Before revision:  As we show in this paper, this issue is not as trivial as it might seem at first sight, especially if any naive generate-and-test procedure has to be avoided. To resolve this issue, we give a formal proof of the correctness of a smart backtracking algorithm that computes the \delta-partitions of \alpha efficiently without a prior construction of the partitions of~\alpha.
After revision:  As we show in this paper, this issue is not as trivial as it might seem at first sight, especially if any naive generate-and-test algorithm would compute all \delta-partitions of \alpha efficiently without a prior construction of the partitions of~\alpha.