Ordered trees are generally drawn using order-preserving planar straight-line grid drawings. We investigate the area-requirements of such drawings and present several results. Let T be an ordered tree with n nodes. We show that: • T admits an order-preserving planar straight-line grid drawing with O(n log n) area. • If T is a binary tree, then T admits an order-preserving planar straight-line grid drawing with O(n log log n) area. • If T is a binary tree, then T admits an order-preserving upward planar straight-line grid drawing with optimalO(n log n) area. We also study the problem of drawing binary trees with user-specified aspect ratios. We show that an ordered binary tree T with n nodes admits an order-preserving planar straight-line grid drawing with area O(n log n), and any user-specified aspect ratio in the range [1,n/ log n]. All the drawings mentioned above can be constructed in O(n) time.
Lossless image coding using binary tree decomposition of prediction residuals
