Combining Binary Search Trees

We present a general transformation for combining a constant number of binary search tree data structures (BSTs) into a single BST whose running time is within a constant factor of the minimum of any “well-behaved” bound on the running time of the given BSTs, for any online access sequence. (A BST has a well-behaved bound with f(n) overhead if it spends at most O(f(n)) time per access and its bound satisfies a weak sense of closure under subsequences.) In particular, we obtain a BST data structure that is O(log logn) competitive, satisfies the working set bound (and thus satisfies the static finger bound and the static optimality bound), satisfies the dynamic finger bound, satisfies the unified bound with an additive O(log logn) factor, and performs each access in worst-case O(logn) time.