3 Search Results for "Ricci, Marco"

Document
DOI: 10.4230/LIPIcs.SoCG.2023.31
Linear Size Universal Point Sets for Classes of Planar Graphs

Authors: Stefan Felsner, Hendrik Schrezenmaier, Felix Schröder, and Raphael Steiner

Published in: LIPIcs, Volume 258, 39th International Symposium on Computational Geometry (SoCG 2023)

Abstract
A finite set P of points in the plane is n-universal with respect to a class 𝒞 of planar graphs if every n-vertex graph in 𝒞 admits a crossing-free straight-line drawing with vertices at points of P. For the class of all planar graphs the best known upper bound on the size of a universal point set is quadratic and the best known lower bound is linear in n. Some classes of planar graphs are known to admit universal point sets of near linear size, however, there are no truly linear bounds for interesting classes beyond outerplanar graphs. In this paper, we show that there is a universal point set of size 2n-2 for the class of bipartite planar graphs with n vertices. The same point set is also universal for the class of n-vertex planar graphs of maximum degree 3. The point set used for the results is what we call an exploding double chain, and we prove that this point set allows planar straight-line embeddings of many more planar graphs, namely of all subgraphs of planar graphs admitting a one-sided Hamiltonian cycle. The result for bipartite graphs also implies that every n-vertex plane graph has a 1-bend drawing all whose bends and vertices are contained in a specific point set of size 4n-6, this improves a bound of 6n-10 for the same problem by Löffler and Tóth.
Cite as

Stefan Felsner, Hendrik Schrezenmaier, Felix Schröder, and Raphael Steiner. Linear Size Universal Point Sets for Classes of Planar Graphs. In 39th International Symposium on Computational Geometry (SoCG 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 258, pp. 31:1-31:16, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2023)

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@InProceedings{felsner_et_al:LIPIcs.SoCG.2023.31,
  author =	{Felsner, Stefan and Schrezenmaier, Hendrik and Schr\"{o}der, Felix and Steiner, Raphael},
  title =	{{Linear Size Universal Point Sets for Classes of Planar Graphs}},
  booktitle =	{39th International Symposium on Computational Geometry (SoCG 2023)},
  pages =	{31:1--31:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-273-0},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{258},
  editor =	{Chambers, Erin W. and Gudmundsson, Joachim},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2023.31},
  URN =		{urn:nbn:de:0030-drops-178814},
  doi =		{10.4230/LIPIcs.SoCG.2023.31},
  annote =	{Keywords: Graph drawing, Universal point set, One-sided Hamiltonian, 2-page book embedding, Separating decomposition, Quadrangulation, 2-tree, Subcubic planar graph}
}
Document
DOI: 10.4230/LIPIcs.SoCG.2023.44
On the Geometric Thickness of 2-Degenerate Graphs

Authors: Rahul Jain, Marco Ricci, Jonathan Rollin, and André Schulz

Published in: LIPIcs, Volume 258, 39th International Symposium on Computational Geometry (SoCG 2023)

Abstract
A graph is 2-degenerate if every subgraph contains a vertex of degree at most 2. We show that every 2-degenerate graph can be drawn with straight lines such that the drawing decomposes into 4 plane forests. Therefore, the geometric arboricity, and hence the geometric thickness, of 2-degenerate graphs is at most 4. On the other hand, we show that there are 2-degenerate graphs that do not admit any straight-line drawing with a decomposition of the edge set into 2 plane graphs. That is, there are 2-degenerate graphs with geometric thickness, and hence geometric arboricity, at least 3. This answers two questions posed by Eppstein [Separating thickness from geometric thickness. In Towards a Theory of Geometric Graphs, vol. 342 of Contemp. Math., AMS, 2004].
Cite as

Rahul Jain, Marco Ricci, Jonathan Rollin, and André Schulz. On the Geometric Thickness of 2-Degenerate Graphs. In 39th International Symposium on Computational Geometry (SoCG 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 258, pp. 44:1-44:15, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2023)

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@InProceedings{jain_et_al:LIPIcs.SoCG.2023.44,
  author =	{Jain, Rahul and Ricci, Marco and Rollin, Jonathan and Schulz, Andr\'{e}},
  title =	{{On the Geometric Thickness of 2-Degenerate Graphs}},
  booktitle =	{39th International Symposium on Computational Geometry (SoCG 2023)},
  pages =	{44:1--44:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-273-0},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{258},
  editor =	{Chambers, Erin W. and Gudmundsson, Joachim},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2023.44},
  URN =		{urn:nbn:de:0030-drops-178946},
  doi =		{10.4230/LIPIcs.SoCG.2023.44},
  annote =	{Keywords: Degeneracy, geometric thickness, geometric arboricity}
}
Document
DOI: 10.4230/LITES-v004-i001-a003
Quantitative Analysis of Consistency in NoSQL Key-Value Stores

Authors: Si Liu, Jatin Ganhotra, Muntasir Raihan Rahman, Son Nguyen, Indranil Gupta, and José Meseguer

Published in: LITES, Volume 4, Issue 1 (2017). Leibniz Transactions on Embedded Systems, Volume 4, Issue 1

Abstract
The promise of high scalability and availability has prompted many companies to replace traditional relational database management systems (RDBMS) with NoSQL key-value stores. This comes at the cost of relaxed consistency guarantees: key-value stores only guarantee eventual consistency in principle. In practice, however, many key-value stores seem to offer stronger consistency. Quantifying how well consistency properties are met is a non-trivial problem.  We address this problem by formally modeling key-value stores as probabilistic systems and quantitatively analyzing their consistency properties by both statistical model checking and implementation evaluation. We present for the first time a formal probabilistic model of Apache Cassandra, a popular NoSQL key-value store, and quantify how much Cassandra achieves various consistency guarantees under various conditions. To validate our model, we evaluate multiple consistency properties using two methods and compare them against each other. The two methods are: (1) an implementation-based evaluation of the source code; and (2) a statistical model checking analysis of our probabilistic model.
Cite as

Si Liu, Jatin Ganhotra, Muntasir Raihan Rahman, Son Nguyen, Indranil Gupta, and José Meseguer. Quantitative Analysis of Consistency in NoSQL Key-Value Stores. In LITES, Volume 4, Issue 1 (2017). Leibniz Transactions on Embedded Systems, Volume 4, Issue 1, pp. 03:1-03:26, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2017)

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@Article{liu_et_al:LITES-v004-i001-a003,
  author =	{Liu, Si and Ganhotra, Jatin and Rahman, Muntasir Raihan and Nguyen, Son and Gupta, Indranil and Meseguer, Jos\'{e}},
  title =	{{Quantitative Analysis of Consistency in NoSQL Key-Value Stores}},
  booktitle =	{LITES, Volume 4, Issue 1 (2017)},
  pages =	{03:1--03:26},
  journal =	{Leibniz Transactions on Embedded Systems},
  ISSN =	{2199-2002},
  year =	{2017},
  volume =	{4},
  number =	{1},
  editor =	{Liu, Si and Ganhotra, Jatin and Rahman, Muntasir Raihan and Nguyen, Son and Gupta, Indranil and Meseguer, Jos\'{e}},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LITES-v004-i001-a003},
  doi =		{10.4230/LITES-v004-i001-a003},
  annote =	{Keywords: NoSQL Key-value Store, Consistency, Statistical Model Checking, Rewriting Logic, Maude}
}
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