Randomness Preserving Deletions on Special Binary Search Trees

Deletions in binary search trees are difficult to analyse as they are not randomness preserving. We will present a new kind of tree which differs slightly from the standard binary search tree. It will be referred to as an ordered binary search tree as it stores a history element in its nodes, which provides information about the order in which the nodes were inserted. Using this extra information it is possible to design a new randomness preserving and order preserving deletion algorithm.