Optimal query/update tradeoffs in versioned dictionaries

TL;DR

This paper introduces the first cache-oblivious and cache-aware external-memory dictionaries that optimize space, query, and update tradeoffs for versioned data structures, enabling efficient version management.

Contribution

It presents novel fully-versioned external-memory dictionary constructions with optimal space, query, and update tradeoffs, including updates in o(1) I/Os.

Findings

Achieves optimal space/query/update tradeoffs for versioned dictionaries.

Supports updates in o(1) I/Os with linear space complexity.

Provides both cache-oblivious and cache-aware solutions.

Abstract

External-memory dictionaries are a fundamental data structure in file systems and databases. Versioned (or fully-persistent) 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.