On the Complexity of Determining the Period of a String
نویسندگان
چکیده
We study the complexity of a classical combinatorial problem of computing the period of a string. We investigate both the averageand the worst-case complexity of the problem. We deliver almost tight bounds for the average-case. We show that every algorithm computing the period must examine Ω( √ m) symbols of an input string of length m. On the other hand we present an algorithm that computes the period by examining on average O q m · log|Σ| m symbols, where |Σ| ≥ 2 stands for the input alphabet. We also present a deterministic algorithm that computes the period of a string using m + O(m) comparisons. This is the first algorithm that have the worstcase complexity m + o(m).
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