14 Search Results for "Prezza, Nicola"

Document
DOI: 10.4230/LIPIcs.ISAAC.2023.22
Prefix Sorting DFAs: A Recursive Algorithm

Authors: Nicola Cotumaccio

Published in: LIPIcs, Volume 283, 34th International Symposium on Algorithms and Computation (ISAAC 2023)

Abstract
In the past thirty years, numerous algorithms for building the suffix array of a string have been proposed. In 2021, the notion of suffix array was extended from strings to DFAs, and it was shown that the resulting data structure can be built in O(m² + n^{5/2}) time, where n is the number of states and m is the number of edges [SODA 2021]. Recently, algorithms running in O(mn) and O(n²log n) time have been described [CPM 2023]. In this paper, we improve the previous bounds by proposing an O(n²) recursive algorithm inspired by Farach’s algorithm for building a suffix tree [FOCS 1997]. To this end, we provide insight into the rich lexicographic and combinatorial structure of a graph, so contributing to the fascinating journey which might lead to solve the long-standing open problem of building the suffix tree of a graph.
Cite as

Nicola Cotumaccio. Prefix Sorting DFAs: A Recursive Algorithm. In 34th International Symposium on Algorithms and Computation (ISAAC 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 283, pp. 22:1-22:15, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2023)

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@InProceedings{cotumaccio:LIPIcs.ISAAC.2023.22,
  author =	{Cotumaccio, Nicola},
  title =	{{Prefix Sorting DFAs: A Recursive Algorithm}},
  booktitle =	{34th International Symposium on Algorithms and Computation (ISAAC 2023)},
  pages =	{22:1--22:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-289-1},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{283},
  editor =	{Iwata, Satoru and Kakimura, Naonori},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2023.22},
  URN =		{urn:nbn:de:0030-drops-193242},
  doi =		{10.4230/LIPIcs.ISAAC.2023.22},
  annote =	{Keywords: Suffix Array, Burrows-Wheeler Transform, FM-index, Recursive Algorithms, Graph Theory, Pattern Matching}
}
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.SEA.2023.7
Simple Runs-Bounded FM-Index Designs Are Fast

Authors: Diego Díaz-Domínguez, Saska Dönges, Simon J. Puglisi, and Leena Salmela

Published in: LIPIcs, Volume 265, 21st International Symposium on Experimental Algorithms (SEA 2023)

Abstract
Given a string X of length n on alphabet σ, the FM-index data structure allows counting all occurrences of a pattern P of length m in O(m) time via an algorithm called backward search. An important difficulty when searching with an FM-index is to support queries on L, the Burrows-Wheeler transform of X, while L is in compressed form. This problem has been the subject of intense research for 25 years now. Run-length encoding of L is an effective way to reduce index size, in particular when the data being indexed is highly-repetitive, which is the case in many types of modern data, including those arising from versioned document collections and in pangenomics. This paper takes a back-to-basics look at supporting backward search in FM-indexes, exploring and engineering two simple designs. The first divides the BWT string into blocks containing b symbols each and then run-length compresses each block separately, possibly introducing new runs (compared to applying run-length encoding once, to the whole string). Each block stores counts of each symbol that occurs before the block. This method supports the operation rank_c(L, i) (i.e., count the number of times c occurs in the prefix L[1..i]) by first determining the block i/b in which i falls and scanning the block to the appropriate position counting occurrences of c along the way. This partial answer to rank_c(L, i) is then added to the stored count of c symbols before the block to determine the final answer. Our second design has a similar structure, but instead divides the run-length-encoded version of L into blocks containing an equal number of runs. The trick then is to determine the block in which a query falls, which is achieved via a predecessor query over the block starting positions. We show via extensive experiments on a wide range of repetitive text collections that these FM-indexes are not only easy to implement, but also fast and space efficient in practice.
Cite as

Diego Díaz-Domínguez, Saska Dönges, Simon J. Puglisi, and Leena Salmela. Simple Runs-Bounded FM-Index Designs Are Fast. In 21st International Symposium on Experimental Algorithms (SEA 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 265, pp. 7:1-7:16, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2023)

