Binary Codes for Fast Determination of Ancestor-Descendant Relationships in Trees

This paper proposes a new coding scheme and an algorithm to determine ancestordescendant relationship among nodes in a tree without tree traversal. Each node in a tree is assigned a unique binary code. The algorithm and the binary coding approach were tested with trees of different heights and widths. The algorithm is of O(1) complexity versus O(d) for tree traversal, where d is the depth of the tree. The algorithm can be used to determine, in O(1) time, the superclass-subclass relationship either at compile-time or at run-time in an object-oriented (OO) programming environment.