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arXiv · 2404.02354

A faster algorithm for the construction of optimal factoring automata

Thomas Erlebach·Kleitos Papadopoulos
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Abstract

The problem of constructing optimal factoring automata arises in the context of unification factoring for the efficient execution of logic programs. Given an ordered set of $n$ strings of length $m$, the problem is to construct a trie-like tree structure of minimum size in which the leaves in left-to-right order represent the input strings in the given order. Contrary to standard tries, the order in which the characters of a string are encountered can be different on different root-to-leaf paths. Dawson et al. [ACM Trans. Program. Lang. Syst. 18(5):528--563, 1996] gave an algorithm that solves the problem in time $O(n^2 m (n+m))$. In this paper, we present an improved algorithm with running-time $O(n^2m)$.

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Thomas Erlebach, Kleitos Papadopoulos. 2024-04-02. A faster algorithm for the construction of optimal factoring automata. https://arxiv.org/abs/2404.02354

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