论文信息 - On Dynamic Optimality for Binary Search Trees

On Dynamic Optimality for Binary Search Trees

Does there exist O(1)-competitive (self-adjusting) binary search tree (BST) algorithms? This is a well-studied problem. A simple offline BST algorithm GreedyFuture was proposed independently by Lucas and Munro, and they conjectured it to be O(1)-competitive. Recently, Demaine et al. gave a geometric view of the BST problem. This view allowed them to give an online algorithm GreedyArb with the same cost as GreedyFuture. However, no o(n)-competitive ratio was known for GreedyArb. In this paper we make progress towards proving O(1)-competitive ratio for GreedyArb by showing that it is O(\log n)-competitive.

Navin Goyal | Manoj Gupta

[1] Prosenjit Bose,et al. An O(log log n)-Competitive Binary Search Tree with Optimal Worst-Case Access Times , 2010, SWAT.

[2] Daniel M. Kane,et al. The geometry of binary search trees , 2009, SODA.

[3] Robert E. Tarjan,et al. Self-adjusting binary search trees , 1985, JACM.

[4] Seth Pettie,et al. Splay trees, Davenport-Schinzel sequences, and the deque conjecture , 2007, SODA '08.

[5] Erik D. Demaine,et al. Dynamic Optimality - Almost , 2004, FOCS.

[6] Daniel Dominic Sleator,et al. A Lower Bound Framework for Binary Search Trees with Rotations , 2005 .

[7] Robert E. Wilber. Lower bounds for accessing binary search trees with rotations , 1986, 27th Annual Symposium on Foundations of Computer Science (sfcs 1986).

[8] J. Ian Munro,et al. On the Competitiveness of Linear Search , 2000, ESA.