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Documents authored by Masillo, Francesco

Document
DOI: 10.4230/LIPIcs.ESA.2024.86
A Textbook Solution for Dynamic Strings

Authors: Zsuzsanna Lipták, Francesco Masillo, and Gonzalo Navarro

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

Abstract
We consider the problem of maintaining a collection of strings while efficiently supporting splits and concatenations on them, as well as comparing two substrings, and computing the longest common prefix between two suffixes. This problem can be solved in optimal time O(log N) whp for the updates and O(1) worst-case time for the queries, where N is the total collection size [Gawrychowski et al., SODA 2018]. We present here a much simpler solution based on a forest of enhanced splay trees (FeST), where both the updates and the substring comparison take O(log n) amortized time, n being the lengths of the strings involved. The longest common prefix of length 𝓁 is computed in O(log n + log²𝓁) amortized time. Our query results are correct whp. Our simpler solution enables other more general updates in O(log n) amortized time, such as reversing a substring and/or mapping its symbols. We can also regard substrings as circular or as their omega extension.
Cite as

Zsuzsanna Lipták, Francesco Masillo, and Gonzalo Navarro. A Textbook Solution for Dynamic Strings. In 32nd Annual European Symposium on Algorithms (ESA 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 308, pp. 86:1-86:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{liptak_et_al:LIPIcs.ESA.2024.86,
  author =	{Lipt\'{a}k, Zsuzsanna and Masillo, Francesco and Navarro, Gonzalo},
  title =	{{A Textbook Solution for Dynamic Strings}},
  booktitle =	{32nd Annual European Symposium on Algorithms (ESA 2024)},
  pages =	{86:1--86:16},
  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.2024.86},
  URN =		{urn:nbn:de:0030-drops-211576},
  doi =		{10.4230/LIPIcs.ESA.2024.86},
  annote =	{Keywords: dynamic strings, splay trees, dynamic data structures, LCP, circular strings}
}
Document
DOI: 10.4230/LIPIcs.CPM.2024.21
BAT-LZ out of hell

Authors: Zsuzsanna Lipták, Francesco Masillo, and Gonzalo Navarro

Published in: LIPIcs, Volume 296, 35th Annual Symposium on Combinatorial Pattern Matching (CPM 2024)

Abstract
Despite consistently yielding the best compression on repetitive text collections, the Lempel-Ziv parsing has resisted all attempts at offering relevant guarantees on the cost to access an arbitrary symbol. This makes it less attractive for use on compressed self-indexes and other compressed data structures. In this paper we introduce a variant we call BAT-LZ (for Bounded Access Time Lempel-Ziv) where the access cost is bounded by a parameter given at compression time. We design and implement a linear-space algorithm that, in time O(nlog³ n), obtains a BAT-LZ parse of a text of length n by greedily maximizing each next phrase length. The algorithm builds on a new linear-space data structure that solves 5-sided orthogonal range queries in rank space, allowing updates to the coordinate where the one-sided queries are supported, in O(log³ n) time for both queries and updates. This time can be reduced to O(log² n) if O(nlog n) space is used. We design a second algorithm that chooses the sources for the phrases in a clever way, using an enhanced suffix tree, albeit no longer guaranteeing longest possible phrases. This algorithm is much slower in theory, but in practice it is comparable to the greedy parser, while achieving significantly superior compression. We then combine the two algorithms, resulting in a parser that always chooses the longest possible phrases, and the best sources for those. Our experimentation shows that, on most repetitive texts, our algorithms reach an access cost close to log₂ n on texts of length n, while incurring almost no loss in the compression ratio when compared with classical LZ-compression. Several open challenges are discussed at the end of the paper.
Cite as

Zsuzsanna Lipták, Francesco Masillo, and Gonzalo Navarro. BAT-LZ out of hell. In 35th Annual Symposium on Combinatorial Pattern Matching (CPM 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 296, pp. 21:1-21:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{liptak_et_al:LIPIcs.CPM.2024.21,
  author =	{Lipt\'{a}k, Zsuzsanna and Masillo, Francesco and Navarro, Gonzalo},
  title =	{{BAT-LZ out of hell}},
  booktitle =	{35th Annual Symposium on Combinatorial Pattern Matching (CPM 2024)},
  pages =	{21:1--21:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-326-3},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{296},
  editor =	{Inenaga, Shunsuke and Puglisi, Simon J.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CPM.2024.21},
  URN =		{urn:nbn:de:0030-drops-201317},
  doi =		{10.4230/LIPIcs.CPM.2024.21},
  annote =	{Keywords: Lempel-Ziv parsing, data compression, compressed data structures, repetitive text collections}
}
Document
DOI: 10.4230/LIPIcs.ESA.2023.83
Matching Statistics Speed up BWT Construction

