A Linear-Time Algorithm for Seeds Computation

A seed in a word is a relaxed version of a period. We show a linear time algorithm computing a compact representation of all the seeds of a word, in particular, the shortest seed. Thus, we solve an open problem stated in the survey by Smyth (2000) and improve upon a previous over 15-year old O(n log n) algorithm by Iliopoulos, Moore and Park (1996). Our approach is based on combinatorial relations between seeds and a variant of the LZ-factorization (used here for the first time in context of seeds).

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