Ancestor problems on pure pointer machines

Abstract

We study several problems related to computing ancestors in dynamic trees on pure pointer machines, i.e., pointer machines with no arithmetic capabilities. The problems are motivated by those that arise in implementation of declarative and search-based programming languages. We provide a data structure that allows us to solve many of these problems including the computation of the nearest common ancestor, determination of precedence in the in-order traversal of the tree and membership of two nodes in the same path in worst-case O(lg h) time per operation where h is the height of the tree. Our solutions work for the fully dynamic case (no preprocessing) and do not use any arithmetic.