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@InProceedings{diazdominguez_et_al:LIPIcs.SEA.2023.7,
  author =	{D{\'\i}az-Dom{\'\i}nguez, Diego and D\"{o}nges, Saska and Puglisi, Simon J. and Salmela, Leena},
  title =	{{Simple Runs-Bounded FM-Index Designs Are Fast}},
  booktitle =	{21st International Symposium on Experimental Algorithms (SEA 2023)},
  pages =	{7:1--7:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-279-2},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{265},
  editor =	{Georgiadis, Loukas},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SEA.2023.7},
  URN =		{urn:nbn:de:0030-drops-183579},
  doi =		{10.4230/LIPIcs.SEA.2023.7},
  annote =	{Keywords: data structures, efficient algorithms}
}
Document
DOI: 10.4230/LIPIcs.CPM.2023.16
Faster Prefix-Sorting Algorithms for Deterministic Finite Automata

Authors: Sung-Hwan Kim, Francisco Olivares, and Nicola Prezza

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

Abstract
Sorting is a fundamental algorithmic pre-processing technique which often allows to represent data more compactly and, at the same time, speeds up search queries on it. In this paper, we focus on the well-studied problem of sorting and indexing string sets. Since the introduction of suffix trees in 1973, dozens of suffix sorting algorithms have been described in the literature. In 2017, these techniques were extended to sets of strings described by means of finite automata: the theory of Wheeler graphs [Gagie et al., TCS'17] introduced automata whose states can be totally-sorted according to the co-lexicographic (co-lex in the following) order of the prefixes of words accepted by the automaton. More recently, in [Cotumaccio, Prezza, SODA'21] it was shown how to extend these ideas to arbitrary automata by means of partial co-lex orders. This work showed that a co-lex order of minimum width (thus optimizing search query times) on deterministic finite automata (DFAs) can be computed in O(m² + n^{5/2}) time, m being the number of transitions and n the number of states of the input DFA. In this paper, we exhibit new combinatorial properties of the minimum-width co-lex order of DFAs and exploit them to design faster prefix sorting algorithms. In particular, we describe two algorithms sorting arbitrary DFAs in O(mn) and O(n² log n) time, respectively, and an algorithm sorting acyclic DFAs in O(m log n) time. Within these running times, all algorithms compute also a smallest chain partition of the partial order (required to index the DFA). We present an experiment result to show that an optimized implementation of the O(n² log n)-time algorithm exhibits a nearly-linear behaviour on large deterministic pan-genomic graphs and is thus also of practical interest.
Cite as

Sung-Hwan Kim, Francisco Olivares, and Nicola Prezza. Faster Prefix-Sorting Algorithms for Deterministic Finite Automata. In 34th Annual Symposium on Combinatorial Pattern Matching (CPM 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 259, pp. 16:1-16:16, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2023)

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@InProceedings{kim_et_al:LIPIcs.CPM.2023.16,
  author =	{Kim, Sung-Hwan and Olivares, Francisco and Prezza, Nicola},
  title =	{{Faster Prefix-Sorting Algorithms for Deterministic Finite Automata}},
  booktitle =	{34th Annual Symposium on Combinatorial Pattern Matching (CPM 2023)},
  pages =	{16:1--16:16},
  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.2023.16},
  URN =		{urn:nbn:de:0030-drops-179707},
  doi =		{10.4230/LIPIcs.CPM.2023.16},
  annote =	{Keywords: String Matching, Deterministic Finite Automata, Graph Indexing, Co-lexicographical Sorting}
}
Document
DOI: 10.4230/LIPIcs.WABI.2021.13
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
DOI: 10.4230/LIPIcs.CPM.2021.16
Compressed Weighted de Bruijn Graphs

Authors: Giuseppe F. Italiano, Nicola Prezza, Blerina Sinaimeri, and Rossano Venturini

Published in: LIPIcs, Volume 191, 32nd Annual Symposium on Combinatorial Pattern Matching (CPM 2021)

Abstract
We propose a new compressed representation for weighted de Bruijn graphs, which is based on the idea of delta-encoding the variations of k-mer abundances on a spanning branching of the graph. Our new data structure is likely to be of practical value: to give an idea, when combined with the compressed BOSS de Bruijn graph representation, it encodes the weighted de Bruijn graph of a 16x-covered DNA read-set (60M distinct k-mers, k = 28) within 4.15 bits per distinct k-mer and can answer abundance queries in about 60 microseconds on a standard machine. In contrast, state of the art tools declare a space usage of at least 30 bits per distinct k-mer for the same task, which is confirmed by our experiments. As a by-product of our new data structure, we exhibit efficient compressed data structures for answering partial sums on edge-weighted trees, which might be of independent interest.
Cite as

