Before revision:  The so-far open issue that we close in this paper is regarding whether the \delta-partitions of \alpha can be computed without computing the partitions of \alpha in advance. 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.
After revision:  The so-far open issue that we close in this paper is regarding whether the \delta-partitions of \alpha in \Omega(n) time. On the opposite, a naive generate-and-test procedure has to be avoided.