Approximate periodicity
Inf. Comput.(2015)
摘要
Finding an approximate period in a given string S of length n is defined as follows. Let S ' be a periodic string closest to S under some distance metric, find the smallest period of S ' . This period is called an approximate period of S under the given metric. Let the distance between the input string S and a closest periodic string under the Hamming distance S ' be k. We develop algorithms that construct an approximate period of S under the Hamming distance in time O ( n k log ¿ log ¿ n ) and under the swap distance in time O ( n 2 ) . Finally, we show an O ( n log ¿ n ) algorithm for finite alphabets, and an O ( n log 3 ¿ n ) algorithm for infinite alphabets, that approximate the minimum number of mismatches between the input string and a closest periodic string under the Hamming distance.
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关键词
periodicity,approximate matching,swap distance,hamming distance,approximate periodicity,string algorithms
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