Performance of B+-trees with partial expansions

The authors mathematically analyze the behavior of B⁺-trees with partial expansions file structure under random insertions, focusing on the expected storage utilization and the expected cost of insertions. The model can be used for studying both the asymptotic and dynamic behavior. The accuracy of the model is confirmed by simulation. Disk space management is found to be more difficult than for standard B⁺-trees. Two simple space-management schemes specifically designed for handling buckets of two different sizes are investigated. It is found that an overall storage utilization of 81% can be achieved in practice