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On Upward-Planar L-Drawings of Graphs

Authors Patrizio Angelini , Steven Chaplick , Sabine Cornelsen , Giordano Da Lozzo

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Author Details

Patrizio Angelini
  • John Cabot University, Rome, Italy
Steven Chaplick
  • Maastricht University, The Netherlands
Sabine Cornelsen
  • University of Konstanz, Germany
Giordano Da Lozzo
  • Roma Tre University, Rome, Italy

Funding

  • Cornelsen, Sabine: Funded by the DFG – Project-ID 50974019 – TRR 161 (B06).
  • Da Lozzo, Giordano: Supported in part by MIUR grant 20174LF3T8 "AHeAD".

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Patrizio Angelini, Steven Chaplick, Sabine Cornelsen, and Giordano Da Lozzo. On Upward-Planar L-Drawings of Graphs. In 47th International Symposium on Mathematical Foundations of Computer Science (MFCS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 241, pp. 10:1-10:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022) https://doi.org/10.4230/LIPIcs.MFCS.2022.10

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.

Subject Classification

ACM Subject Classification
  • Mathematics of computing → Graph theory
  • Mathematics of computing → Graphs and surfaces
Keywords
  • graph drawing
  • planar L-drawings
  • directed graphs
  • bitonic st-ordering
  • upward planarity
  • series-parallel graphs

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References

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