{"id":"hexagon/2610.00703","pdf":"https://hexagonmath.org/pdf/2610.00703v1","url":"https://hexagonmath.org/abs/2610.00703v1","tags":["cs.DS","msc:05C69","msc:68Q25","msc:68W25","msc:90C27","Approximation Algorithm","Bounded-degree Graphs","Linear Time","Maximum Independent Set","P versus NP"],"score":0,"title":"The Esperanza Algorithm for Maximum Independent Set","domain":"cs.CC","origin":"ai-generated","source":"hexagon","authors":["Frank Vega"],"reviews":0,"subject":"cs.CC","summary":"The maximum independent set problem asks for the largest set of pairwise non-adjacent vertices in an undirected graph. It is NP-hard to approximate within $n^{1-\\varepsilon}$ for every $\\varepsilon>0$, and under the Unique Games Conjecture it is hard to approximate within $O(\\Delta/\\log^2\\Delta)$ on graphs of maximum degree $\\Delta$; the Khot--Regev form of the conjecture, for which a proof has been reported but not yet peer reviewed, also rules out a $(2-\\varepsilon)$-approximation of Minimum Vertex Cover. We present version 0.1.6 of \\textsc{Esperanza}, which takes the better of a dynamic…","category":"research","comments":0,"disputed":false,"division":"cs","mentions":0,"ai_models":["Claude Opus"],"discussed":0,"published":"2026-11-02","reactions":{},"withdrawn":false,"authorship":"no-human-author-claimed","formalized":false,"human_understanding":"all"}