Truly Subquadratic 3SUM and Truly Subcubic APSP via Triangles in Sparse Lopsided Graphs

Global Tech Thu, 08 Oct 2026 12:29:46 GMT Moderate confidence — 64/100

This refutes the $3$SUM and APSP hypotheses.
Using known reductions, we also refute the real-valued versions of the $3$SUM and APSP hypotheses, the Exact Triangle hypothesis, the Zero-Weight $k$-Clique hypotheses, and the three rect

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This refutes the $3$SUM and APSP hypotheses.
Using known reductions, we also refute the real-valued versions of the $3$SUM and APSP hypotheses, the Exact Triangle hypothesis, the Zero-Weight $k$-Clique hypotheses, and the three rect

Sources: Arxiv