Giuseppe F. Italiano, Nicola Prezza, Blerina Sinaimeri, and Rossano Venturini. Compressed Weighted de Bruijn Graphs. In 32nd Annual Symposium on Combinatorial Pattern Matching (CPM 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 191, pp. 16:1-16:16, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2021)

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@InProceedings{italiano_et_al:LIPIcs.CPM.2021.16,
  author =	{Italiano, Giuseppe F. and Prezza, Nicola and Sinaimeri, Blerina and Venturini, Rossano},
  title =	{{Compressed Weighted de Bruijn Graphs}},
  booktitle =	{32nd Annual Symposium on Combinatorial Pattern Matching (CPM 2021)},
  pages =	{16:1--16:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-186-3},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{191},
  editor =	{Gawrychowski, Pawe{\l} and Starikovskaya, Tatiana},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CPM.2021.16},
  URN =		{urn:nbn:de:0030-drops-139675},
  doi =		{10.4230/LIPIcs.CPM.2021.16},
  annote =	{Keywords: weighted de Bruijn graphs, k-mer annotation, compressed data structures, partial sums}
}
Document
Invited Talk
DOI: 10.4230/LIPIcs.SEA.2020.3
Indexing Compressed Text: A Tale of Time and Space (Invited Talk)

Authors: Nicola Prezza

Published in: LIPIcs, Volume 160, 18th International Symposium on Experimental Algorithms (SEA 2020)

Abstract
Text indexing is a classical algorithmic problem that has been studied for over four decades. The earliest optimal-time solution to the problem, the suffix tree [Weiner, 1973], dates back to 1973 and requires up to two orders of magnitude more space than the text to be stored. In the year 2000, two breakthrough works [Grossi and Vitter, 2000; Ferragina and Manzini, 2000] showed that this space overhead is not necessary: both the index and the text can be stored in a space proportional to the text’s entropy. These contributions had an enormous impact in bioinformatics: nowadays, the two most widely-used DNA aligners employ compressed indexes [Li and Durbin, 2009; Langmead et al., 2009]. In recent years, it became apparent that entropy had reached its limits: modern datasets (for example, collections of thousands of human genomes) are extremely large but very repetitive and, by its very definition, entropy cannot compress repetitive texts [S. Kreft and G. Navarro, 2013]. To overcome this problem, a new generation of indexes based on dictionary compressors (for example, LZ77 and run-length BWT) emerged [S. Kreft and G. Navarro, 2013; Gagie et al., 2020; F. Claude and G. Navarro, 2012], together with generalizations of the indexing problem to labeled graphs [Ferragina et al., 2009; Sirén et al., 2014; Travis Gagie et al., 2017]. This talk is a short and friendly survey of the landmarks of this fascinating path that took us from suffix trees to the most modern compressed indexes on labeled graphs.
Cite as

Nicola Prezza. Indexing Compressed Text: A Tale of Time and Space (Invited Talk). In 18th International Symposium on Experimental Algorithms (SEA 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 160, pp. 3:1-3:2, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2020)

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@InProceedings{prezza:LIPIcs.SEA.2020.3,
  author =	{Prezza, Nicola},
  title =	{{Indexing Compressed Text: A Tale of Time and Space}},
  booktitle =	{18th International Symposium on Experimental Algorithms (SEA 2020)},
  pages =	{3:1--3:2},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-148-1},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{160},
  editor =	{Faro, Simone and Cantone, Domenico},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SEA.2020.3},
  URN =		{urn:nbn:de:0030-drops-120772},
  doi =		{10.4230/LIPIcs.SEA.2020.3},
  annote =	{Keywords: Compressed Text Indexing}
}
Document
DOI: 10.4230/LIPIcs.CPM.2020.27
On Extensions of Maximal Repeats in Compressed Strings

Authors: Julian Pape-Lange

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

Abstract
This paper provides upper bounds for several subsets of maximal repeats and maximal pairs in compressed strings and also presents a formerly unknown relationship between maximal pairs and the run-length Burrows-Wheeler transform. This relationship is used to obtain a different proof for the Burrows-Wheeler conjecture which has recently been proven by Kempa and Kociumaka in "Resolution of the Burrows-Wheeler Transform Conjecture". More formally, this paper proves that the run-length Burrows-Wheeler transform of a string S with z_S LZ77-factors has at most 73(log₂ |S|)(z_S+2)² runs, and if S does not contain q-th powers, the number of arcs in the compacted directed acyclic word graph of S is bounded from above by 18q(1+log_q |S|)(z_S+2)².
Cite as

