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Documents authored by Cenzato, Davide

Document
DOI: 10.4230/LIPIcs.CPM.2024.1
Computing the LCP Array of a Labeled Graph

Authors: Jarno N. Alanko, Davide Cenzato, Nicola Cotumaccio, Sung-Hwan Kim, Giovanni Manzini, and Nicola Prezza

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

Abstract
The LCP array is an important tool in stringology, allowing to speed up pattern matching algorithms and enabling compact representations of the suffix tree. Recently, Conte et al. [DCC 2023] and Cotumaccio et al. [SPIRE 2023] extended the definition of this array to Wheeler DFAs and, ultimately, to arbitrary labeled graphs, proving that it can be used to efficiently solve matching statistics queries on the graph’s paths. In this paper, we provide the first efficient algorithm building the LCP array of a directed labeled graph with n nodes and m edges labeled over an alphabet of size σ. The first step is to transform the input graph G into a deterministic Wheeler pseudoforest G_{is} with O(n) edges encoding the lexicographically- smallest and largest strings entering in each node of the original graph. Using state-of-the-art algorithms, this step runs in O(min{mlog n, m+n²}) time on arbitrary labeled graphs, and in O(m) time on Wheeler DFAs. The LCP array of G stores the longest common prefixes between those strings, i.e. it can easily be derived from the LCP array of G_{is}. After arguing that the natural generalization of a compact-space LCP-construction algorithm by Beller et al. [J. Discrete Algorithms 2013] runs in time Ω(nσ) on pseudoforests, we present a new algorithm based on dynamic range stabbing building the LCP array of G_{is} in O(nlog σ) time and O(nlogσ) bits of working space. Combined with our reduction, we obtain the first efficient algorithm to build the LCP array of an arbitrary labeled graph. An implementation of our algorithm is publicly available at https://github.com/regindex/Labeled-Graph-LCP.
Cite as

Jarno N. Alanko, Davide Cenzato, Nicola Cotumaccio, Sung-Hwan Kim, Giovanni Manzini, and Nicola Prezza. Computing the LCP Array of a Labeled Graph. In 35th Annual Symposium on Combinatorial Pattern Matching (CPM 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 296, pp. 1:1-1:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{alanko_et_al:LIPIcs.CPM.2024.1,
  author =	{Alanko, Jarno N. and Cenzato, Davide and Cotumaccio, Nicola and Kim, Sung-Hwan and Manzini, Giovanni and Prezza, Nicola},
  title =	{{Computing the LCP Array of a Labeled Graph}},
  booktitle =	{35th Annual Symposium on Combinatorial Pattern Matching (CPM 2024)},
  pages =	{1:1--1:15},
  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.2024.1},
  URN =		{urn:nbn:de:0030-drops-201113},
  doi =		{10.4230/LIPIcs.CPM.2024.1},
  annote =	{Keywords: LCP array, Wheeler automata, prefix sorting, pattern matching, sorting}
}
Document
DOI: 10.4230/LIPIcs.CPM.2024.5
Random Wheeler Automata

Authors: Ruben Becker, Davide Cenzato, Sung-Hwan Kim, Bojana Kodric, Riccardo Maso, and Nicola Prezza

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

Abstract
Wheeler automata were introduced in 2017 as a tool to generalize existing indexing and compression techniques based on the Burrows-Wheeler transform. Intuitively, an automaton is said to be Wheeler if there exists a total order on its states reflecting the natural co-lexicographic order of the strings labeling the automaton’s paths; this property makes it possible to represent the automaton’s topology in a constant number of bits per transition, as well as efficiently solving pattern matching queries on its accepted regular language. After their introduction, Wheeler automata have been the subject of a prolific line of research, both from the algorithmic and language-theoretic points of view. A recurring issue faced in these studies is the lack of large datasets of Wheeler automata on which the developed algorithms and theories could be tested. One possible way to overcome this issue is to generate random Wheeler automata. Motivated by this observation of practical nature, in this paper we initiate the theoretical study of random Wheeler automata, focusing our attention on the deterministic case (Wheeler DFAs - WDFAs). We start by naturally extending the Erdős-Rényi random graph model to WDFAs, and proceed by providing an algorithm generating uniform WDFAs according to this model. Our algorithm generates a uniform WDFA with n states, m transitions, and alphabet’s cardinality σ in O(m) expected time (O(mlog m) time w.h.p.) and constant working space for all alphabets of size σ ≤ m/ln m. The output WDFA is streamed directly to the output. As a by-product, we also give formulas for the number of distinct WDFAs and obtain that nσ + (n - σ) log σ bits are necessary and sufficient to encode a WDFA with n states and alphabet of size σ, up to an additive Θ(n) term. We present an implementation of our algorithm and show that it is extremely fast in practice, with a throughput of over 8 million transitions per second.
Cite as

Ruben Becker, Davide Cenzato, Sung-Hwan Kim, Bojana Kodric, Riccardo Maso, and Nicola Prezza. Random Wheeler Automata. In 35th Annual Symposium on Combinatorial Pattern Matching (CPM 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 296, pp. 5:1-5:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{becker_et_al:LIPIcs.CPM.2024.5,
  author =	{Becker, Ruben and Cenzato, Davide and Kim, Sung-Hwan and Kodric, Bojana and Maso, Riccardo and Prezza, Nicola},
  title =	{{Random Wheeler Automata}},
  booktitle =	{35th Annual Symposium on Combinatorial Pattern Matching (CPM 2024)},
  pages =	{5:1--5:15},
  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.2024.5},
  URN =		{urn:nbn:de:0030-drops-201157},
  doi =		{10.4230/LIPIcs.CPM.2024.5},
  annote =	{Keywords: Wheeler automata, Burrows-Wheeler transform, random graphs}
}
Document
DOI: 10.4230/LIPIcs.ESA.2023.15
Sorting Finite Automata via Partition Refinement

