
  annote =	{Keywords: overabundant words, avoided words, suffix tree, DNA sequence analysis}
}
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