2013 IEEE 54th Annual Symposium on Foundations of Computer Science (1999)

New York, New York

Oct. 17, 1999 to Oct. 18, 1999

ISSN: 0272-5428

ISBN: 0-7695-0409-4

pp: 596

Gregory Kucherov , LORIA/INRIA-Lorraine

Roman Kolpakov , Moscow University

ABSTRACT

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.

INDEX TERMS

word combinatorics, algorithm, time complexity, repetitions, periodicities, maximal repetitions

CITATION

Gregory Kucherov,
Roman Kolpakov,
"Finding Maximal Repetitions in a Word in Linear Time",

*2013 IEEE 54th Annual Symposium on Foundations of Computer Science*, vol. 00, no. , pp. 596, 1999, doi:10.1109/SFFCS.1999.814634