3 Search Results for "Punzi, Giulia"

Document
DOI: 10.4230/LIPIcs.ISAAC.2023.21
A Compact DAG for Storing and Searching Maximal Common Subsequences

Authors: Alessio Conte, Roberto Grossi, Giulia Punzi, and Takeaki Uno

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

Abstract
Maximal Common Subsequences (MCSs) between two strings X and Y are subsequences of both X and Y that are maximal under inclusion. MCSs relax and generalize the well known and widely used concept of Longest Common Subsequences (LCSs), which can be seen as MCSs of maximum length. While the number both LCSs and MCSs can be exponential in the length of the strings, LCSs have been long exploited for string and text analysis, as simple compact representations of all LCSs between two strings, built via dynamic programming or automata, have been known since the '70s. MCSs appear to have a more challenging structure: even listing them efficiently was an open problem open until recently, thus narrowing the complexity difference between the two problems, but the gap remained significant. In this paper we close the complexity gap: we show how to build DAG of polynomial size - in polynomial time - which allows for efficient operations on the set of all MCSs such as enumeration in Constant Amortized Time per solution (CAT), counting, and random access to the i-th element (i.e., rank and select operations). Other than improving known algorithmic results, this work paves the way for new sequence analysis methods based on MCSs.
Cite as

Alessio Conte, Roberto Grossi, Giulia Punzi, and Takeaki Uno. A Compact DAG for Storing and Searching Maximal Common Subsequences. In 34th International Symposium on Algorithms and Computation (ISAAC 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 283, pp. 21:1-21:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{conte_et_al:LIPIcs.ISAAC.2023.21,
  author =	{Conte, Alessio and Grossi, Roberto and Punzi, Giulia and Uno, Takeaki},
  title =	{{A Compact DAG for Storing and Searching Maximal Common Subsequences}},
  booktitle =	{34th International Symposium on Algorithms and Computation (ISAAC 2023)},
  pages =	{21:1--21:15},
  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-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2023.21},
  URN =		{urn:nbn:de:0030-drops-193231},
  doi =		{10.4230/LIPIcs.ISAAC.2023.21},
  annote =	{Keywords: Maximal common subsequence, DAG, Compact data structures, Enumeration, Constant amortized time, Random access}
}
Document
DOI: 10.4230/LIPIcs.CPM.2022.16
On Strings Having the Same Length- k Substrings

Authors: Giulia Bernardini, Alessio Conte, Esteban Gabory, Roberto Grossi, Grigorios Loukides, Solon P. Pissis, Giulia Punzi, and Michelle Sweering

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

Abstract
Let Substr_k(X) denote the set of length-k substrings of a given string X for a given integer k > 0. We study the following basic string problem, called z-Shortest 𝒮_k-Equivalent Strings: Given a set 𝒮_k of n length-k strings and an integer z > 0, list z shortest distinct strings T₁,…,T_z such that Substr_k(T_i) = 𝒮_k, for all i ∈ [1,z]. The z-Shortest 𝒮_k-Equivalent Strings problem arises naturally as an encoding problem in many real-world applications; e.g., in data privacy, in data compression, and in bioinformatics. The 1-Shortest 𝒮_k-Equivalent Strings, referred to as Shortest 𝒮_k-Equivalent String, asks for a shortest string X such that Substr_k(X) = 𝒮_k. Our main contributions are summarized below: - Given a directed graph G(V,E), the Directed Chinese Postman (DCP) problem asks for a shortest closed walk that visits every edge of G at least once. DCP can be solved in 𝒪̃(|E||V|) time using an algorithm for min-cost flow. We show, via a non-trivial reduction, that if Shortest 𝒮_k-Equivalent String over a binary alphabet has a near-linear-time solution then so does DCP. - We show that the length of a shortest string output by Shortest 𝒮_k-Equivalent String is in 𝒪(k+n²). We generalize this bound by showing that the total length of z shortest strings is in 𝒪(zk+zn²+z²n). We derive these upper bounds by showing (asymptotically tight) bounds on the total length of z shortest Eulerian walks in general directed graphs. - We present an algorithm for solving z-Shortest 𝒮_k-Equivalent Strings in 𝒪(nk+n²log²n+zn²log n+|output|) time. If z = 1, the time becomes 𝒪(nk+n²log²n) by the fact that the size of the input is Θ(nk) and the size of the output is 𝒪(k+n²).
Cite as

