TY - GEN
T1 - Low ply drawings of trees
AU - Angelini, Patrizio
AU - Bekos, Michael A.
AU - Bruckdorfer, Till
AU - Hančl, Jaroslav
AU - Kaufmann, Michael
AU - Kobourov, Stephen
AU - Symvonis, Antonios
AU - Valtr, Pavel
N1 - Funding Information:
An open access version of the full-text of the paper is also available []. Research partially supported by DFG grant Ka812/17-1. The research by Pavel Valtr was supported by the grant GAČR 14-14179S of the Czech Science Foundation.
Publisher Copyright:
© Springer International Publishing AG 2016.
PY - 2016
Y1 - 2016
N2 - We consider the recently introduced model of low ply graph drawing, in which the ply-disks of the vertices do not have many common overlaps, which results in a good distribution of the vertices in the plane. The ply-disk of a vertex in a straight-line drawing is the disk centered at it whose radius is half the length of its longest incident edge. The largest number of ply-disks having a common overlap is called the ply-number of the drawing. We focus on trees. We first consider drawings of trees with constant ply-number, proving that they may require exponential area, even for stars, and that they may not even exist for bounded-degree trees. Then, we turn our attention to drawings with logarithmic ply-number and show that trees with maximum degree 6 always admit such drawings in polynomial area.
AB - We consider the recently introduced model of low ply graph drawing, in which the ply-disks of the vertices do not have many common overlaps, which results in a good distribution of the vertices in the plane. The ply-disk of a vertex in a straight-line drawing is the disk centered at it whose radius is half the length of its longest incident edge. The largest number of ply-disks having a common overlap is called the ply-number of the drawing. We focus on trees. We first consider drawings of trees with constant ply-number, proving that they may require exponential area, even for stars, and that they may not even exist for bounded-degree trees. Then, we turn our attention to drawings with logarithmic ply-number and show that trees with maximum degree 6 always admit such drawings in polynomial area.
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U2 - 10.1007/978-3-319-50106-2_19
DO - 10.1007/978-3-319-50106-2_19
M3 - Conference contribution
AN - SCOPUS:85007290867
SN - 9783319501055
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 236
EP - 248
BT - Graph Drawing and Network Visualization - 24th International Symposium, GD 2016, Revised Selected Papers
A2 - Nollenburg, Martin
A2 - Hu, Yifan
PB - Springer-Verlag
T2 - 24th International Symposium on Graph Drawing and Network Visualization, GD 2016
Y2 - 19 September 2016 through 21 September 2016
ER -