Julian Pape-Lange. On Extensions of Maximal Repeats in Compressed Strings. In 31st Annual Symposium on Combinatorial Pattern Matching (CPM 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 161, pp. 27:1-27:13, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2020)

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@InProceedings{papelange:LIPIcs.CPM.2020.27,
  author =	{Pape-Lange, Julian},
  title =	{{On Extensions of Maximal Repeats in Compressed Strings}},
  booktitle =	{31st Annual Symposium on Combinatorial Pattern Matching (CPM 2020)},
  pages =	{27:1--27:13},
  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.2020.27},
  URN =		{urn:nbn:de:0030-drops-121523},
  doi =		{10.4230/LIPIcs.CPM.2020.27},
  annote =	{Keywords: Maximal repeats, Extensions of maximal repeats, Combinatorics on compressed strings, LZ77, Burrows-Wheeler transform, Burrows-Wheeler transform conjecture, Compact suffix automata, CDAWGs}
}
Document
DOI: 10.4230/LIPIcs.CPM.2019.4
Optimal Rank and Select Queries on Dictionary-Compressed Text

Authors: Nicola Prezza

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

Abstract
We study the problem of supporting queries on a string S of length n within a space bounded by the size gamma of a string attractor for S. In the paper introducing string attractors it was shown that random access on S can be supported in optimal O(log(n/gamma)/log log n) time within O(gamma polylog n) space. In this paper, we extend this result to rank and select queries and provide lower bounds matching our upper bounds on alphabets of polylogarithmic size. Our solutions are given in the form of a space-time trade-off that is more general than the one previously known for grammars and that improves existing bounds on LZ77-compressed text by a log log n time-factor in select queries. We also provide matching lower and upper bounds for partial sum and predecessor queries within attractor-bounded space, and extend our lower bounds to encompass navigation of dictionary-compressed tree representations.
Cite as

Nicola Prezza. Optimal Rank and Select Queries on Dictionary-Compressed Text. In 30th Annual Symposium on Combinatorial Pattern Matching (CPM 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 128, pp. 4:1-4:12, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2019)

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@InProceedings{prezza:LIPIcs.CPM.2019.4,
  author =	{Prezza, Nicola},
  title =	{{Optimal Rank and Select Queries on Dictionary-Compressed Text}},
  booktitle =	{30th Annual Symposium on Combinatorial Pattern Matching (CPM 2019)},
  pages =	{4:1--4:12},
  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.2019.4},
  URN =		{urn:nbn:de:0030-drops-104756},
  doi =		{10.4230/LIPIcs.CPM.2019.4},
  annote =	{Keywords: Rank, Select, Dictionary compression, String Attractors}
}
Document
DOI: 10.4230/LIPIcs.CPM.2019.7
Space-Efficient Computation of the LCP Array from the Burrows-Wheeler Transform

Authors: Nicola Prezza and Giovanna Rosone

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

Abstract
We show that the Longest Common Prefix Array of a text collection of total size n on alphabet [1,sigma] can be computed from the Burrows-Wheeler transformed collection in O(n log sigma) time using o(n log sigma) bits of working space on top of the input and output. Our result improves (on small alphabets) and generalizes (to string collections) the previous solution from Beller et al., which required O(n) bits of extra working space. We also show how to merge the BWTs of two collections of total size n within the same time and space bounds. The procedure at the core of our algorithms can be used to enumerate suffix tree intervals in succinct space from the BWT, which is of independent interest. An engineered implementation of our first algorithm on DNA alphabet induces the LCP of a large (16 GiB) collection of short (100 bases) reads at a rate of 2.92 megabases per second using in total 1.5 Bytes per base in RAM. Our second algorithm merges the BWTs of two short-reads collections of 8 GiB each at a rate of 1.7 megabases per second and uses 0.625 Bytes per base in RAM. An extension of this algorithm that computes also the LCP array of the merged collection processes the data at a rate of 1.48 megabases per second and uses 1.625 Bytes per base in RAM.
Cite as

Nicola Prezza and Giovanna Rosone. Space-Efficient Computation of the LCP Array from the Burrows-Wheeler Transform. In 30th Annual Symposium on Combinatorial Pattern Matching (CPM 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 128, pp. 7:1-7:18, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2019)

