Still Simpler Static Level Ancestors

Abstract

A level-ancestor or LA query about a rooted tree $T$ takes as arguments a node $v$ in $T$, of depth $d_v$, say, and an integer $d$ with $0\le d\le d_v$ and returns the ancestor of $v$ in $T$ of depth $d$. The static LA problem is to process a given rooted tree $T$ so as to support efficient subsequent processing of LA queries about $T$. All previous efficient solutions to the static LA problem work by reducing a given instance of the problem to a smaller instance of the same or a related problem, solved with a less efficient data structure, and a collection of small micro-instances for which a different solution is provided. We indicate the first efficient solution to the static LA problem that works directly, without resorting to reductions or micro-instances.