Emerging behavior as binary search trees are symmetrically updated

Abstract

When repeated updates are made to a binary search tree, the expected search cost tends to improve, as observed by Knott. For the case in which the updates use an asymmetric deletion algorithm, the Knott effect is swamped by the behavior discovered by Eppinger. The Knott effect applies also to updates using symmetric deletion algorithms, and it remains unexplained, along with several other trends in the tree distribution. It is believed that updates using symmetric deletion do not cause search cost to deteriorate, but the evidence is all experimental. The contribution of this paper is to model separately several different trends which may contribute to or detract from the Knott effect, including a previously unreported centripetal tendency.