Key-independent optimality is a property of some binary search tree data structures in computer science proposed by John Iacono. Suppose that key-value pairs are stored in a data structure, and that the keys have no relation to their paired values. A data structure has key-independent optimality if, when randomly assigning the keys, the expected performance of the data structure is within a constant factor of the optimal data structure. Key-independent optimality is related to dynamic optimality. Definitions There are many binary search tree algorithms that can look up a sequence of keys , where each is a number between and . For each sequence , let be the fastest binary search tree algorithm that looks up the elements in in order. Let be one of the possible permutation of the sequence , chosen at random, where is the th entry of . Let . Iacono defined, for a sequence , that . A data structure has key-independent optimality if it can lookup the elements in in time . Relationship with other bounds Key-independent optimality has been proved to be asymptotically equivalent to the working set theorem. Splay trees are known to have key-independent optimality. References Trees (data structures)