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Documents authored by Cunial, Fabio

Document
DOI: 10.4230/LIPIcs.CPM.2019.10
Fully-Functional Bidirectional Burrows-Wheeler Indexes and Infinite-Order De Bruijn Graphs

Authors: Djamal Belazzougui and Fabio Cunial

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

Abstract
Given a string T on an alphabet of size sigma, we describe a bidirectional Burrows-Wheeler index that takes O(|T| log sigma) bits of space, and that supports the addition and removal of one character, on the left or right side of any substring of T, in constant time. Previously known data structures that used the same space allowed constant-time addition to any substring of T, but they could support removal only from specific substrings of T. We also describe an index that supports bidirectional addition and removal in O(log log |T|) time, and that takes a number of words proportional to the number of left and right extensions of the maximal repeats of T. We use such fully-functional indexes to implement bidirectional, frequency-aware, variable-order de Bruijn graphs with no upper bound on their order, and supporting natural criteria for increasing and decreasing the order during traversal.
Cite as

Djamal Belazzougui and Fabio Cunial. Fully-Functional Bidirectional Burrows-Wheeler Indexes and Infinite-Order De Bruijn Graphs. In 30th Annual Symposium on Combinatorial Pattern Matching (CPM 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 128, pp. 10:1-10:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{belazzougui_et_al:LIPIcs.CPM.2019.10,
  author =	{Belazzougui, Djamal and Cunial, Fabio},
  title =	{{Fully-Functional Bidirectional Burrows-Wheeler Indexes and Infinite-Order De Bruijn Graphs}},
  booktitle =	{30th Annual Symposium on Combinatorial Pattern Matching (CPM 2019)},
  pages =	{10:1--10:15},
  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.2019.10},
  URN =		{urn:nbn:de:0030-drops-104811},
  doi =		{10.4230/LIPIcs.CPM.2019.10},
  annote =	{Keywords: BWT, suffix tree, CDAWG, de Bruijn graph, maximal repeat, string depth, contraction, bidirectional index}
}
Document
DOI: 10.4230/LIPIcs.SEA.2018.17
Fast matching statistics in small space

Authors: Djamal Belazzougui, Fabio Cunial, and Olgert Denas

Published in: LIPIcs, Volume 103, 17th International Symposium on Experimental Algorithms (SEA 2018)

Abstract
Computing the matching statistics of a string S with respect to a string T on an alphabet of size sigma is a fundamental primitive for a number of large-scale string analysis applications, including the comparison of entire genomes, for which space is a pressing issue. This paper takes from theory to practice an existing algorithm that uses just O(|T|log{sigma}) bits of space, and that computes a compact encoding of the matching statistics array in O(|S|log{sigma}) time. The techniques used to speed up the algorithm are of general interest, since they optimize queries on the existence of a Weiner link from a node of the suffix tree, and parent operations after unsuccessful Weiner links. Thus, they can be applied to other matching statistics algorithms, as well as to any suffix tree traversal that relies on such calls. Some of our optimizations yield a matching statistics implementation that is up to three times faster than a plain version of the algorithm, depending on the similarity between S and T. In genomic datasets of practical significance we achieve speedups of up to 1.8, but our fastest implementations take on average twice the time of an existing code based on the LCP array. The key advantage is that our implementations need between one half and one fifth of the competitor's memory, and they approach comparable running times when S and T are very similar.
Cite as

Djamal Belazzougui, Fabio Cunial, and Olgert Denas. Fast matching statistics in small space. In 17th International Symposium on Experimental Algorithms (SEA 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 103, pp. 17:1-17:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{belazzougui_et_al:LIPIcs.SEA.2018.17,
  author =	{Belazzougui, Djamal and Cunial, Fabio and Denas, Olgert},
  title =	{{Fast matching statistics in small space}},
  booktitle =	{17th International Symposium on Experimental Algorithms (SEA 2018)},
  pages =	{17:1--17:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-070-5},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{103},
  editor =	{D'Angelo, Gianlorenzo},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SEA.2018.17},
  URN =		{urn:nbn:de:0030-drops-89528},
  doi =		{10.4230/LIPIcs.SEA.2018.17},
  annote =	{Keywords: Matching statistics, maximal repeat, Burrows-Wheeler transform, wavelet tree, suffix tree topology}
}
Document
DOI: 10.4230/LIPIcs.CPM.2017.7
Representing the Suffix Tree with the CDAWG

Authors: Djamal Belazzougui and Fabio Cunial

Published in: LIPIcs, Volume 78, 28th Annual Symposium on Combinatorial Pattern Matching (CPM 2017)

Abstract
Given a string T, it is known that its suffix tree can be represented using the compact directed acyclic word graph (CDAWG) with e_T arcs, taking overall O(e_T+e_REV(T)) words of space, where REV(T) is the reverse of T, and supporting some key operations in time between O(1) and O(log(log(n))) in the worst case. This representation is especially appealing for highly repetitive strings, like collections of similar genomes or of version-controlled documents, in which e_T grows sublinearly in the length of T in practice. In this paper we augment such representation, supporting a number of additional queries in worst-case time between O(1) and O(log(n)) in the RAM model, without increasing space complexity asymptotically. Our technique, based on a heavy path decomposition of the suffix tree, enables also a representation of the suffix array, of the inverse suffix array, and of T itself, that takes O(e_T) words of space, and that supports random access in O(log(n)) time. Furthermore, we establish a connection between the reversed CDAWG of T and a context-free grammar that produces T and only T, which might have independent interest.
Cite as

Djamal Belazzougui and Fabio Cunial. Representing the Suffix Tree with the CDAWG. In 28th Annual Symposium on Combinatorial Pattern Matching (CPM 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 78, pp. 7:1-7:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{belazzougui_et_al:LIPIcs.CPM.2017.7,
  author =	{Belazzougui, Djamal and Cunial, Fabio},
  title =	{{Representing the Suffix Tree with the CDAWG}},
  booktitle =	{28th Annual Symposium on Combinatorial Pattern Matching (CPM 2017)},
  pages =	{7:1--7:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-039-2},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{78},
  editor =	{K\"{a}rkk\"{a}inen, Juha and Radoszewski, Jakub and Rytter, Wojciech},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CPM.2017.7},
  URN =		{urn:nbn:de:0030-drops-73402},
  doi =		{10.4230/LIPIcs.CPM.2017.7},
  annote =	{Keywords: CDAWG, suffix tree, heavy path decomposition, maximal repeat, context-free grammar}
}
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