Skip to main content
Article thumbnail
Location of Repository

Efficient Seeds Computation Revisited

By Michalis Christou, Maxime Crochemore, Costas S. Iliopoulos, Marcin Kubica, Solon P. Pissis, Jakub Radoszewski, Wojciech Rytter, Bartosz Szreder and Tomasz Walen

Abstract

The notion of the cover is a generalization of a period of a string, and there are linear time algorithms for finding the shortest cover. The seed is a more complicated generalization of periodicity, it is a cover of a superstring of a given string, and the shortest seed problem is of much higher algorithmic difficulty. The problem is not well understood, no linear time algorithm is known. In the paper we give linear time algorithms for some of its versions --- computing shortest left-seed array, longest left-seed array and checking for seeds of a given length. The algorithm for the last problem is used to compute the seed array of a string (i.e., the shortest seeds for all the prefixes of the string) in $O(n^2)$ time. We describe also a simpler alternative algorithm computing efficiently the shortest seeds. As a by-product we obtain an $O(n\log{(n/m)})$ time algorithm checking if the shortest seed has length at least $m$ and finding the corresponding seed. We also correct some important details missing in the previously known shortest-seed algorithm (Iliopoulos et al., 1996).Comment: 14 pages, accepted to CPM 201

Topics: Computer Science - Data Structures and Algorithms
Year: 2011
OAI identifier: oai:arXiv.org:1104.3153
Download PDF:
Sorry, we are unable to provide the full text but you may find it at the following location(s):
  • http://arxiv.org/abs/1104.3153 (external link)
  • Suggested articles


    To submit an update or takedown request for this paper, please submit an Update/Correction/Removal Request.