We present an O(lg lg n)-competitive online binary search tree, improving upon the best previous (trivial) competitive ratio of O(lg n). This is the first major progress on Sleator and Tarjan?s dynamic optimality conjecture of 1985 that O(1)-competitive binary search trees exist.
Citation:
Erik D. Demaine, Dion Harmon, John Iacono, Mihai Pătraşcu, "Dynamic Optimality — Almost," focs, pp.484-490, 45th Annual IEEE Symposium on Foundations of Computer Science (FOCS'04), 2004