The results obtained in the study can be extended to other families of trees, including binary trees. The key lies in understanding the structural similarities and differences between ordered trees and binary trees. By analyzing the recursive nature of tree structures and the traversal algorithms like BFS and DFS, we can adapt the formulas and calculations to apply to binary trees as well.
For binary trees, the average time complexity of BFS and DFS for searching a random target at a fixed level can be compared using similar techniques as those used for ordered trees. The threshold for when BFS outperforms DFS asymptotically can be determined by analyzing the expected number of steps for both algorithms in binary trees. By considering the occupation measure of Brownian excursions and combinatorial identities related to lattice paths, we can derive explicit formulas for the average time complexity of BFS and DFS in binary trees.
Overall, the generalization to other families of trees involves understanding the underlying principles of tree structures and traversal algorithms and applying the analytical techniques developed for ordered trees to these different tree families.