The Power and Limitations of Static Binary Search Trees with Lazy Finger [article]

Prosenjit Bose and Karim Douïeb and John Iacono and Stefan Langerman
2013 arXiv   pre-print
A static binary search tree where every search starts from where the previous one ends (lazy finger) is considered. Such a search method is more powerful than that of the classic optimal static trees, where every search starts from the root (root finger), and less powerful than when rotations are allowed---where finding the best rotation based tree is the topic of the dynamic optimality conjecture of Sleator and Tarjan. The runtime of the classic root-finger tree can be expressed in terms of
more » ... entropy of the distribution of the searches, but we show that this is not the case for the optimal lazy finger tree. A non-entropy based asymptotically-tight expression for the runtime of the optimal lazy finger trees is derived, and a dynamic programming-based method is presented to compute the optimal tree.
arXiv:1304.6897v1 fatcat:pnvqojayjzh3ljat3axgnlwebm