  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.