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@InProceedings{prezza_et_al:LIPIcs.CPM.2019.7,
  author =	{Prezza, Nicola and Rosone, Giovanna},
  title =	{{Space-Efficient Computation of the LCP Array from the Burrows-Wheeler Transform}},
  booktitle =	{30th Annual Symposium on Combinatorial Pattern Matching (CPM 2019)},
  pages =	{7:1--7:18},
  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.2019.7},
  URN =		{urn:nbn:de:0030-drops-104782},
  doi =		{10.4230/LIPIcs.CPM.2019.7},
  annote =	{Keywords: Burrows-Wheeler Transform, LCP array, DNA reads}
}
Document
DOI: 10.4230/LIPIcs.ESA.2018.52
String Attractors: Verification and Optimization

Authors: Dominik Kempa, Alberto Policriti, Nicola Prezza, and Eva Rotenberg

Published in: LIPIcs, Volume 112, 26th Annual European Symposium on Algorithms (ESA 2018)

Abstract
String attractors [STOC 2018] are combinatorial objects recently introduced to unify all known dictionary compression techniques in a single theory. A set Gamma subseteq [1..n] is a k-attractor for a string S in Sigma^n if and only if every distinct substring of S of length at most k has an occurrence crossing at least one of the positions in Gamma. Finding the smallest k-attractor is NP-hard for k >= 3, but polylogarithmic approximations can be found using reductions from dictionary compressors. It is easy to reduce the k-attractor problem to a set-cover instance where the string's positions are interpreted as sets of substrings. The main result of this paper is a much more powerful reduction based on the truncated suffix tree. Our new characterization of the problem leads to more efficient algorithms for string attractors: we show how to check the validity and minimality of a k-attractor in near-optimal time and how to quickly compute exact solutions. For example, we prove that a minimum 3-attractor can be found in O(n) time when |Sigma| in O(sqrt[3+epsilon]{log n}) for some constant epsilon > 0, despite the problem being NP-hard for large Sigma.
Cite as

Dominik Kempa, Alberto Policriti, Nicola Prezza, and Eva Rotenberg. String Attractors: Verification and Optimization. In 26th Annual European Symposium on Algorithms (ESA 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 112, pp. 52:1-52:13, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2018)

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@InProceedings{kempa_et_al:LIPIcs.ESA.2018.52,
  author =	{Kempa, Dominik and Policriti, Alberto and Prezza, Nicola and Rotenberg, Eva},
  title =	{{String Attractors: Verification and Optimization}},
  booktitle =	{26th Annual European Symposium on Algorithms (ESA 2018)},
  pages =	{52:1--52:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-081-1},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{112},
  editor =	{Azar, Yossi and Bast, Hannah 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.2018.52},
  URN =		{urn:nbn:de:0030-drops-95153},
  doi =		{10.4230/LIPIcs.ESA.2018.52},
  annote =	{Keywords: Dictionary compression, String attractors, Set cover}
}
Document
DOI: 10.4230/LIPIcs.WABI.2018.3
Detecting Mutations by eBWT

Authors: Nicola Prezza, Nadia Pisanti, Marinella Sciortino, and Giovanna Rosone

Published in: LIPIcs, Volume 113, 18th International Workshop on Algorithms in Bioinformatics (WABI 2018)

Abstract
In this paper we develop a theory describing how the extended Burrows-Wheeler Transform (eBWT) of a collection of DNA fragments tends to cluster together the copies of nucleotides sequenced from a genome G. Our theory accurately predicts how many copies of any nucleotide are expected inside each such cluster, and how an elegant and precise LCP array based procedure can locate these clusters in the eBWT. Our findings are very general and can be applied to a wide range of different problems. In this paper, we consider the case of alignment-free and reference-free SNPs discovery in multiple collections of reads. We note that, in accordance with our theoretical results, SNPs are clustered in the eBWT of the reads collection, and we develop a tool finding SNPs with a simple scan of the eBWT and LCP arrays. Preliminary results show that our method requires much less coverage than state-of-the-art tools while drastically improving precision and sensitivity.
Cite as

Nicola Prezza, Nadia Pisanti, Marinella Sciortino, and Giovanna Rosone. Detecting Mutations by eBWT. In 18th International Workshop on Algorithms in Bioinformatics (WABI 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 113, pp. 3:1-3:15, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2018)

