Optimal query/update tradeoffs in versioned dictionaries

External-memory dictionaries are a fundamental data structure in file systems and databases. Versioned (or fullypersistent) dictionaries have an associated version tree where queries can be performed at any version, updates can be performed on leaf versions, and any version can be ‘cloned’ by adding a child. Various query/update tradeoffs are known for unversioned dictionaries, many of them with matching upper and lower bounds. No fully-versioned external-memory dictionaries are known with optimal space/query/update tradeoffs. In particular, no versioned constructions are known that offer updates in o(1) I/Os using O(N) space. We present the first cache-oblivious and cache-aware constructions that achieve a wide range of optimal points on this tradeoff. General Terms Cache-oblivious algorithms, External-memory algorithms, Versioned data structures