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Documents authored by Ortali, Giacomo

Document
DOI: 10.4230/LIPIcs.ISAAC.2023.26
Rectilinear-Upward Planarity Testing of Digraphs

Authors: Walter Didimo, Michael Kaufmann, Giuseppe Liotta, Giacomo Ortali, and Maurizio Patrignani

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

Abstract
A rectilinear-upward planar drawing of a digraph G is a crossing-free drawing of G where each edge is either a horizontal or a vertical segment, and such that no directed edge points downward. Rectilinear-Upward Planarity Testing is the problem of deciding whether a digraph G admits a rectilinear-upward planar drawing. We show that: (i) Rectilinear-Upward Planarity Testing is NP-complete, even if G is biconnected; (ii) it can be solved in linear time when an upward planar embedding of G is fixed; (iii) the problem is polynomial-time solvable for biconnected digraphs of treewidth at most two, i.e., for digraphs whose underlying undirected graph is a series-parallel graph; (iv) for any biconnected digraph the problem is fixed-parameter tractable when parameterized by the number of sources and sinks in the digraph.
Cite as

Walter Didimo, Michael Kaufmann, Giuseppe Liotta, Giacomo Ortali, and Maurizio Patrignani. Rectilinear-Upward Planarity Testing of Digraphs. In 34th International Symposium on Algorithms and Computation (ISAAC 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 283, pp. 26:1-26:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{didimo_et_al:LIPIcs.ISAAC.2023.26,
  author =	{Didimo, Walter and Kaufmann, Michael and Liotta, Giuseppe and Ortali, Giacomo and Patrignani, Maurizio},
  title =	{{Rectilinear-Upward Planarity Testing of Digraphs}},
  booktitle =	{34th International Symposium on Algorithms and Computation (ISAAC 2023)},
  pages =	{26:1--26:20},
  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.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2023.26},
  URN =		{urn:nbn:de:0030-drops-193283},
  doi =		{10.4230/LIPIcs.ISAAC.2023.26},
  annote =	{Keywords: Graph drawing, orthogonal drawings, upward drawings, rectilinear planarity, upward planarity}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2023.18
On the Parameterized Complexity of Computing st-Orientations with Few Transitive Edges

Authors: Carla Binucci, Giuseppe Liotta, Fabrizio Montecchiani, Giacomo Ortali, and Tommaso Piselli

Published in: LIPIcs, Volume 272, 48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023)

Abstract
Orienting the edges of an undirected graph such that the resulting digraph satisfies some given constraints is a classical problem in graph theory, with multiple algorithmic applications. In particular, an st-orientation orients each edge of the input graph such that the resulting digraph is acyclic, and it contains a single source s and a single sink t. Computing an st-orientation of a graph can be done efficiently, and it finds notable applications in graph algorithms and in particular in graph drawing. On the other hand, finding an st-orientation with at most k transitive edges is more challenging and it was recently proven to be NP-hard already when k = 0. We strengthen this result by showing that the problem remains NP-hard even for graphs of bounded diameter, and for graphs of bounded vertex degree. These computational lower bounds naturally raise the question about which structural parameters can lead to tractable parameterizations of the problem. Our main result is a fixed-parameter tractable algorithm parameterized by treewidth.
Cite as

Carla Binucci, Giuseppe Liotta, Fabrizio Montecchiani, Giacomo Ortali, and Tommaso Piselli. On the Parameterized Complexity of Computing st-Orientations with Few Transitive Edges. In 48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 272, pp. 18:1-18:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{binucci_et_al:LIPIcs.MFCS.2023.18,
  author =	{Binucci, Carla and Liotta, Giuseppe and Montecchiani, Fabrizio and Ortali, Giacomo and Piselli, Tommaso},
  title =	{{On the Parameterized Complexity of Computing st-Orientations with Few Transitive Edges}},
  booktitle =	{48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023)},
  pages =	{18:1--18:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-292-1},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{272},
  editor =	{Leroux, J\'{e}r\^{o}me and Lombardy, Sylvain and Peleg, David},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2023.18},
  URN =		{urn:nbn:de:0030-drops-185524},
  doi =		{10.4230/LIPIcs.MFCS.2023.18},
  annote =	{Keywords: st-orientations, parameterized complexity, graph drawing}
}
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