General suffix automaton construction algorithm and space bounds

General suffix automaton construction algorithm and space bounds

Suffix automata and factor automata are efficient data structures for representing the full index of a set of strings. They are minimal deterministic automata representing the set of all suffixes or substrings of a set of strings. This paper presents a novel analysis of the size of the suffix automaton or factor automaton of a set of strings. It shows that the suffix automaton or factor automat...

Sparse Suffix Tree Construction in Small Space

Sparse Suffix Tree Construction with Small Space

We consider the problem of constructing a sparse suffix tree (or suffix array) for b suffixes of a given text T of size n, using only O(b) words of space during construction time. Breaking the naive bound of Ω(nb) time for this problem has occupied many algorithmic researchers since a different structure, the (evenly spaced) sparse suffix tree, was introduced by Kärkkäinen and Ukkonen in 1996. ...

From Nondeterministic Suffix Automaton to Lazy Suffix Tree

Given two strings, a pattern P of length m and a text T of length n over some alphabet Σ of size σ, we consider the exact string matching problem, i.e. we want to report all occurrences of P in T . The well-known Backward-Nondeterministic-DAWG-Matching (BNDM) algorithm is one of the most efficient algorithm for short to moderate length patterns. In this paper – as a prelude – we take the underl...

Sparse Suffix Tree Construction in Optimal Time and Space

Suffix tree (and the closely related suffix array) are fundamental structures capturing all substrings of a given text essentially by storing all its suffixes in the lexicographical order. In some applications, such as sparse text indexing, we work with a subset of b interesting suffixes, which are stored in the so-called sparse suffix tree. Because the size of this structure is Θ(b), it is nat...