On the joint distribution of the insertion path length and the number of comparisons in search trees

Abstract A search tree grown from an n -long random file of numerical records is studied. Each node of the tree accommodates an ordered subfile consisting of at most ( m −1) records; no particular assumptions are made about how the local search within a node is executed. The depth and the total number of comparisons of the search are shown to be asymptotically Gaussian with means a 1 ln n , a 2 ln n , and covariance matrix ∥ a ij ln n ∥. The a 's depend on m and the first and second order moments of the local search time. The locally binary and sequential cases serve as an illustration.