Shu ing Biological Sequences

This paper considers the following sequence shu ing problem Given a biological sequence either DNA or protein s generate a random instance among all the permutations of s that exhibit the same frequencies of k lets e g dinucleotides doublets of amino acids triplets etc Since certain biases in the usage of k lets are fundamental to biological sequences e ective generation of such sequences is essential for the evaluation of the results of many sequence analysis tools This paper introduces two sequence shu ing algorithms A simple swapping based algorithm is shown to generate a near random instance and appears to work well although its e ciency is unproven a generation algorithm based on Euler tours is proven to produce a precisely uniform instance and hence solve the sequence shu ing problem in time not much more than linear in the sequence length