Key Comparison Optimal 2-3 Trees with Maximum Utilization

To study the relationship between key-comparison cost and utilization (space efficiency) of 2-3 trees, we define a class of 2-3 trees called kcu-optimal trees, which, out of all 2-3 trees with optimal key-comparison cost, have maximum utilization. A characterization theorem for this class is proved and the “average” utilization is found to be 64.7%, showing that these properties are not totally incompatible. Finally, a linear-time algorithm is given to create a kcu-optimal tree from a sorted array of keys.