Truly subcubic APSP and truly subquadratic 3SUM breakthrough reshapes fine-grained complexity
thegautamkamath · x · 2026-10-06
- Researchers report two major breakthroughs in fine-grained complexity: APSP (all-pairs shortest paths) solved in truly subcubic time, and 3SUM in truly subquadratic time.
- Commenters call these "truly remarkable results" but note they strip away much of the field's fun: the APSP and 3SUM hypotheses were the standard bases for conditional lower bounds, and algorithmic progress now undermines them.
- The deeper question is how future research proceeds — many conditional lower-bound results built on these assumptions may need revisiting, opening significant "new" questions about how the field should be done.
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