Authors: Francesco Masillo

Published in: LIPIcs, Volume 274, 31st Annual European Symposium on Algorithms (ESA 2023)

Abstract
Due to the exponential growth of genomic data, constructing dedicated data structures has become the principal bottleneck in common bioinformatics applications. In particular, the Burrows-Wheeler Transform (BWT) is the basis of some of the most popular self-indexes for genomic data, due to its known favourable behaviour on repetitive data. Some tools that exploit the intrinsic repetitiveness of biological data have risen in popularity, due to their speed and low space consumption. We introduce a new algorithm for computing the BWT, which takes advantage of the redundancy of the data through a compressed version of matching statistics, the CMS of [Lipták et al., WABI 2022]. We show that it suffices to sort a small subset of suffixes, lowering both computation time and space. Our result is due to a new insight which links the so-called insert-heads of [Lipták et al., WABI 2022] to the well-known run boundaries of the BWT. We give two implementations of our algorithm, called CMS-BWT, both competitive in our experimental validation on highly repetitive real-life datasets. In most cases, they outperform other tools w.r.t. running time, trading off a higher memory footprint, which, however, is still considerably smaller than the total size of the input data.
Cite as

Francesco Masillo. Matching Statistics Speed up BWT Construction. In 31st Annual European Symposium on Algorithms (ESA 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 274, pp. 83:1-83:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{masillo:LIPIcs.ESA.2023.83,
  author =	{Masillo, Francesco},
  title =	{{Matching Statistics Speed up BWT Construction}},
  booktitle =	{31st Annual European Symposium on Algorithms (ESA 2023)},
  pages =	{83:1--83:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-295-2},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{274},
  editor =	{G{\o}rtz, Inge Li and Farach-Colton, Martin and Puglisi, Simon J. 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.2023.83},
  URN =		{urn:nbn:de:0030-drops-187360},
  doi =		{10.4230/LIPIcs.ESA.2023.83},
  annote =	{Keywords: Burrows-Wheeler Transform, matching statistics, string collections, compressed representation, data structures, efficient algorithms}
}
Document
DOI: 10.4230/LIPIcs.WABI.2022.20
Suffix Sorting via Matching Statistics

Authors: Zsuzsanna Lipták, Francesco Masillo, and Simon J. Puglisi

Published in: LIPIcs, Volume 242, 22nd International Workshop on Algorithms in Bioinformatics (WABI 2022)

Abstract
We introduce a new algorithm for constructing the generalized suffix array of a collection of highly similar strings. As a first step, we construct a compressed representation of the matching statistics of the collection with respect to a reference string. We then use this data structure to distribute suffixes into a partial order, and subsequently to speed up suffix comparisons to complete the generalized suffix array. Our experimental evidence with a prototype implementation (a tool we call sacamats) shows that on string collections with highly similar strings we can construct the suffix array in time competitive with or faster than the fastest available methods. Along the way, we describe a heuristic for fast computation of the matching statistics of two strings, which may be of independent interest.
Cite as

Zsuzsanna Lipták, Francesco Masillo, and Simon J. Puglisi. Suffix Sorting via Matching Statistics. In 22nd International Workshop on Algorithms in Bioinformatics (WABI 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 242, pp. 20:1-20:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{liptak_et_al:LIPIcs.WABI.2022.20,
  author =	{Lipt\'{a}k, Zsuzsanna and Masillo, Francesco and Puglisi, Simon J.},
  title =	{{Suffix Sorting via Matching Statistics}},
  booktitle =	{22nd International Workshop on Algorithms in Bioinformatics (WABI 2022)},
  pages =	{20:1--20:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-243-3},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{242},
  editor =	{Boucher, Christina and Rahmann, Sven},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.WABI.2022.20},
  URN =		{urn:nbn:de:0030-drops-170545},
  doi =		{10.4230/LIPIcs.WABI.2022.20},
  annote =	{Keywords: Generalized suffix array, matching statistics, string collections, compressed representation, data structures, efficient algorithms}
}
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