Showing papers by "William F. Smyth published in 1997"
TL;DR: This paper provides a characterization of all the squares in F, hence in every prefix Fn; this characterization naturally gives rise to a algorithm which specifiesall the squares of Fn in an appropriate encoding.
88 citations
Journal Article•
TL;DR: It is proved that this algorithm which computes all the weak repetitions in a given string of length n defined on an arbitrary alphabet A is asymptotically optimal over all known encodings of the output.
Abstract: A weak repetition in a string consists of two or more adjacent substrings which are permutations of each other. We describe a straightforward \Theta(n 2 ) algorithm which computes all the weak repetitions in a given string of length n defined on an arbitrary alphabet A. Using results on Fibonacci and other simple strings, we prove that this algorithm is asymptotically optimal over all known encodings of the output.
43 citations
01 Jan 1997
TL;DR: In this article, the authors discuss three algorithms for approximate periods: an Abelian generator, a cover, and a seed, and show that each of them is a seed of itself.
Abstract: In many application areas (for instance, DNA sequence analysis) it becomes important to compute various kinds of “approximate period” of a given string y. Here we discuss three such approximate periods and the algorithms which compute them: an Abelian generator, a cover, and a seed. Let u be a substring of y. Then u is an Abelian generator of y iff y is a concatenation of substrings which are permutations of u: u is a cover of y iff every letter of y is contained in an occurrence of u in y and u is a seed of y iff y is a substring of a string y with cover u. Observe that, according to these definitions, y is an Abelian generator, a cover, and a seed of itself.
1 citations