16 research outputs found
Upward Point-Set Embeddability
We study the problem of Upward Point-Set Embeddability, that is the problem
of deciding whether a given upward planar digraph has an upward planar
embedding into a point set . We show that any switch tree admits an upward
planar straight-line embedding into any convex point set. For the class of
-switch trees, that is a generalization of switch trees (according to this
definition a switch tree is a -switch tree), we show that not every
-switch tree admits an upward planar straight-line embedding into any convex
point set, for any . Finally we show that the problem of Upward
Point-Set Embeddability is NP-complete
Improved Bounds for Drawing Trees on Fixed Points with L-shaped Edges
Let be an -node tree of maximum degree 4, and let be a set of
points in the plane with no two points on the same horizontal or vertical line.
It is an open question whether always has a planar drawing on such that
each edge is drawn as an orthogonal path with one bend (an "L-shaped" edge). By
giving new methods for drawing trees, we improve the bounds on the size of the
point set for which such drawings are possible to: for
maximum degree 4 trees; for maximum degree 3 (binary) trees; and
for perfect binary trees.
Drawing ordered trees with L-shaped edges is harder---we give an example that
cannot be done and a bound of points for L-shaped drawings of
ordered caterpillars, which contrasts with the known linear bound for unordered
caterpillars.Comment: Appears in the Proceedings of the 25th International Symposium on
Graph Drawing and Network Visualization (GD 2017
Embedding Vertices at Points: Few Bends Suffice for Planar Graphs
The existing literature gives efficient algorithms for mapping trees or less restrictively outerplanar graphs on a given set of points in a plane, so that the edges are drawn planar and as straight lines. We relax the latter requirement and allow very few bends on each edge while considering general plane graphs. Our results show two algorithms for mapping four-connected plane graphs with at most one bend per edge and for mapping general plane graphs with at most two bends per edge. Furthermore we give a point set, where for arbitrary plane graphs it is NP-complete to decide whether there is an mapping such that each edge has at most one bend