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On Upward-Planar L-Drawings of Graphs

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Abstract

In an upward-planar L-drawing of a directed acyclic graph (DAG) each edge e is represented as a polyline composed of a vertical segment with its lowest endpoint at the tail of e and of a horizontal segment ending at the head of e. Distinct edges may overlap, but not cross. Recently, upward-planar L-drawings have been studied for st-graphs, i.e., planar DAGs with a single source s and a single sink t containing an edge directed from s to t. It is known that a plane st-graph, i.e., an embedded st-graph in which the edge (s,t) is incident to the outer face, admits an upward-planar L-drawing if and only if it admits a bitonic st-ordering, which can be tested in linear time.
We study upward-planar L-drawings of DAGs that are not necessarily st-graphs. On the combinatorial side, we show that a plane DAG admits an upward-planar L-drawing if and only if it is a subgraph of a plane st-graph admitting a bitonic st-ordering. This allows us to show that not every tree with a fixed bimodal embedding admits an upward-planar L-drawing. Moreover, we prove that any acyclic cactus with a single source (or a single sink) admits an upward-planar L-drawing, which respects a given outerplanar embedding if there are no transitive edges. On the algorithmic side, we consider DAGs with a single source (or a single sink). We give linear-time testing algorithms for these DAGs in two cases: (i) when the drawing must respect a prescribed embedding and (ii) when no restriction is given on the embedding, but the DAG is biconnected and series-parallel.

BibTeX - Entry

@InProceedings{angelini_et_al:LIPIcs.MFCS.2022.10,
  author =	{Angelini, Patrizio and Chaplick, Steven and Cornelsen, Sabine and Da Lozzo, Giordano},
  title =	{{On Upward-Planar L-Drawings of Graphs}},
  booktitle =	{47th International Symposium on Mathematical Foundations of Computer Science (MFCS 2022)},
  pages =	{10:1--10:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-256-3},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{241},
  editor =	{Szeider, Stefan and Ganian, Robert and Silva, Alexandra},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2022/16808},
  URN =		{urn:nbn:de:0030-drops-168085},
  doi =		{10.4230/LIPIcs.MFCS.2022.10},
  annote =	{Keywords: graph drawing, planar L-drawings, directed graphs, bitonic st-ordering, upward planarity, series-parallel graphs}
}

Keywords: graph drawing, planar L-drawings, directed graphs, bitonic st-ordering, upward planarity, series-parallel graphs
Seminar: 47th International Symposium on Mathematical Foundations of Computer Science (MFCS 2022)
Issue date: 2022
Date of publication: 22.08.2022


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