Equivalence between Priority Queues and Sorting in External Memory

TL;DR

This paper demonstrates that in the external memory model, priority queues and sorting are computationally equivalent, allowing lower bounds for one to inform bounds for the other.

Contribution

It extends the known equivalence between priority queues and sorting from RAM to external memory models under mild assumptions.

Findings

Proves external memory priority queues are equivalent to external sorting.

Enables deriving lower bounds for sorting from priority queue complexity.

Provides a framework for analyzing external memory data structures.

Abstract

A priority queue is a fundamental data structure that maintains a dynamic ordered set of keys and supports the followig basic operations: insertion of a key, deletion of a key, and finding the smallest key. The complexity of the priority queue is closely related to that of sorting: A priority queue can be used to implement a sorting algorithm trivially. Thorup \cite{thorup2007equivalence} proved that the converse is also true in the RAM model. In particular, he designed a priority queue that uses the sorting algorithm as a black box, such that the per-operation cost of the priority queue is asymptotically the same as the per-key cost of sorting. In this paper, we prove an analogous result in the external memory model, showing that priority queues are computationally equivalent to sorting in external memory, under some mild assumptions. The reduction provides a possibility for proving lower bounds for external sorting via showing a lower bound for priority queues.