{"paper":{"title":"A Deterministic Polynomial Space Construction for eps-nets under any Norm","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CC","authors_text":"Daniel Dadush","submitted_at":"2013-11-26T14:00:52Z","abstract_excerpt":"We give a deterministic polynomial space construction for nearly optimal eps-nets with respect to any input n-dimensional convex body K and norm |.|. More precisely, our algorithm can build and iterate over an eps-net of K with respect to |.| in time 2^O(n) x (size of the optimal net) using only poly(n)-space. This improves on previous constructions of Alon et al [STOC 2013] which achieve either a 2^O(n) approximation or an n^O(n) approximation of the optimal net size using 2^n space and poly(n)-space respectively. As in their work, our algorithm relies on the mathematically classical approach"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.6671","kind":"arxiv","version":3},"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"}