{"paper":{"title":"Kinetic $k$-Semi-Yao Graph and its Applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CG","authors_text":"Mohammad Ali Abam, Sue Whitesides, Valerie King, Zahed Rahmati","submitted_at":"2014-12-18T01:34:32Z","abstract_excerpt":"This paper introduces a new proximity graph, called the $k$-Semi-Yao graph ($k$-SYG), on a set $P$ of points in $\\mathbb{R}^d$, which is a supergraph of the $k$-nearest neighbor graph ($k$-NNG) of $P$. We provide a kinetic data structure (KDS) to maintain the $k$-SYG on moving points, where the trajectory of each point is a polynomial function whose degree is bounded by some constant. Our technique gives the first KDS for the theta graph (\\ie, $1$-SYG) in $\\mathbb{R}^d$. It generalizes and improves on previous work on maintaining the theta graph in $\\mathbb{R}^2$.\n  As an application, we use t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.5697","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"}