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 $\mathcal{O}(f(n))$ time per access and its bound satisfies a weak sense of closure under subsequences.) In particular, we obtain a BST data structure that is $\mathcal{O}(\log\log n)$ 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 $\mathcal{O}(\log\log n)$ factor, and performs each access in worst-case $\mathcal{O}(\log n)$ time.