TY - GEN

T1 - On the right-seed array of a string

AU - Christou, Michalis

AU - Crochemore, Maxime

AU - Guth, Ondrej

AU - Iliopoulos, Costas S.

AU - Pissis, Solon P.

PY - 2011/8/29

Y1 - 2011/8/29

N2 - 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 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.

AB - 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 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.

KW - algorithms on strings

KW - covers

KW - periodicity

KW - seeds

UR - http://www.scopus.com/inward/record.url?scp=80051994885&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=80051994885&partnerID=8YFLogxK

U2 - 10.1007/978-3-642-22685-4_43

DO - 10.1007/978-3-642-22685-4_43

M3 - Conference contribution

AN - SCOPUS:80051994885

SN - 9783642226847

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 492

EP - 502

BT - Computing and Combinatorics - 17th Annual International Conference, COCOON 2011, Proceedings

T2 - 17th Annual International Computing and Combinatorics Conference, COCOON 2011

Y2 - 14 August 2011 through 16 August 2011

ER -