2 Search Results for "Safe, Martín D."

Document
DOI: 10.4230/LIPIcs.ICDT.2022.11
Practical Relational Calculus Query Evaluation

Authors: Martin Raszyk, David Basin, Srđan Krstić, and Dmitriy Traytel

Published in: LIPIcs, Volume 220, 25th International Conference on Database Theory (ICDT 2022)

Abstract
The relational calculus (RC) is a concise, declarative query language. However, existing RC query evaluation approaches are inefficient and often deviate from established algorithms based on finite tables used in database management systems. We devise a new translation of an arbitrary RC query into two safe-range queries, for which the finiteness of the query’s evaluation result is guaranteed. Assuming an infinite domain, the two queries have the following meaning: The first is closed and characterizes the original query’s relative safety, i.e., whether given a fixed database, the original query evaluates to a finite relation. The second safe-range query is equivalent to the original query, if the latter is relatively safe. We compose our translation with other, more standard ones to ultimately obtain two SQL queries. This allows us to use standard database management systems to evaluate arbitrary RC queries. We show that our translation improves the time complexity over existing approaches, which we also empirically confirm in both realistic and synthetic experiments.
Cite as

Martin Raszyk, David Basin, Srđan Krstić, and Dmitriy Traytel. Practical Relational Calculus Query Evaluation. In 25th International Conference on Database Theory (ICDT 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 220, pp. 11:1-11:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{raszyk_et_al:LIPIcs.ICDT.2022.11,
  author =	{Raszyk, Martin and Basin, David and Krsti\'{c}, Sr{\d}an and Traytel, Dmitriy},
  title =	{{Practical Relational Calculus Query Evaluation}},
  booktitle =	{25th International Conference on Database Theory (ICDT 2022)},
  pages =	{11:1--11:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-223-5},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{220},
  editor =	{Olteanu, Dan and Vortmeier, Nils},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICDT.2022.11},
  URN =		{urn:nbn:de:0030-drops-158857},
  doi =		{10.4230/LIPIcs.ICDT.2022.11},
  annote =	{Keywords: Relational calculus, relative safety, safe-range, query translation}
}
Document
DOI: 10.4230/LIPIcs.AofA.2020.4
Two Arithmetical Sources and Their Associated Tries

Authors: Valérie Berthé, Eda Cesaratto, Frédéric Paccaut, Pablo Rotondo, Martín D. Safe, and Brigitte Vallée

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

Abstract
This article is devoted to the study of two arithmetical sources associated with classical partitions, that are both defined through the mediant of two fractions. The Stern-Brocot source is associated with the sequence of all the mediants, while the Sturm source only keeps mediants whose denominator is "not too large". Even though these sources are both of zero Shannon entropy, with very similar Renyi entropies, their probabilistic features yet appear to be quite different. We then study how they influence the behaviour of tries built on words they emit, and we notably focus on the trie depth. The paper deals with Analytic Combinatorics methods, and Dirichlet generating functions, that are usually used and studied in the case of good sources with positive entropy. To the best of our knowledge, the present study is the first one where these powerful methods are applied to a zero-entropy context. In our context, the generating function associated with each source is explicit and related to classical functions in Number Theory, as the ζ function, the double ζ function or the transfer operator associated with the Gauss map. We obtain precise asymptotic estimates for the mean value of the trie depth that prove moreover to be quite different for each source. Then, these sources provide explicit and natural instances which lead to two unusual and different trie behaviours.
Cite as

Valérie Berthé, Eda Cesaratto, Frédéric Paccaut, Pablo Rotondo, Martín D. Safe, and Brigitte Vallée. Two Arithmetical Sources and Their Associated Tries. 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. 4:1-4:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{berthe_et_al:LIPIcs.AofA.2020.4,
  author =	{Berth\'{e}, Val\'{e}rie and Cesaratto, Eda and Paccaut, Fr\'{e}d\'{e}ric and Rotondo, Pablo and Safe, Mart{\'\i}n D. and Vall\'{e}e, Brigitte},
  title =	{{Two Arithmetical Sources and Their Associated Tries}},
  booktitle =	{31st International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2020)},
  pages =	{4:1--4:19},
  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-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.AofA.2020.4},
  URN =		{urn:nbn:de:0030-drops-120345},
  doi =		{10.4230/LIPIcs.AofA.2020.4},
  annote =	{Keywords: Combinatorics of words, Information Theory, Probabilistic analysis, Analytic combinatorics, Dirichlet generating functions, Sources, Partitions, Trie structure, Continued fraction expansion, Farey map, Sturm words, Transfer operator}
}
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