{"paper":{"title":"Kinetic Data Structures for the Semi-Yao Graph and All Nearest Neighbors in R^d","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":"2013-07-10T07:13:38Z","abstract_excerpt":"This paper presents a simple kinetic data structure for maintaining all the nearest neighbors of a set of $n$ moving points in $\\mathbb{R}^d$, where the trajectory of each point is an algebraic function of at most constant degree $s$. The approach is based on maintaining the edges of the Semi-Yao graph, a sparse graph whose edge set includes the pairs of nearest neighbors as a subset.\n  Our kinetic data structure (KDS) for maintaining all the nearest neighbors is deterministic. It processes $O(n^2\\beta_{2s+2}^2(n)\\log n)$ events with a total cost of $O(n^2\\beta_{2s+2}(n)\\log^{d+1} n)$. Here, $"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.2700","kind":"arxiv","version":4},"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"}