Authors: Ruben Becker, Manuel Cáceres, Davide Cenzato, Sung-Hwan Kim, Bojana Kodric, Francisco Olivares, and Nicola Prezza

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

Abstract
Wheeler nondeterministic finite automata (WNFAs) were introduced in (Gagie et al., TCS 2017) as a powerful generalization of prefix sorting from strings to labeled graphs. WNFAs admit optimal solutions to classic hard problems on labeled graphs and languages such as compression and regular expression matching. The problem of deciding whether a given NFA is Wheeler is known to be NP-complete (Gibney and Thankachan, ESA 2019). Recently, however, Alanko et al. (Information and Computation 2021) showed how to side-step this complexity by switching to preorders: letting Q be the set of states and δ the set of transitions, they provided a O(|δ|⋅|Q|²)-time algorithm computing a totally-ordered partition (i.e. equivalence relation) of the WNFA’s states such that (1) equivalent states recognize the same regular language, and (2) the order of (the classes of) non-equivalent states is consistent with any Wheeler order, when one exists. As a result, the output is a preorder of the states as useful for pattern matching as standard Wheeler orders. Further extensions of this line of work (Cotumaccio et al., SODA 2021 and DCC 2022) generalized these concepts to arbitrary NFAs by introducing co-lex partial preorders: in general, any NFA admits a partial preorder of its states reflecting the co-lexicographic order of their accepted strings; the smaller the width of such preorder is, the faster regular expression matching queries can be performed. To date, the fastest algorithm for computing the smallest-width partial preorder on NFAs runs in O(|δ|² + |Q|^{5/2}) time (Cotumaccio, DCC 2022), while on DFAs the same task can be accomplished in O(min(|Q|²log|Q|, |δ|⋅|Q|)) time (Kim et al., CPM 2023). In this paper, we provide much more efficient solutions to the co-lex order computation problem. Our results are achieved by extending a classic algorithm for the relational coarsest partition refinement problem of Paige and Tarjan to work with ordered partitions. More specifically, we provide a O(|δ|log|Q|)-time algorithm computing a co-lex total preorder when the input is a Wheeler NFA, and an algorithm with the same time complexity computing the smallest-width co-lex partial order of any DFA. In addition, we present implementations of our algorithms and show that they are very efficient also in practice.
Cite as

Ruben Becker, Manuel Cáceres, Davide Cenzato, Sung-Hwan Kim, Bojana Kodric, Francisco Olivares, and Nicola Prezza. Sorting Finite Automata via Partition Refinement. In 31st Annual European Symposium on Algorithms (ESA 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 274, pp. 15:1-15:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{becker_et_al:LIPIcs.ESA.2023.15,
  author =	{Becker, Ruben and C\'{a}ceres, Manuel and Cenzato, Davide and Kim, Sung-Hwan and Kodric, Bojana and Olivares, Francisco and Prezza, Nicola},
  title =	{{Sorting Finite Automata via Partition Refinement}},
  booktitle =	{31st Annual European Symposium on Algorithms (ESA 2023)},
  pages =	{15:1--15:15},
  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.2023.15},
  URN =		{urn:nbn:de:0030-drops-186684},
  doi =		{10.4230/LIPIcs.ESA.2023.15},
  annote =	{Keywords: Wheeler automata, prefix sorting, pattern matching, graph compression, sorting, partition refinement}
}
Document
DOI: 10.4230/LIPIcs.CPM.2022.25
A Theoretical and Experimental Analysis of BWT Variants for String Collections

Authors: Davide Cenzato and Zsuzsanna Lipták

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

Abstract
The extended Burrows-Wheeler-Transform (eBWT), introduced by Mantaci et al. [Theor. Comput. Sci., 2007], is a generalization of the Burrows-Wheeler-Transform (BWT) to multisets of strings. While the original BWT is based on the lexicographic order, the eBWT uses the omega-order, which differs from the lexicographic order in important ways. A number of tools are available that compute the BWT of string collections; however, the data structures they generate in most cases differ from the one originally defined, as well as from each other. In this paper, we review the differences between these BWT variants, both from a theoretical and from a practical point of view, comparing them on several real-life datasets with different characteristics. We find that the differences can be extensive, depending on the dataset characteristics, and are largest on collections of many highly similar short sequences. The widely-used parameter r, the number of runs of the BWT, also shows notable variation between the different BWT variants; on our datasets, it varied by a multiplicative factor of up to 4.2.
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Davide Cenzato and Zsuzsanna Lipták. A Theoretical and Experimental Analysis of BWT Variants for String Collections. In 33rd Annual Symposium on Combinatorial Pattern Matching (CPM 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 223, pp. 25:1-25:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{cenzato_et_al:LIPIcs.CPM.2022.25,
  author =	{Cenzato, Davide and Lipt\'{a}k, Zsuzsanna},
  title =	{{A Theoretical and Experimental Analysis of BWT Variants for String Collections}},
  booktitle =	{33rd Annual Symposium on Combinatorial Pattern Matching (CPM 2022)},
  pages =	{25:1--25:18},
  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.2022.25},
  URN =		{urn:nbn:de:0030-drops-161529},
  doi =		{10.4230/LIPIcs.CPM.2022.25},
  annote =	{Keywords: Burrows-Wheeler-Transform, extended BWT, string collections, repetitiveness measures, r, compression}
}
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