TY - GEN
T1 - Improved bounds for drawing trees on fixed points with L-Shaped edges
AU - Biedl, Therese
AU - Chan, Timothy M.
AU - Derka, Martin
AU - Jain, Kshitij
AU - Lubiw, Anna
N1 - Publisher Copyright:
© Springer International Publishing AG 2018.
PY - 2018
Y1 - 2018
N2 - Let T be an n-node tree of maximum degree 4, and let P be a set of n points in the plane with no two points on the same horizontal or vertical line. It is an open question whether T always has a planar drawing on P 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 P for which such drawings are possible to: O(n1.55) for maximum degree 4 trees; O(n1.22) for maximum degree 3 (binary) trees; and O(n1.142) 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 O(n log n) points for L-shaped drawings of ordered caterpillars, which contrasts with the known linear bound for unordered caterpillars.
AB - Let T be an n-node tree of maximum degree 4, and let P be a set of n points in the plane with no two points on the same horizontal or vertical line. It is an open question whether T always has a planar drawing on P 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 P for which such drawings are possible to: O(n1.55) for maximum degree 4 trees; O(n1.22) for maximum degree 3 (binary) trees; and O(n1.142) 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 O(n log n) points for L-shaped drawings of ordered caterpillars, which contrasts with the known linear bound for unordered caterpillars.
UR - https://www.scopus.com/pages/publications/85041848404
UR - https://www.scopus.com/pages/publications/85041848404#tab=citedBy
U2 - 10.1007/978-3-319-73915-1_24
DO - 10.1007/978-3-319-73915-1_24
M3 - Conference contribution
AN - SCOPUS:85041848404
SN - 9783319739144
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 305
EP - 317
BT - Graph Drawing and Network Visualization - 25th International Symposium, GD 2017, Revised Selected Papers
A2 - Ma, Kwan-Liu
A2 - Frati, Fabrizio
PB - Springer
T2 - 25th International Symposium on Graph Drawing and Network Visualization, GD 2017
Y2 - 25 September 2017 through 27 September 2017
ER -