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We concentrate on the generalized string regularities and study the minimum approximate λ-cover problem and the minimum approximate λ-seed problem of a string. Given a string x of length n and an integer λ, the minimum approximate λ-cover (resp. seed) problem is to find a set of λ substrings each of equal length that covers x (resp. a superstring of x) with the minimum error, under a variety of distance models containing the Hamming distance, the edit distance and the weighted edit distance. Both problems can be solved in polynomial time.doi:10.1080/00207160701389168 fatcat:qnrb7ega45fdjidtz6yqwwlopa