Drawing unordered trees on k-grids

We present almost linear area bounds for drawing complete trees on the octagonal grid. For 7-ary trees we establish an upper and lower bound of Θ(n1.129) and for ternary trees the bounds of $\O(n^{1.048})$ and Θ(n), where the latter needs edge bends. We explore the unit edge length and area complexity of drawing unordered trees on k-grids with k∈{4, 6, 8} and generalize the $\mathcal{NP}$-hardness results of the orthogonal and hexagonal grid to the octagonal grid.