Research output per year
Research output per year
Patrizio Angelini, Steven Chaplick, Sabine Cornelsen, Giordano Da lozzo
Research output: Contribution to journal › Article › Academic › peer-review
In an upward-planar L-drawing of a directed acyclic graph (DAG) each edge e = (v, w) is represented as a polyline composed of a vertical segment with its lowest endpoint at the tail v of e and of a horizontal segment ending at the head w of e. Distinct edges may overlap, but must 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. As a combinatorial result, 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 directed 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: (a) when the drawing must respect a prescribed embedding and (b) when no restriction is given on the embedding, but the underlying undirected graph is series-parallel. For the single-sink case of (b) it even suffices that each biconnected component is series-parallel.
Original language | English |
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Pages (from-to) | 275-299 |
Journal | Journal of Graph Algorithms and Applications |
Volume | 28 |
Issue number | 1 |
DOIs | |
Publication status | Published - 9 Jul 2024 |
Research output: Working paper / Preprint › Preprint
Research output: Chapter in Book/Report/Conference proceeding › Chapter › Academic