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We consider the problem of finding repetitive structures and inherentpatterns in a given string $\s{s}$ of length $n$ over a finite totally orderedalphabet. A border $\s{u}$ of a string $\s{s}$ is both a prefix and a suffix of$\s{s}$ such that $\s{u} \not= \s{s}$. The computation of the border array of astring $\s{s}$, namely the borders of each prefix of $\s{s}$, is stronglyrelated to the string matching problem: given a string $\s{w}$, find all of itsoccurrences in $\s{s}$. A {\itshape Lyndon word} is a primitive word (i.e., itis not a power of another word) which is minimal for the lexicographical orderof its conjugacy class (i.e., the set of words obtained by cyclic rotations ofthe letters). In this paper we combine these concepts to introduce the\emph{Lyndon Border Array} $\mathcal L \beta$ of $\s{s}$, whose $i$-th entry$\mathcal L \beta(\s{s})[i]$ is the length of the longest border of $\s{s}[1\dd i]$ which is also a Lyndon word. We propose linear-time and linear-spacealgorithms for computing $\mathcal L \beta (\s{s})$. %in the case of bothbinary and bounded alphabets. Further, we introduce the \emph{Lyndon SuffixArray}, and by modifying the efficient suffix array technique of Ko and Aluru\cite{KA03} outline a linear time and space algorithm for its construction.

Linear Algorithms for Computing the Lyndon Border Array and the Lyndon Suffix Array