Suppose that a rooted tree T is given for preprocessing. The Level-Ancestor
Problem is to answer quickly queries of the following form. Given a vertex v
and an integer i > 0, find the i-th vertex on the path from the root to v.
Algorithms that achieve a linear time bound for preprocessing and a constant
time bound for a query have been published by Dietz (1991), Alstrup and Holm
(2000), and Bender and Farach (2002). The first two algorithms address dynamic
versions of the problem; the last addresses the static version only and is the
simplest so far. The purpose of this note is to expose another simple
algorithm, derived from a complicated PRAM algorithm by Berkman and Vishkin
(1990,1994). We further show some easy extensions of its functionality, adding
queries for descendants and level successors as well as ancestors, extensions
for which the formerly known algorithms are less suitable.