The left-right-imbalance of binary search trees

Abstract. We present a detailed study of left-right-imbalance measures for random binary search trees under the random permutation model, i.e., where binary search trees are generated by random permutations of {1, 2, . . . , n}. For random binary search trees of size n we study (i) the difference between the left and the right depth of a randomly chosen node, (ii) the difference between the left and the right depth of a specified node j = j(n), and (iii) the difference between the left and the right pathlength, and show for all three imbalance measures limiting distribution results.