COCOON 2011: Computing and Combinatorics pp 492-502

# On the Right-Seed Array of a String

• Michalis Christou
• Maxime Crochemore
• Ondrej Guth
• Costas S. Iliopoulos
• Solon P. Pissis
Conference paper

DOI: 10.1007/978-3-642-22685-4_43

Volume 6842 of the book series Lecture Notes in Computer Science (LNCS)
Cite this paper as:
Christou M., Crochemore M., Guth O., Iliopoulos C.S., Pissis S.P. (2011) On the Right-Seed Array of a String. In: Fu B., Du DZ. (eds) Computing and Combinatorics. COCOON 2011. Lecture Notes in Computer Science, vol 6842. Springer, Berlin, Heidelberg

## Abstract

We consider the problem of finding the repetitive structure of a given fixed string y. A factor u of y is a cover of y, if every letter of y falls within some occurrence of u in y. A factor v of y is a seed of y, if it is a cover of a superstring of y. There exist linear-time algorithms for solving the minimal cover problem. The minimal seed problem is of much higher algorithmic difficulty, and no linear-time algorithm is known. In this article, we solve one of its variants – computing the minimal and maximal right-seed array of a given string. A right seed of y is the shortest suffix of y that it is a cover of a superstring of y. An integer array RS is the minimal right-seed (resp. maximal right-seed) array of y, if RS[i] is the minimal (resp. maximal) length of right seeds of $$y[0\mathinner{\ldotp\ldotp} i]$$. We present an $$\ensuremath{\mathcal{O}}(n\log n)$$ time algorithm that computes the minimal right-seed array of a given string, and a linear-time solution to compute the maximal right-seed array by detecting border-free prefixes of the given string.

### Keywords

algorithms on strings periodicity covers seeds

## Authors and Affiliations

• Michalis Christou
• 1
• Maxime Crochemore
• 1
• 2
• Ondrej Guth
• 4
• Costas S. Iliopoulos
• 1
• 3
• Solon P. Pissis
• 1
1. 1.Dept. of InformaticsKing’s College LondonLondonUK
2. 2.Université Paris-EstFrance
3. 3.Digital Ecosystems & Business Intelligence InstituteCurtin UniversityPerthAustralia
4. 4.Dept. of Theoretical Computer Science, Faculty of Information TechnologyCzech Technical University in Prague