{"paper":{"title":"Tighter Estimates for epsilon-nets for Disks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CG","authors_text":"Nabil H. Mustafa, Norbert Bus, Saurabh Ray, Shashwat Garg","submitted_at":"2015-01-14T04:56:50Z","abstract_excerpt":"The geometric hitting set problem is one of the basic geometric combinatorial optimization problems: given a set $P$ of points, and a set $\\mathcal{D}$ of geometric objects in the plane, the goal is to compute a small-sized subset of $P$ that hits all objects in $\\mathcal{D}$. In 1994, Bronniman and Goodrich made an important connection of this problem to the size of fundamental combinatorial structures called $\\epsilon$-nets, showing that small-sized $\\epsilon$-nets imply approximation algorithms with correspondingly small approximation ratios. Very recently, Agarwal and Pan showed that their"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.03246","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"}