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Bioinformatics Vol. 17 no. 90001 2001
Pages S5-S12
© 2001 Oxford University Press

An efficient algorithm for finding short approximate non-tandem repeats

Ezekiel F. Adebiyi 1, Tao Jiang 2 and Michael Kaufmann 1

1 Wilhelm-Schickard-Institut für Informatik, Universität Tübingen, Sand 13, Tübingen, 72076, Germany
2 Department of Computer Science and Engineering, College of Engineering, University of California, Riverside, USA

Received on February 6, 2001 ; revised on April 2, 2001 ; accepted on April 2, 2001

We study the problem of approximate non-tandem repeat {dagger}extraction. Given a long subject string S of length N over a finite alphabet {Sigma} and a threshold D, we would like to find all short substrings of S of length P that repeat with at most D differences, i.e., insertions, deletions, and mismatches. We give a careful theoretical characterization of the set of seeds (i.e., some maximal exact repeats) required by the algorithm, and prove a sublinear bound on their expected numbers. Using this result, we present a sub-quadratic algorithm for finding all short (i.e., of length O(log N)) approximate repeats. The running time of our algorithm is O(DN3pow({epsilon})-1log N), where {epsilon} = D/P and pow({epsilon}) is an increasing, concave function that is 0 when {epsilon} = 0 and about 0.9 for DNA and protein sequences.

Contact: adebiyi{at}informatik.uni-tuebingen.de

{dagger} Throughout the paper we only consider non-tandem repeats.


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