sentences:  It is an online binary search tree that achieves an formula_1 competitive ratio relative to the offline optimal binary search tree, while only using formula_1 additional bits of memory per node.This improved upon the previous best known competitive ratio, which was formula_3.Tango trees work by partitioning a binary search tree into a set of "preferred paths", which are themselves stored in auxiliary trees (so the tango tree is represented as a tree of trees).