@inbook{f59c4f52d4af4ce98aa8cc46e96b5eeb,

title = "On the Right-Seed Array of a String",

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..i]. We present an \ensuremathO(nlogn) 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",

author = "Michalis Christou and Maxime Crochemore and Ondrej Guth and Iliopoulos, {Costas S.} and Pissis, {Solon P.}",

year = "2011",

doi = "10.1007/978-3-642-22685-4_43",

language = "English",

isbn = "978-3-642-22684-7",

volume = "6842",

series = "Lecture Notes in Computer Science",

publisher = "Springer Berlin Heidelberg",

pages = "492--502",

editor = "Bin Fu and Ding-Zhu Du",

booktitle = "Computing and Combinatorics",

}