An Accept-and-Reject Algorithm to Sample from a Set of Permutations Restricted by a Time Constraint

A modification of an accept-and-reject algorithm to sample from a set of restricted permutations is proposed. By concentrating on a special class of matrices obtained by restriction of the permutation in time, assuming the objects to be permuted to be events in time, the modified algorithm's running time can be shown to be linear instead of geometric in the number of elements. The implementation of the algorithm in the language R is presented in a Literate Programming style.