We extend the binary search tree model of probability to simply generated families of trees. In the resulting statistics, well-balanced trees are more likely than linear trees. Using this balanced model, analyses are more complex than in the uniform case, but still feasible. We illustrate our point by working out some particular simple cases of study: the computation of occupancy (a measure of the degree of balancing in trees) and the average size of the intersection of two m-ary trees. The results are then compared with those obtained using the uniform model. © 1993.
Casas, R., Díaz, J., & Martínez, C. (1993). Average-case analysis on simple families of trees using a balanced probability model. Theoretical Computer Science, 117(1–2), 99–112. https://doi.org/10.1016/0304-3975(93)90306-E