Giulia Bernardini, Alessio Conte, Esteban Gabory, Roberto Grossi, Grigorios Loukides, Solon P. Pissis, Giulia Punzi, and Michelle Sweering. On Strings Having the Same Length- k Substrings. In 33rd Annual Symposium on Combinatorial Pattern Matching (CPM 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 223, pp. 16:1-16:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{bernardini_et_al:LIPIcs.CPM.2022.16,
  author =	{Bernardini, Giulia and Conte, Alessio and Gabory, Esteban and Grossi, Roberto and Loukides, Grigorios and Pissis, Solon P. and Punzi, Giulia and Sweering, Michelle},
  title =	{{On Strings Having the Same Length- k Substrings}},
  booktitle =	{33rd Annual Symposium on Combinatorial Pattern Matching (CPM 2022)},
  pages =	{16:1--16:17},
  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-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.CPM.2022.16},
  URN =		{urn:nbn:de:0030-drops-161439},
  doi =		{10.4230/LIPIcs.CPM.2022.16},
  annote =	{Keywords: string algorithms, combinatorics on words, de Bruijn graph, Chinese Postman}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2020.25
Enumeration of s-d Separators in DAGs with Application to Reliability Analysis in Temporal Graphs

Authors: Alessio Conte, Pierluigi Crescenzi, Andrea Marino, and Giulia Punzi

Published in: LIPIcs, Volume 170, 45th International Symposium on Mathematical Foundations of Computer Science (MFCS 2020)

Abstract
Temporal graphs are graphs in which arcs have temporal labels, specifying at which time they can be traversed. Motivated by recent results concerning the reliability analysis of a temporal graph through the enumeration of minimal cutsets in the corresponding line graph, in this paper we attack the problem of enumerating minimal s-d separators in s-d directed acyclic graphs (in short, s-d DAGs), also known as 2-terminal DAGs or s-t digraphs. Our main result is an algorithm for enumerating all the minimal s-d separators in a DAG with O(nm) delay, where n and m are respectively the number of nodes and arcs, and the delay is the time between the output of two consecutive solutions. To this aim, we give a characterization of the minimal s-d separators in a DAG through vertex cuts of an expanded version of the DAG itself. As a consequence of our main result, we provide an algorithm for enumerating all the minimal s-d cutsets in a temporal graph with delay O(m³), where m is the number of temporal arcs.
Cite as

Alessio Conte, Pierluigi Crescenzi, Andrea Marino, and Giulia Punzi. Enumeration of s-d Separators in DAGs with Application to Reliability Analysis in Temporal Graphs. In 45th International Symposium on Mathematical Foundations of Computer Science (MFCS 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 170, pp. 25:1-25:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{conte_et_al:LIPIcs.MFCS.2020.25,
  author =	{Conte, Alessio and Crescenzi, Pierluigi and Marino, Andrea and Punzi, Giulia},
  title =	{{Enumeration of s-d Separators in DAGs with Application to Reliability Analysis in Temporal Graphs}},
  booktitle =	{45th International Symposium on Mathematical Foundations of Computer Science (MFCS 2020)},
  pages =	{25:1--25:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-159-7},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{170},
  editor =	{Esparza, Javier and Kr\'{a}l', Daniel},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2020.25},
  URN =		{urn:nbn:de:0030-drops-126932},
  doi =		{10.4230/LIPIcs.MFCS.2020.25},
  annote =	{Keywords: minimal cutset, temporal graph, minimal separator, directed acyclic graph}
}
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