Reductions in binary search trees

We analyze two bottom-up reduction algorithms over binary trees that represent replaceable data within a certain system, assuming the binary search tree (BST) probabilistic model. These reductions are based on idempotent and nilpotent operators, respectively. In both cases, the average size of the reduced tree, as well as the cost to obtain it, is asymptotically linear with respect to the size of the original tree. Additionally, the limiting distributions of the size of the trees obtained by means of these reductions satisfy a central limit law of Gaussian type.