{"paper":{"title":"Querying Probabilistic Neighborhoods in Spatial Data Sets Efficiently","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Henning Meyerhenke, Moritz von Looz","submitted_at":"2015-09-07T11:31:09Z","abstract_excerpt":"$\\newcommand{\\dist}{\\operatorname{dist}}$ In this paper we define the notion of a probabilistic neighborhood in spatial data: Let a set $P$ of $n$ points in $\\mathbb{R}^d$, a query point $q \\in \\mathbb{R}^d$, a distance metric $\\dist$, and a monotonically decreasing function $f : \\mathbb{R}^+ \\rightarrow [0,1]$ be given. Then a point $p \\in P$ belongs to the probabilistic neighborhood $N(q, f)$ of $q$ with respect to $f$ with probability $f(\\dist(p,q))$. We envision applications in facility location, sensor networks, and other scenarios where a connection between two entities becomes less like"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.01990","kind":"arxiv","version":2},"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"}