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Documents authored by Frati, Fabrizio

Document
DOI: 10.4230/LIPIcs.SoCG.2022.26
Parameterized Algorithms for Upward Planarity

Authors: Steven Chaplick, Emilio Di Giacomo, Fabrizio Frati, Robert Ganian, Chrysanthi N. Raftopoulou, and Kirill Simonov

Published in: LIPIcs, Volume 224, 38th International Symposium on Computational Geometry (SoCG 2022)

Abstract
We obtain new parameterized algorithms for the classical problem of determining whether a directed acyclic graph admits an upward planar drawing. Our results include a new fixed-parameter algorithm parameterized by the number of sources, an XP-algorithm parameterized by treewidth, and a fixed-parameter algorithm parameterized by treedepth. All three algorithms are obtained using a novel framework for the problem that combines SPQR tree-decompositions with parameterized techniques. Our approach unifies and pushes beyond previous tractability results for the problem on series-parallel digraphs, single-source digraphs and outerplanar digraphs.
Cite as

Steven Chaplick, Emilio Di Giacomo, Fabrizio Frati, Robert Ganian, Chrysanthi N. Raftopoulou, and Kirill Simonov. Parameterized Algorithms for Upward Planarity. In 38th International Symposium on Computational Geometry (SoCG 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 224, pp. 26:1-26:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{chaplick_et_al:LIPIcs.SoCG.2022.26,
  author =	{Chaplick, Steven and Di Giacomo, Emilio and Frati, Fabrizio and Ganian, Robert and Raftopoulou, Chrysanthi N. and Simonov, Kirill},
  title =	{{Parameterized Algorithms for Upward Planarity}},
  booktitle =	{38th International Symposium on Computational Geometry (SoCG 2022)},
  pages =	{26:1--26:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-227-3},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{224},
  editor =	{Goaoc, Xavier and Kerber, Michael},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2022.26},
  URN =		{urn:nbn:de:0030-drops-160349},
  doi =		{10.4230/LIPIcs.SoCG.2022.26},
  annote =	{Keywords: Upward planarity, parameterized algorithms, SPQR trees, treewidth, treedepth}
}
Document
DOI: 10.4230/LIPIcs.SoCG.2017.33
On Planar Greedy Drawings of 3-Connected Planar Graphs

Authors: Giordano Da Lozzo, Anthony D'Angelo, and Fabrizio Frati

Published in: LIPIcs, Volume 77, 33rd International Symposium on Computational Geometry (SoCG 2017)

Abstract
A graph drawing is greedy if, for every ordered pair of vertices (x,y), there is a path from x to y such that the Euclidean distance to y decreases monotonically at every vertex of the path. Greedy drawings support a simple geometric routing scheme, in which any node that has to send a packet to a destination "greedily" forwards the packet to any neighbor that is closer to the destination than itself, according to the Euclidean distance in the drawing. In a greedy drawing such a neighbor always exists and hence this routing scheme is guaranteed to succeed. In 2004 Papadimitriou and Ratajczak stated two conjectures related to greedy drawings. The greedy embedding conjecture states that every 3-connected planar graph admits a greedy drawing. The convex greedy embedding conjecture asserts that every 3-connected planar graph admits a planar greedy drawing in which the faces are delimited by convex polygons. In 2008 the greedy embedding conjecture was settled in the positive by Leighton and Moitra. In this paper we prove that every 3-connected planar graph admits a planar greedy drawing. Apart from being a strengthening of Leighton and Moitra's result, this theorem constitutes a natural intermediate step towards a proof of the convex greedy embedding conjecture.
Cite as

Giordano Da Lozzo, Anthony D'Angelo, and Fabrizio Frati. On Planar Greedy Drawings of 3-Connected Planar Graphs. In 33rd International Symposium on Computational Geometry (SoCG 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 77, pp. 33:1-33:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{dalozzo_et_al:LIPIcs.SoCG.2017.33,
  author =	{Da Lozzo, Giordano and D'Angelo, Anthony and Frati, Fabrizio},
  title =	{{On Planar Greedy Drawings of 3-Connected Planar Graphs}},
  booktitle =	{33rd International Symposium on Computational Geometry (SoCG 2017)},
  pages =	{33:1--33:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-038-5},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{77},
  editor =	{Aronov, Boris and Katz, Matthew J.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2017.33},
  URN =		{urn:nbn:de:0030-drops-72095},
  doi =		{10.4230/LIPIcs.SoCG.2017.33},
  annote =	{Keywords: Greedy drawings, 3-connectivity, planar graphs, convex drawings}
}
Document
DOI: 10.4230/LIPIcs.SOCG.2015.126
Optimal Morphs of Convex Drawings

Authors: Patrizio Angelini, Giordano Da Lozzo, Fabrizio Frati, Anna Lubiw, Maurizio Patrignani, and Vincenzo Roselli

Published in: LIPIcs, Volume 34, 31st International Symposium on Computational Geometry (SoCG 2015)

Abstract
We give an algorithm to compute a morph between any two convex drawings of the same plane graph. The morph preserves the convexity of the drawing at any time instant and moves each vertex along a piecewise linear curve with linear complexity. The linear bound is asymptotically optimal in the worst case.
Cite as

Patrizio Angelini, Giordano Da Lozzo, Fabrizio Frati, Anna Lubiw, Maurizio Patrignani, and Vincenzo Roselli. Optimal Morphs of Convex Drawings. In 31st International Symposium on Computational Geometry (SoCG 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 34, pp. 126-140, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)

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@InProceedings{angelini_et_al:LIPIcs.SOCG.2015.126,
  author =	{Angelini, Patrizio and Da Lozzo, Giordano and Frati, Fabrizio and Lubiw, Anna and Patrignani, Maurizio and Roselli, Vincenzo},
  title =	{{Optimal Morphs of Convex Drawings}},
  booktitle =	{31st International Symposium on Computational Geometry (SoCG 2015)},
  pages =	{126--140},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-83-5},
  ISSN =	{1868-8969},
  year =	{2015},
  volume =	{34},
  editor =	{Arge, Lars and Pach, J\'{a}nos},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SOCG.2015.126},
  URN =		{urn:nbn:de:0030-drops-51333},
  doi =		{10.4230/LIPIcs.SOCG.2015.126},
  annote =	{Keywords: Convex Drawings, Planar Graphs, Morphing, Geometric Representations}
}
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