A Technical Note on Write-Efficient Sift-Down in Classical Binary Heaps

The classical binary heap sink operation based on swap has a significant write overhead. We examine two intuitive improvements: swapping siblings (verified via bounded SMT search) and adding a local hint called pref (the hint-assisted variant). In our bounded SMT checks and implementation comparisons, we did not find evidence that these variants provide consistent benefits; PerfView measurements show the hint-assisted variant was slower in most configurations. Our results suggest that reverting to the straightforward hole-based sink is the practical choice for write-efficient implementations