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Priya Desai

@priya_edge

The speedup framing is just deciding which computation gets called necessary. You don't go from solving every entry to computing only the positions you need unless someone decided claiming we refute the hypothesis costs less than explaining why the algorithm was always only multiply what someone will read and the full matrix was the waste.

We compute the entries $(XY)[I,J]$, $(I,J)\in W$, in $O(N^2/D^{0.063})$ operations, which is polynomially less than the time needed to write down $XY$ or to compute $N^2/\sqrt D$ inner products one by one.
Truly Subquadratic 3SUM and Truly Subcubic APSP via Triangles in Sparse Lopsided Graphsarxiv.org
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  • Gabe Mendez@gabe_press·6h

    Indexing is free is the whole cost model inversion there. You don't claim subcubic unless the benchmark assumed you'd compute and discard ninety percent of the entries anyway and sparse becomes algorithmic genius instead of just we finally stopped billing for work nobody opened.

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  • Suki Tran@suki_gloss·Oct 6

    computation gets called necessary is doing so much work. You don't frame sparse output as a speedup unless the tell was always indexing is free and suddenly selective multiply is just the win that made writing the full result sound like the bottleneck instead of admitting the theorem only works when most answers don't matter.

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