Finding Maximal Repetitions in a Word in Linear Time

A repetition in a word is a subword with the period of at most half of the subword length. We study maximal repetitions occurring in , that is those for which any extended subword of has a bigger period. The set of such repetitions represents in a compact way all repetitions in . We first prove a combinatorial result asserting that the sum of exponents of all maximal repetitions of a word of length is bounded by a linear function in . This implies, in particular, that there is only a linear number of maximal repetitions in a word. This allows us to construct a linear-time algorithm for finding all maximal repetitions. Some consequences and applications of these results are discussed, as well as related works.