Randomness Preserving Deletions on Special Binary Search Trees

Deletions in binary search trees are difficult to analyse as they are not randomness preserving. We present a new kind of tree which differs slightly from the standard binary search tree. It is 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 deletion algorithm. We introduce this algorithm, explain why it works and prove that it is indeed randomness preserving. As well as that we show through experimental analysis that it actually runs faster than one of the other main random binary search tree deletion algorithms currently in use.