Competitive Online Search Trees on Trees

We consider the design of adaptive data structures for searching elements a tree-structured space. use natural generalization rotation-based online binary search tree model in which underlying space is set vertices tree. This based on simple structure decomposing graphs, previously known under several names including elimination trees, vertex rankings, and tubings. The equivalent to classical exactly when path. describe an O (log log n )-competitive this model, where number vertices. matches best-known competitive ratio trees. Our method inspired by Tango algorithm, but critically needs new notions one that we call Steiner-closed may be independent interest. Moreover, our technique novel two levels decomposition, first from trees and, second, these into paths.