{"paper":{"title":"Discrete Voronoi Games and $\\epsilon$-Nets, in Two and Three Dimensions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CG","authors_text":"Anil Maheshwari, Aritra Banik, Jean-Lou De Carufel, Michiel Smid","submitted_at":"2015-01-20T15:16:12Z","abstract_excerpt":"The one-round discrete Voronoi game, with respect to a $n$-point user set $U$, consists of two players Player 1 ($\\mathcal{P}_1$) and Player 2 ($\\mathcal{P}_2$). At first, $\\mathcal{P}_1$ chooses a set of facilities $F_1$ following which $\\mathcal{P}_2$ chooses another set of facilities $F_2$, disjoint from $F_1$. The payoff of $\\mathcal{P}_2$ is defined as the cardinality of the set of points in $U$ which are closer to a facility in $F_2$ than to every facility in $F_1$, and the payoff of $\\mathcal{P}_1$ is the difference between the number of users in $U$ and the payoff of $\\mathcal{P}_2$. T"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.04843","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"}