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Monuses and Heaps
This post is about a simple algebraic structure that I have found useful for algorithms that involve searching or sorting based on some ordered weight. I used it a bit in a pair of papers on graph search (2021; 2025), and more recently I used it to implement a version of the Phases type (Easterly 2019) that supported arbitrary keys, inspired by some work by Blöndal (2025a; 2025b) and Visscher (2025).
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