{"paper":{"title":"On One-Round Discrete Voronoi Games","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.GT"],"primary_cat":"cs.CG","authors_text":"Mark de Berg, Mehran Mehr, S\\'andor Kisfaludi-Bak","submitted_at":"2019-02-25T12:42:21Z","abstract_excerpt":"Let $V$ be a multiset of $n$ points in $\\mathbb{R}^d$, which we call voters, and let $k\\geq 1$ and $\\ell\\geq 1$ be two given constants. We consider the following game, where two players $\\mathcal{P}$ and $\\mathcal{Q}$ compete over the voters in $V$: First, player $\\mathcal{P}$ selects $k$ points in $\\mathbb{R}^d$, and then player $\\mathcal{Q}$ selects $\\ell$ points in $\\mathbb{R}^d$. Player $\\mathcal{P}$ wins a voter $v\\in V$ iff $\\mathrm{dist}(v,P) \\leq \\mathrm{dist}(v,Q)$, where $\\mathrm{dist}(v,P) := \\min_{p\\in P} \\mathrm{dist}(v,p)$ and $\\mathrm{dist}(v,Q)$ is defined similarly. Player $\\m"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.09234","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"}