# Equivalence between priority queues and sorting

```@article{Thorup2007EquivalenceBP,
title={Equivalence between priority queues and sorting},
author={Mikkel Thorup},
journal={J. ACM},
year={2007},
volume={54},
pages={28}
}```
• M. Thorup
• Published 2007
• Mathematics, Computer Science
• J. ACM
We present a general deterministic linear space reduction from priority queues to sorting implying that if we can sort up to <i>n</i> keys in <i>S</i>(<i>n</i>) time per key, then there is a priority queue supporting delete and insert in <i>O</i>(<i>S</i>(<i>n</i>)) time and find-min in constant time. Conversely, a priority queue can trivially be used for sorting: first insert all keys to be sorted, then extract them in sorted order by repeatedly deleting the minimum. Asymptotically, this… Expand
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