Optimization At a High-level of Abstraction

This paper presents an optimization to an insertion algorithm for nearly complete binary search trees. The original algorithm was published recently by T.E. Gerasch in the Communications of the ACM ([Ger88]). Its insertion time is logarithmic in the best case, and linear in the worst case. With the optimization proposed here, some insertions that would require linear time with Gerasch's algorithm are handled in logarithmic time. The proposed optimization does not modify the worst case nor the best case behaviour of the algorithm.