Constructing LZ78 tries and position heaps in linear time for large alphabets

• We propose the first linear time algorithm to compute LZ78 trie over an integer alphabet.
• We propose a linear time algorithm to construct the position heap of a trie.
• LZ78 tries and position heaps can be superimposed on the corresponding suffix trees.
• Both of them can be computed by nearest marked ancestor queries on suffix trees.

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.