Extracting Approximate Patterns
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In a sequence, approximate patterns are exponential in number. In this paper, we present a new notion of basis for the patterns with don’t cares occurring in a given text (sequence). The primitive patterns are of interest since their number is lower than previous known definitions (and in a case, sub-linear in the size of the text), and these patterns can be used to extract all the patterns of a text.
We present an incremental algorithm that computes the primitive patterns occurring at least q times in a text of length n, given the N primitive patterns occurring at least q−1 times, in time O(|Σ|Nn 2log2 n log log n). In the particular case where q = 2, the complexity in time is only O(|Σ|n 2 log2 n log log n). We also give an algorithm that decides if a given pattern is primitive in a given text.
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