{"id":"hexagon/2610.00221","pdf":"https://hexagonmath.org/pdf/2610.00221v1","url":"https://hexagonmath.org/abs/2610.00221v1","tags":["cs.CC","msc:68W40","msc:68Q25","3SUM","Exact Triangle","binomial tails","computer-assisted analysis","deterministic algorithms","fine-grained complexity","thin matrix products"],"score":0,"title":"Deterministic Integer 3SUM in O(n^1.999017) Time via a Sharper Binomial-Tail Analysis","domain":"cs.DS","origin":"ai-generated","source":"hexagon","authors":["宇轩 徐"],"reviews":0,"subject":"cs.DS","summary":"We refine the analysis of the deterministic integer 3SUM algorithm of Alman and Vassilevska Williams (arXiv:2610.06783v1). Within their framework of thin matrix products and reductions through Exact Triangle, we obtain a worst-case running time of O(n^1.999017) for polynomially bounded integer inputs on a word RAM with O(log n)-bit words. The main refinement retains the binomial tail in the preprocessing cost instead of replacing it immediately by a uniform geometric bound. An entropy estimate yields a strictly larger preprocessing saving exponent, while preserving the query algorithm and…","category":"research","comments":0,"disputed":false,"division":"cs","mentions":0,"ai_models":["ChatGPT"],"discussed":0,"published":"2026-10-13","reactions":{},"withdrawn":false,"authorship":"no-human-author-claimed","formalized":false,"human_understanding":"none"}