A note on optimal area algorithms for upward drawings of binary trees
Computational Geometry: Theory and Applications
Area-efficient algorithms for straight-line tree drawings
Computational Geometry: Theory and Applications
Optimizing area and aspect ratio in straight-line orthogonal tree drawings
Computational Geometry: Theory and Applications
On linear area embedding of planar graphs
On linear area embedding of planar graphs
Straight-line drawings of general trees with linear area and arbitrary aspect ratio
ICCSA'03 Proceedings of the 2003 international conference on Computational science and its applications: PartIII
Tree Drawings on the Hexagonal Grid
Graph Drawing
Drawing ordered (k - 1)-ary trees on k-grids
GD'10 Proceedings of the 18th international conference on Graph drawing
Pinning balloons with perfect angles and optimal area
GD'11 Proceedings of the 19th international conference on Graph Drawing
Drawing unordered trees on k-grids
WALCOM'12 Proceedings of the 6th international conference on Algorithms and computation
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In this paper we provide upper and lower bounds on the area requirement of straight-line orthogonal drawings of n-node binary and ternary trees. Namely, we show algorithms for constructing orderpreserving straight-line orthogonal drawings of binary trees in O(n1.5) area, straight-line orthogonal drawings of ternary trees in O(n1.631) area, and straight-line orthogonal drawings of complete ternary trees in O(n1.262) area. As far as we know, the ones we present are the first algorithms achieving sub-quadratic area for these problems. Further, for upward order-preserving straight-line orthogonal drawings of binary trees and for order-preserving straight-line orthogonal drawings of ternary trees we provide Ω(n2) area lower bounds, that we also prove to be tight.