{"paper":{"title":"Efficient Nearest-Neighbor Search for Dynamical Systems with Nonholonomic Constraints","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC","cs.RO","cs.SY"],"primary_cat":"cs.CG","authors_text":"Brian Paden, Dmitry Yershov, Emilio Frazzoli, Valerio Varricchio","submitted_at":"2017-09-22T07:06:12Z","abstract_excerpt":"Nearest-neighbor search dominates the asymptotic complexity of sampling-based motion planning algorithms and is often addressed with k-d tree data structures. While it is generally believed that the expected complexity of nearest-neighbor queries is $O(log(N))$ in the size of the tree, this paper reveals that when a classic k-d tree approach is used with sub-Riemannian metrics, the expected query complexity is in fact $\\Theta(N^p \\log(N))$ for a number $p \\in [0, 1)$ determined by the degree of nonholonomy of the system. These metrics arise naturally in nonholonomic mechanical systems, includi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.07610","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"}