4 Search Results for "Bassino, Frédérique"


Document
Binary Search Trees of Permuton Samples

Authors: Benoît Corsini, Victor Dubach, and Valentin Féray

Published in: LIPIcs, Volume 302, 35th International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2024)


Abstract
Binary search trees (BST) are a popular type of structure when dealing with ordered data. They allow efficient access and modification of data, with their height corresponding to the worst retrieval time. From a probabilistic point of view, BSTs associated with data arriving in a uniform random order are well understood, but less is known when the input is a non-uniform permutation. We consider here the case where the input comes from i.i.d. random points in the plane with law μ, a model which we refer to as a permuton sample. Our results show that the asymptotic proportion of nodes in each subtree only depends on the behavior of the measure μ at its left boundary, while the height of the BST has a universal asymptotic behavior for a large family of measures μ. Our approach involves a mix of combinatorial and probabilistic tools, namely combinatorial properties of binary search trees, coupling arguments, and deviation estimates.

Cite as

Benoît Corsini, Victor Dubach, and Valentin Féray. Binary Search Trees of Permuton Samples. In 35th International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 302, pp. 21:1-21:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)


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@InProceedings{corsini_et_al:LIPIcs.AofA.2024.21,
  author =	{Corsini, Beno\^{i}t and Dubach, Victor and F\'{e}ray, Valentin},
  title =	{{Binary Search Trees of Permuton Samples}},
  booktitle =	{35th International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2024)},
  pages =	{21:1--21:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-329-4},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{302},
  editor =	{Mailler, C\'{e}cile and Wild, Sebastian},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.AofA.2024.21},
  URN =		{urn:nbn:de:0030-drops-204562},
  doi =		{10.4230/LIPIcs.AofA.2024.21},
  annote =	{Keywords: Binary search trees, random permutations, permutons}
}
Document
The Complexity of the Approximate Multiple Pattern Matching Problem for Random Strings

Authors: Frédérique Bassino, Tsinjo Rakotoarimalala, and Andrea Sportiello

Published in: LIPIcs, Volume 159, 31st International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2020)


Abstract
We describe a multiple string pattern matching algorithm which is well-suited for approximate search and dictionaries composed of words of different lengths. We prove that this algorithm has optimal complexity rate up to a multiplicative constant, for arbitrary dictionaries. This extends to arbitrary dictionaries the classical results of Yao [SIAM J. Comput. 8, 1979], and Chang and Marr [Proc. CPM94, 1994].

Cite as

Frédérique Bassino, Tsinjo Rakotoarimalala, and Andrea Sportiello. The Complexity of the Approximate Multiple Pattern Matching Problem for Random Strings. In 31st International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 159, pp. 3:1-3:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)


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@InProceedings{bassino_et_al:LIPIcs.AofA.2020.3,
  author =	{Bassino, Fr\'{e}d\'{e}rique and Rakotoarimalala, Tsinjo and Sportiello, Andrea},
  title =	{{The Complexity of the Approximate Multiple Pattern Matching Problem for Random Strings}},
  booktitle =	{31st International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2020)},
  pages =	{3:1--3:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-147-4},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{159},
  editor =	{Drmota, Michael and Heuberger, Clemens},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.AofA.2020.3},
  URN =		{urn:nbn:de:0030-drops-120336},
  doi =		{10.4230/LIPIcs.AofA.2020.3},
  annote =	{Keywords: Average-case analysis of algorithms, String Pattern Matching, Computational Complexity bounds}
}
Document
Asymptotic enumeration of Minimal Automata

Authors: Frédérique Bassino, Julien David, and Andrea Sportiello

Published in: LIPIcs, Volume 14, 29th International Symposium on Theoretical Aspects of Computer Science (STACS 2012)


Abstract
We determine the asymptotic proportion of minimal automata, within n-state accessible deterministic complete automata over a k-letter alphabet, with the uniform distribution over the possible transition structures, and a binomial distribution over terminal states, with arbitrary parameter b. It turns out that a fraction ~ 1-C(k,b) n^{-k+2} of automata is minimal, with C(k,b) a function, explicitly determined, involving the solution of a transcendental equation.

Cite as

Frédérique Bassino, Julien David, and Andrea Sportiello. Asymptotic enumeration of Minimal Automata. In 29th International Symposium on Theoretical Aspects of Computer Science (STACS 2012). Leibniz International Proceedings in Informatics (LIPIcs), Volume 14, pp. 88-99, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2012)


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@InProceedings{bassino_et_al:LIPIcs.STACS.2012.88,
  author =	{Bassino, Fr\'{e}d\'{e}rique and David, Julien and Sportiello, Andrea},
  title =	{{Asymptotic enumeration of Minimal Automata}},
  booktitle =	{29th International Symposium on Theoretical Aspects of Computer Science (STACS 2012)},
  pages =	{88--99},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-35-4},
  ISSN =	{1868-8969},
  year =	{2012},
  volume =	{14},
  editor =	{D\"{u}rr, Christoph and Wilke, Thomas},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2012.88},
  URN =		{urn:nbn:de:0030-drops-34328},
  doi =		{10.4230/LIPIcs.STACS.2012.88},
  annote =	{Keywords: minimal automata, regular languages, enumeration of random structures}
}
Document
On the Average Complexity of Moore's State Minimization Algorithm

Authors: Frederique Bassino, Julien David, and Cyril Nicaud

Published in: LIPIcs, Volume 3, 26th International Symposium on Theoretical Aspects of Computer Science (2009)


Abstract
We prove that, for any arbitrary finite alphabet and for the uniform distribution over deterministic and accessible automata with $n$ states, the average complexity of Moore's state minimization algorithm is in $\mathcal{O}(n \log n)$. Moreover this bound is tight in the case of unary automata.

Cite as

Frederique Bassino, Julien David, and Cyril Nicaud. On the Average Complexity of Moore's State Minimization Algorithm. In 26th International Symposium on Theoretical Aspects of Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 3, pp. 123-134, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2009)


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@InProceedings{bassino_et_al:LIPIcs.STACS.2009.1822,
  author =	{Bassino, Frederique and David, Julien and Nicaud, Cyril},
  title =	{{On the Average Complexity of Moore's State Minimization Algorithm}},
  booktitle =	{26th International Symposium on Theoretical Aspects of Computer Science},
  pages =	{123--134},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-09-5},
  ISSN =	{1868-8969},
  year =	{2009},
  volume =	{3},
  editor =	{Albers, Susanne and Marion, Jean-Yves},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2009.1822},
  URN =		{urn:nbn:de:0030-drops-18222},
  doi =		{10.4230/LIPIcs.STACS.2009.1822},
  annote =	{Keywords: Finite automata, State minimization, Moore’s algorithm, Average complexity}
}
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