The small discrepancy between the threshold λ and the average level of nodes in ordered trees can be attributed to the specific characteristics of ordered trees and the nature of the search algorithms (BFS and DFS) being analyzed.
The threshold λ represents the point at which BFS becomes asymptotically faster than DFS in terms of average time complexity when searching for a random target at a fixed level in ordered trees. This threshold is determined by intricate calculations involving the expected number of steps for both BFS and DFS.
On the other hand, the average level of nodes in ordered trees, as shown in the study, is slightly higher than the threshold λ. This discrepancy could be due to the distribution of nodes at different levels in ordered trees, leading to a subtle shift in the average level compared to the threshold for algorithmic efficiency.
Further analysis may be needed to delve deeper into the specific structural properties of ordered trees that contribute to this discrepancy and to explore whether similar discrepancies exist in other tree structures.