Shortest Covers Of All Cyclic Shifts Of A String
WALCOM: ALGORITHMS AND COMPUTATION (WALCOM 2020)(2020)
摘要
A factor W of a string X is called a cover of X, if X can be constructed by concatenations and superpositions of W. Breslauer (IPL, 1992) proposed a well-known O(n)-time algorithm that computes the shortest cover of every prefix of a string of length n. We show an O(n log n)-time algorithm that computes the shortest cover of every cyclic shift of a string and an O(n)-time algorithm that computes the shortest among these covers. A related problem is the number of different lengths of shortest covers of cyclic shifts of the same string of length n. We show that this number is Omega(log n).
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关键词
Cover, Quasiperiod, Seed, Fibonacci string
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