Abstract
In this paper we study approximate regularities of strings, that is, approximate periods, approximate covers and approximate seeds. We explore their similarities and differences and we implement algorithms for solving the smallest distance approximate period/cover/seed problem and the restricted smallest approximate period/cover/seed problem in polynomial time, under a variety of distance rules (the Hamming distance, the edit distance, and the weighted edit distance). We then analyse our experimental results to find out the time complexity of the algorithms in practice.
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