for RE# we use an approach similar to the lazy DFA in RE2, but with a twist - we skip the NFA entirely and construct the DFA directly from the regex using derivatives. this derivative-based lazy DFA construction technique comes from the .NET NonBacktracking engine (2023).
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Nature, Published online: 25 February 2026; doi:10.1038/d41586-026-00544-6
The dashed circle shows the current best distance. As the algorithm finds closer points, the circle shrinks, which causes more subtrees to fail the "could contain a closer point?" test and get pruned. The search usually gets cheaper as it progresses.