{"paper":{"title":"Approximating geodesics via random points","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OC","math.ST","stat.TH"],"primary_cat":"math.PR","authors_text":"Erik Davis, Sunder Sethuraman","submitted_at":"2017-11-19T01:54:54Z","abstract_excerpt":"Given a `cost' functional $F$ on paths $\\gamma$ in a domain $D\\subset\\mathbb{R}^d$, in the form $F(\\gamma) = \\int_0^1 f(\\gamma(t),\\dot\\gamma(t))dt$, it is of interest to approximate its minimum cost and geodesic paths. Let $X_1,\\ldots, X_n$ be points drawn independently from $D$ according to a distribution with a density. Form a random geometric graph on the points where $X_i$ and $X_j$ are connected when $0<|X_i - X_j|<\\epsilon$, and the length scale $\\epsilon=\\epsilon_n$ vanishes at a suitable rate.\n  For a general class of functionals $F$, associated to Finsler and other distances on $D$, u"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.06952","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"}