{"paper":{"title":"Continuous Yao Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CG","authors_text":"Andr\\'e van Renssen, Jean-Lou De Carufel, Luis Barba, Mirela Damian, Perouz Taslakian, Prosenjit Bose, Rolf Fagerberg, Sander Verdonschot","submitted_at":"2014-08-18T19:08:25Z","abstract_excerpt":"In this paper, we introduce a variation of the well-studied Yao graphs. Given a set of points $S\\subset \\mathbb{R}^2$ and an angle $0 < \\theta \\leq 2\\pi$, we define the continuous Yao graph $cY(\\theta)$ with vertex set $S$ and angle $\\theta$ as follows. For each $p,q\\in S$, we add an edge from $p$ to $q$ in $cY(\\theta)$ if there exists a cone with apex $p$ and aperture $\\theta$ such that $q$ is the closest point to $p$ inside this cone.\n  We study the spanning ratio of $cY(\\theta)$ for different values of $\\theta$. Using a new algebraic technique, we show that $cY(\\theta)$ is a spanner when $\\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.4099","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"}