{"paper":{"title":"Finding Small Hitting Sets in Infinite Range Spaces of Bounded VC-dimension","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CG","authors_text":"Khaled Elbassioni","submitted_at":"2016-10-12T18:21:42Z","abstract_excerpt":"We consider the problem of finding a small hitting set in an {\\it infinite} range space $\\cF=(Q,\\cR)$ of bounded VC-dimension. We show that, under reasonably general assumptions, the infinite dimensional convex relaxation can be solved (approximately) efficiently by multiplicative weight updates. As a consequence, we get an algorithm that finds, for any $\\delta>0$, a set of size $O(s_{\\cF}(z^*_\\cF))$ that hits $(1-\\delta)$-fraction of $\\cR$ (with respect to a given measure) in time proportional to $\\log(\\frac{1}{\\delta})$, where $s_{\\cF}(\\frac{1}{\\epsilon})$ is the size of the smallest $\\epsil"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.03812","kind":"arxiv","version":2},"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"}