40th Annual Symposium on Foundations of Computer Science (Cat. No.99CB37039) (1999)
New York, New York
Oct. 17, 1999 to Oct. 18, 1999
Roman Kolpakov , Moscow University
Gregory Kucherov , LORIA/INRIA-Lorraine
A repetition in a word w is a sub-word with the period of at most half of the sub-word length. We study maximal repetitions occurring in w, that is those for which any extended sub-word of w has a bigger period. The set of such repetitions represents in a compact way all repetitions in w.We first prove a combinatorial result asserting that the sum of exponents of all maximal repetitions of a word of length n is bounded by a linear function in n. 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.
word combinatorics, algorithm, time complexity, repetitions, periodicities, maximal repetitions
G. Kucherov and R. Kolpakov, "Finding Maximal Repetitions in a Word in Linear Time," 40th Annual Symposium on Foundations of Computer Science (Cat. No.99CB37039)(FOCS), New York, New York, 1999, pp. 596.