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Comparing the Average Time Complexity of Breadth-First Search (BFS) and Depth-First Search (DFS) for Random Targets in Ordered Trees

There exists a unique threshold λ ≈ 0.789004 such that BFS is asymptotically faster than DFS in expectation if and only if the target node is at a level less than or equal to λ√n, where n is the number of edges in the ordered tree.