Constructing LZ78 Tries and Position Heaps in Linear Time for Large Alphabets

TL;DR

This paper introduces a worst-case linear-time algorithm for constructing LZ78 tries and position heaps over large alphabets, leveraging nearest marked ancestor queries on suffix trees.

Contribution

It presents the first linear-time algorithms for LZ78 factorization and position heap construction for large alphabets, improving efficiency over previous methods.

Findings

Linear-time LZ78 factorization algorithm for large alphabets

Linear-time construction of position heaps from tries

Utilization of nearest marked ancestor queries on suffix trees

Abstract

We present the first worst-case linear-time algorithm to compute the Lempel-Ziv 78 factorization of a given string over an integer alphabet. Our algorithm is based on nearest marked ancestor queries on the suffix tree of the given string. We also show that the same technique can be used to construct the position heap of a set of strings in worst-case linear time, when the set of strings is given as a trie.