Weighted Ancestors in Suffix Trees Revisited

TL;DR

This paper introduces a new data structure for weighted ancestors in suffix trees that achieves constant query time and can be constructed efficiently in linear time, improving practical usability for string processing tasks.

Contribution

It presents a linear-time construction algorithm for a weighted ancestor data structure in suffix trees with constant query time, based on irreducible LCP values.

Findings

Achieves constant query time for weighted ancestor queries in suffix trees.

Provides a linear-time construction algorithm for the data structure.

Enhances the practical applicability of suffix tree algorithms.

Abstract

The weighted ancestor problem is a well-known generalization of the predecessor problem to trees. It is known to require $\Omega(\log\log n)$ time for queries provided $O(n\mathop{\mathrm{polylog}} n)$ space is available and weights are from $[0..n]$, where $n$ is the number of tree nodes. However, when applied to suffix trees, the problem, surprisingly, admits an $O(n)$-space solution with constant query time, as was shown by Gawrychowski, Lewenstein, and Nicholson (Proc. ESA 2014). This variant of the problem can be reformulated as follows: given the suffix tree of a string $s$, we need a data structure that can locate in the tree any substring $s[p..q]$ of $s$ in $O(1)$ time (as if one descended from the root reading $s[p..q]$ along the way). Unfortunately, the data structure of Gawrychowski et al. has no efficient construction algorithm, limiting its wider usage as an algorithmic tool. In this paper we resolve this issue, describing a data structure for weighted ancestors in suffix trees with constant query time and a linear construction algorithm. Our solution is based on a novel approach using so-called irreducible LCP values.