Dynamic LCA queries on trees

We show how to maintain a data structure on trees which allows for the following operations, all in worst-case constant time: 1. insertion of leaves and internal nodes, 2. deletion of leaves, 3. deletion of internal nodes with only one child, 4. determining the least common ancestor of any two nodes. We also generalize the Dietz - Sleator cup-filling scheduling methodology, which may be of independent interest.