De-amortizing Binary Search Trees

We present a general method for de-amortizing essentially any Binary Search Tree (BST) algorithm. In particular, by transforming Splay Trees, our method produces a BST that has the same asymptotic cost as Splay Trees on any access sequence while performing each search in O(log n) worst case time. By transforming Multi-Splay Trees, we obtain a BST that is O(log log n) competitive, satisfies the scanning theorem, the static optimality theorem, the static finger theorem, the working set theorem, and performs each search in O(log n) worst case time. Moreover, we prove that if there is a dynamically optimal BST algorithm, then there is a dynamically optimal BST algorithm that answers every search in O(log n) worst case time. ∗School of Computer Science, Carleton University. Email: [email protected]. Research supported in part by NSERC. †Chargé de recherches du F.R.S.-FNRS, Dpartement d’Informatique, Université Libre de Bruxelles. Email: [email protected]. ‡Department of Mathematics and Computer Science, University of Southern Denmark. Email: [email protected]. Partially supported by the Danish Council for Independent Research, Natural Sciences. §Mâıtre de recherches du F.R.S.-FNRS, Dpartement d’Informatique, Université Libre de Bruxelles. Email: [email protected]. ar X iv :1 11 1. 16 65 v1 [ cs .D S] 7 N ov 2 01 1