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We first describe three algorithms for computing the Lyndon array that havebeen suggested in the literature, but for which no structured exposition hasbeen given. Two of these algorithms execute in quadratic time in the worstcase, the third achieves linear time, but at the expense of prior computationof both the suffix array and the inverse suffix array of x. We then go on todescribe two variants of a new algorithm that avoids prior computation ofglobal data structures and executes in worst-case n log n time. Experimentalevidence suggests that all but one of these five algorithms require only linearexecution time in practice, with the two new algorithms faster by a smallfactor. We conjecture that there exists a fast and worst-case linear-timealgorithm to compute the Lyndon array that is also elementary (making no use ofglobal data structures such as the suffix array).

Algorithms to Compute the Lyndon Array