{"paper":{"title":"Inapproximability of VC Dimension and Littlestone's Dimension","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CC","authors_text":"Aviad Rubinstein, Pasin Manurangsi","submitted_at":"2017-05-26T10:38:01Z","abstract_excerpt":"We study the complexity of computing the VC Dimension and Littlestone's Dimension. Given an explicit description of a finite universe and a concept class (a binary matrix whose $(x,C)$-th entry is $1$ iff element $x$ belongs to concept $C$), both can be computed exactly in quasi-polynomial time ($n^{O(\\log n)}$). Assuming the randomized Exponential Time Hypothesis (ETH), we prove nearly matching lower bounds on the running time, that hold even for approximation algorithms."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.09517","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"}