Succinct Representation of Balanced Parentheses and Static Trees

We consider the implementation of abstract data types for the static objects: binary tree, rooted ordered tree, and a balanced sequence of parentheses. Our representations use an amount of space within a lower order term of the information theoretic minimum and support, in constant time, a richer set of navigational operations than has previously been considered in similar work. In the case of binary trees, for instance, we can move from a node to its left or right child or to the parent in constant time while retaining knowledge of the size of the subtree at which we are positioned. The approach is applied to produce a succinct representation of planar graphs in which one can test adjacency in constant time.