{"paper":{"title":"When the Optimum is also Blind: a New Perspective on Universal Optimization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CC","authors_text":"Fabrizio Grandoni, Marek Adamczyk, MIchal Wlodarczyk, Stefano Leonardi","submitted_at":"2017-07-06T09:30:22Z","abstract_excerpt":"Consider the following variant of the set cover problem. We are given a universe $U=\\{1,...,n\\}$ and a collection of subsets $\\mathcal{C} = \\{S_1,...,S_m\\}$ where $S_i \\subseteq U$. For every element $u \\in U$ we need to find a set $\\phi(u) \\in \\mathcal C$ such that $u\\in \\phi(u)$. Once we construct and fix the mapping $\\phi:U \\rightarrow \\mathcal{C}$ a subset $X \\subseteq U$ of the universe is revealed, and we need to cover all elements from $X$ with exactly $\\phi(X):=\\cup_{u\\in X} \\phi(u)$. The goal is to find a mapping such that the cover $\\phi(X)$ is as cheap as possible.\n  This is an exam"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.01702","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}