Shuffling biological sequences with motif constraints

We study the following problem: given a biological sequence S  , a multiset MM of motifs and an integer k, generate uniformly random sequences which contain the given motifs and have exactly the same frequencies of occurrence of k-lets (i.e. factors of length k) of S. We notably prove that the problem of deciding whether a sequence respects the given motif constraints is NP-complete. Nevertheless, we give a random generation algorithm which turns out to be experimentally efficient.