Anzeige
Erschienen in:
2013 | OriginalPaper | Buchkapitel
On Two-Dimensional Lyndon Words
verfasst von : Shoshana Marcus, Dina Sokol
Erschienen in: String Processing and Information Retrieval
Verlag: Springer International Publishing
Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.
Wählen Sie Textabschnitte aus um mit Künstlicher Intelligenz passenden Patente zu finden. powered by
Markieren Sie Textabschnitte, um KI-gestützt weitere passende Inhalte zu finden. powered by
A Lyndon word is a primitive string which is lexicographically smallest among cyclic permutations of its characters. Lyndon words are used for constructing bases in free algebras, constructing de Bruijn sequences, finding the lexicographically smallest or largest substring in a string, and succinct suffix-prefix matching of highly periodic strings. In this paper, we extend the concept of the Lyndon word to two dimensions. We introduce the 2D Lyndon word and use it to capture 2D horizontal periodicity of a matrix in which each row is highly periodic, and to efficiently solve 2D horizontal suffix-prefix matching among a set of patterns. This yields a succinct and efficient algorithm for 2D dictionary matching. We present several algorithms that compute the 2D Lyndon word that represents a matrix. The final algorithm achieves linear time complexity even when the least common multiple of the periods of the rows is exponential in the matrix width.