6 Search Results for "Gourdel, Garance"


Document
Track A: Algorithms, Complexity and Games
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
Track A: Algorithms, Complexity and Games
Õptimal Dynamic Time Warping on Run-Length Encoded Strings

Authors: Itai Boneh, Shay Golan, Shay Mozes, and Oren Weimann

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


Abstract
Dynamic Time Warping (DTW) distance is the optimal cost of matching two strings when extending runs of letters is for free. Therefore, it is natural to measure the time complexity of DTW in terms of the number of runs n (rather than the string lengths N). In this paper, we give an Õ(n²) time algorithm for computing the DTW distance. This matches (up to log factors) the known (conditional) lower bound, and should be compared with the previous fastest O(n³) time exact algorithm and the Õ(n²) time approximation algorithm. Our method also immediately implies an Õ(nk) time algorithm when the distance is bounded by k. This should be compared with the previous fastest O(n²k) and O(Nk) time exact algorithms and the Õ(nk) time approximation algorithm.

Cite as

Itai Boneh, Shay Golan, Shay Mozes, and Oren Weimann. Õptimal Dynamic Time Warping on Run-Length Encoded Strings. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 30:1-30:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)


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@InProceedings{boneh_et_al:LIPIcs.ICALP.2024.30,
  author =	{Boneh, Itai and Golan, Shay and Mozes, Shay and Weimann, Oren},
  title =	{{\~{O}ptimal Dynamic Time Warping on Run-Length Encoded Strings}},
  booktitle =	{51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)},
  pages =	{30:1--30:17},
  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.2024.30},
  URN =		{urn:nbn:de:0030-drops-201730},
  doi =		{10.4230/LIPIcs.ICALP.2024.30},
  annote =	{Keywords: Dynamic time warping, Fr\'{e}chet distance, edit distance, run-length encoding}
}
Document
Compressed Indexing for Consecutive Occurrences

Authors: Paweł Gawrychowski, Garance Gourdel, Tatiana Starikovskaya, and Teresa Anna Steiner

Published in: LIPIcs, Volume 259, 34th Annual Symposium on Combinatorial Pattern Matching (CPM 2023)


Abstract
The fundamental question considered in algorithms on strings is that of indexing, that is, preprocessing a given string for specific queries. By now we have a number of efficient solutions for this problem when the queries ask for an exact occurrence of a given pattern P. However, practical applications motivate the necessity of considering more complex queries, for example concerning near occurrences of two patterns. Recently, Bille et al. [CPM 2021] introduced a variant of such queries, called gapped consecutive occurrences, in which a query consists of two patterns P₁ and P₂ and a range [a,b], and one must find all consecutive occurrences (q₁,q₂) of P₁ and P₂ such that q₂-q₁ ∈ [a,b]. By their results, we cannot hope for a very efficient indexing structure for such queries, even if a = 0 is fixed (although at the same time they provided a non-trivial upper bound). Motivated by this, we focus on a text given as a straight-line program (SLP) and design an index taking space polynomial in the size of the grammar that answers such queries in time optimal up to polylog factors.

Cite as

Paweł Gawrychowski, Garance Gourdel, Tatiana Starikovskaya, and Teresa Anna Steiner. Compressed Indexing for Consecutive Occurrences. In 34th Annual Symposium on Combinatorial Pattern Matching (CPM 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 259, pp. 12:1-12:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)


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@InProceedings{gawrychowski_et_al:LIPIcs.CPM.2023.12,
  author =	{Gawrychowski, Pawe{\l} and Gourdel, Garance and Starikovskaya, Tatiana and Steiner, Teresa Anna},
  title =	{{Compressed Indexing for Consecutive Occurrences}},
  booktitle =	{34th Annual Symposium on Combinatorial Pattern Matching (CPM 2023)},
  pages =	{12:1--12:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-276-1},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{259},
  editor =	{Bulteau, Laurent and Lipt\'{a}k, Zsuzsanna},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CPM.2023.12},
  URN =		{urn:nbn:de:0030-drops-179666},
  doi =		{10.4230/LIPIcs.CPM.2023.12},
  annote =	{Keywords: Compressed indexing, two patterns, consecutive occurrences}
}
Document
Compressing and Indexing Aligned Readsets

Authors: Travis Gagie, Garance Gourdel, and Giovanni Manzini

Published in: LIPIcs, Volume 201, 21st International Workshop on Algorithms in Bioinformatics (WABI 2021)


Abstract
Compressed full-text indexes are one of the main success stories of bioinformatics data structures but even they struggle to handle some DNA readsets. This may seem surprising since, at least when dealing with short reads from the same individual, the readset will be highly repetitive and, thus, highly compressible. If we are not careful, however, this advantage can be more than offset by two disadvantages: first, since most base pairs are included in at least tens reads each, the uncompressed readset is likely to be at least an order of magnitude larger than the individual’s uncompressed genome; second, these indexes usually pay some space overhead for each string they store, and the total overhead can be substantial when dealing with millions of reads. The most successful compressed full-text indexes for readsets so far are based on the Extended Burrows-Wheeler Transform (EBWT) and use a sorting heuristic to try to reduce the space overhead per read, but they still treat the reads as separate strings and thus may not take full advantage of the readset’s structure. For example, if we have already assembled an individual’s genome from the readset, then we can usually use it to compress the readset well: e.g., we store the gap-coded list of reads' starting positions; we store the list of their lengths, which is often highly compressible; and we store information about the sequencing errors, which are rare with short reads. There is nowhere, however, where we can plug an assembled genome into the EBWT. In this paper we show how to use one or more assembled or partially assembled genome as the basis for a compressed full-text index of its readset. Specifically, we build a labelled tree by taking the assembled genome as a trunk and grafting onto it the reads that align to it, at the starting positions of their alignments. Next, we compute the eXtended Burrows-Wheeler Transform (XBWT) of the resulting labelled tree and build a compressed full-text index on that. Although this index can occasionally return false positives, it is usually much more compact than the alternatives. Following the established practice for datasets with many repetitions, we compare different full-text indices by looking at the number of runs in the transformed strings. For a human Chr19 readset our preliminary experiments show that eliminating separators characters from the EBWT reduces the number of runs by 19%, from 220 million to 178 million, and using the XBWT reduces it by a further 15%, to 150 million.

