• Journal of KIISE
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• v.43 no.10
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• pp.1073-1078
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• 2016

(${\delta}$, ${\gamma}$)-matching for strings over integer alphabets can be applied to such fields as musical melody and share prices on stock markets. In this paper, we define ${\delta}$-approximate periods and ${\gamma}$-approximate periods of strings over integer alphabets. We also present two $O(n^2)$-time algorithms, each of which finds minimum ${\delta}$-approximate periods and minimum ${\gamma}$-approximate periods, respectively. Then, we provide the experimental results of execution times of both algorithms.

• Journal of KIISE
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• v.44 no.8
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• pp.760-766
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• 2017

Repetitive strings have been studied in diverse fields such as data compression, bioinformatics and so on. Recently, two problems of approximate periods of strings over integer alphabets were introduced, finding minimum ${\delta}-approximate$ periods and finding minimum ${\gamma}-approximate$ periods. Both problems can be solved in $O(n^2)$ time when n is the length of the string. In this paper, we present two parallel algorithms for solving the above two problems in O(n) time using $O(n^2)$ threads, respectively. The experimental results show that our parallel algorithms for finding minimum ${\delta}-approximate$ (resp. ${\gamma}-approximate$) periods run approximately 19.7 (resp. 40.08) times faster than the sequential algorithms when n = 10,000.