PRUNER: algorithms for finding monad patterns in DNA sequences

We present new algorithms for discovering monad patterns in DNA sequences. Monad patterns are of the form (l,d)-k, where l is the length of the pattern, d is the maximum number of mismatches allowed, and k is the minimum number of times the pattern is repeated in the given sample. The time-complexity of some of the best known algorithms to date is O(nt/sup 2/l/sup d/|/spl Sigma/|/sup d/2/), where t is the number of input sequences, and n is the length of each input sequence. The first algorithm that we present takes O(n/sup 2/t/sup 2/l/sup d/2/|/spl Sigma/|/sup d/2/) and space O(ntl/sup d/2/|/spl Sigma/|/sup d/2/), and the second algorithm takes O(n/sup 3/t/sup 3/l/sup d/2/|/spl Sigma/|/sup d/2/ time using O(l/sup d/2/|/spl Sigma/|/sup d/2/) space. In practice, our algorithms have much better performance provided the d/l ratio is small.