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@InProceedings{prezza_et_al:LIPIcs.WABI.2018.3,
  author =	{Prezza, Nicola and Pisanti, Nadia and Sciortino, Marinella and Rosone, Giovanna},
  title =	{{Detecting Mutations by eBWT}},
  booktitle =	{18th International Workshop on Algorithms in Bioinformatics (WABI 2018)},
  pages =	{3:1--3:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-082-8},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{113},
  editor =	{Parida, Laxmi and Ukkonen, Esko},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.WABI.2018.3},
  URN =		{urn:nbn:de:0030-drops-93051},
  doi =		{10.4230/LIPIcs.WABI.2018.3},
  annote =	{Keywords: BWT, LCP Array, SNPs, Reference-free, Assembly-free}
}
Document
DOI: 10.4230/LIPIcs.SEA.2017.11
A Framework of Dynamic Data Structures for String Processing

Authors: Nicola Prezza

Published in: LIPIcs, Volume 75, 16th International Symposium on Experimental Algorithms (SEA 2017)

Abstract
In this paper we present DYNAMIC, an open-source C++ library implementing dynamic compressed data structures for string manipulation. Our framework includes useful tools such as searchable partial sums, succinct/gap-encoded bitvectors, and entropy/run-length compressed strings and FM indexes. We prove close-to-optimal theoretical bounds for the resources used by our structures, and show that our theoretical predictions are empirically tightly verified in practice. To conclude, we turn our attention to applications. We compare the performance of five recently-published compression algorithms implemented using DYNAMIC with those of state-of-the-art tools performing the same task. Our experiments show that algorithms making use of dynamic compressed data structures can be up to three orders of magnitude more space-efficient (albeit slower) than classical ones performing the same tasks.
Cite as

Nicola Prezza. A Framework of Dynamic Data Structures for String Processing. In 16th International Symposium on Experimental Algorithms (SEA 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 75, pp. 11:1-11:15, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2017)

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@InProceedings{prezza:LIPIcs.SEA.2017.11,
  author =	{Prezza, Nicola},
  title =	{{A Framework of Dynamic Data Structures for String Processing}},
  booktitle =	{16th International Symposium on Experimental Algorithms (SEA 2017)},
  pages =	{11:1--11:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-036-1},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{75},
  editor =	{Iliopoulos, Costas S. and Pissis, Solon P. and Puglisi, Simon J. and Raman, Rajeev},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SEA.2017.11},
  URN =		{urn:nbn:de:0030-drops-76028},
  doi =		{10.4230/LIPIcs.SEA.2017.11},
  annote =	{Keywords: C++, dynamic, compression, data structure, bitvector, string}
}
Document
DOI: 10.4230/LIPIcs.CPM.2017.17
From LZ77 to the Run-Length Encoded Burrows-Wheeler Transform, and Back

Authors: Alberto Policriti and Nicola Prezza

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

Abstract
The Lempel-Ziv factorization (LZ77) and the Run-Length encoded Burrows-Wheeler Transform (RLBWT) are two important tools in text compression and indexing, being their sizes z and r closely related to the amount of text self-repetitiveness. In this paper we consider the problem of converting the two representations into each other within a working space proportional to the input and the output. Let n be the text length. We show that RLBWT can be converted to LZ77 in O(n log r) time and O(r) words of working space. Conversely, we provide an algorithm to convert LZ77 to RLBWT in O(n(log r + log z)) time and O(r+z) words of working space. Note that r and z can be constant if the text is highly repetitive, and our algorithms can operate with (up to) exponentially less space than naive solutions based on full decompression.
Cite as

Alberto Policriti and Nicola Prezza. From LZ77 to the Run-Length Encoded Burrows-Wheeler Transform, and Back. In 28th Annual Symposium on Combinatorial Pattern Matching (CPM 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 78, pp. 17:1-17:10, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2017)

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@InProceedings{policriti_et_al:LIPIcs.CPM.2017.17,
  author =	{Policriti, Alberto and Prezza, Nicola},
  title =	{{From LZ77 to the Run-Length Encoded Burrows-Wheeler Transform, and Back}},
  booktitle =	{28th Annual Symposium on Combinatorial Pattern Matching (CPM 2017)},
  pages =	{17:1--17:10},
  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.2017.17},
  URN =		{urn:nbn:de:0030-drops-73215},
  doi =		{10.4230/LIPIcs.CPM.2017.17},
  annote =	{Keywords: Lempel-Ziv, Burrows-Wheeler transform, compressed computation, repetitive text collections}
}
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