Cite as

Travis Gagie, Garance Gourdel, and Giovanni Manzini. Compressing and Indexing Aligned Readsets. In 21st International Workshop on Algorithms in Bioinformatics (WABI 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 201, pp. 13:1-13:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)


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@InProceedings{gagie_et_al:LIPIcs.WABI.2021.13,
  author =	{Gagie, Travis and Gourdel, Garance and Manzini, Giovanni},
  title =	{{Compressing and Indexing Aligned Readsets}},
  booktitle =	{21st International Workshop on Algorithms in Bioinformatics (WABI 2021)},
  pages =	{13:1--13:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-200-6},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{201},
  editor =	{Carbone, Alessandra and El-Kebir, Mohammed},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.WABI.2021.13},
  URN =		{urn:nbn:de:0030-drops-143660},
  doi =		{10.4230/LIPIcs.WABI.2021.13},
  annote =	{Keywords: data compression, compact data structures, FM-index, Burrows-Wheeler Transform, EBWT, XBWT, DNA reads}
}
Document
Approximating Longest Common Substring with k mismatches: Theory and Practice

Authors: Garance Gourdel, Tomasz Kociumaka, Jakub Radoszewski, and Tatiana Starikovskaya

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


Abstract
In the problem of the longest common substring with k mismatches we are given two strings X, Y and must find the maximal length 𝓁 such that there is a length-𝓁 substring of X and a length-𝓁 substring of Y that differ in at most k positions. The length 𝓁 can be used as a robust measure of similarity between X, Y. In this work, we develop new approximation algorithms for computing 𝓁 that are significantly more efficient that previously known solutions from the theoretical point of view. Our approach is simple and practical, which we confirm via an experimental evaluation, and is probably close to optimal as we demonstrate via a conditional lower bound.

Cite as

Garance Gourdel, Tomasz Kociumaka, Jakub Radoszewski, and Tatiana Starikovskaya. Approximating Longest Common Substring with k mismatches: Theory and Practice. In 31st Annual Symposium on Combinatorial Pattern Matching (CPM 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 161, pp. 16:1-16:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)


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@InProceedings{gourdel_et_al:LIPIcs.CPM.2020.16,
  author =	{Gourdel, Garance and Kociumaka, Tomasz and Radoszewski, Jakub and Starikovskaya, Tatiana},
  title =	{{Approximating Longest Common Substring with k mismatches: Theory and Practice}},
  booktitle =	{31st Annual Symposium on Combinatorial Pattern Matching (CPM 2020)},
  pages =	{16:1--16:15},
  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.2020.16},
  URN =		{urn:nbn:de:0030-drops-121410},
  doi =		{10.4230/LIPIcs.CPM.2020.16},
  annote =	{Keywords: approximation algorithms, string similarity, LSH, conditional lower bounds}
}
Document
String Periods in the Order-Preserving Model

Authors: Garance Gourdel, Tomasz Kociumaka, Jakub Radoszewski, Wojciech Rytter, Arseny Shur, and Tomasz Walen

Published in: LIPIcs, Volume 96, 35th Symposium on Theoretical Aspects of Computer Science (STACS 2018)


Abstract
The order-preserving model (op-model, in short) was introduced quite recently but has already attracted significant attention because of its applications in data analysis. We introduce several types of periods in this setting (op-periods). Then we give algorithms to compute these periods in time O(n), O(n log log n), O(n log^2 log n/log log log n), O(n log n) depending on the type of periodicity. In the most general variant the number of different periods can be as big as Omega(n^2), and a compact representation is needed. Our algorithms require novel combinatorial insight into the properties of such periods.

Cite as

Garance Gourdel, Tomasz Kociumaka, Jakub Radoszewski, Wojciech Rytter, Arseny Shur, and Tomasz Walen. String Periods in the Order-Preserving Model. In 35th Symposium on Theoretical Aspects of Computer Science (STACS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 96, pp. 38:1-38:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)


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@InProceedings{gourdel_et_al:LIPIcs.STACS.2018.38,
  author =	{Gourdel, Garance and Kociumaka, Tomasz and Radoszewski, Jakub and Rytter, Wojciech and Shur, Arseny and Walen, Tomasz},
  title =	{{String Periods in the Order-Preserving Model}},
  booktitle =	{35th Symposium on Theoretical Aspects of Computer Science (STACS 2018)},
  pages =	{38:1--38:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-062-0},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{96},
  editor =	{Niedermeier, Rolf and Vall\'{e}e, Brigitte},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2018.38},
  URN =		{urn:nbn:de:0030-drops-85064},
  doi =		{10.4230/LIPIcs.STACS.2018.38},
  annote =	{Keywords: order-preserving pattern matching, period, efficient algorithm}
}
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