{"paper":{"title":"A probabilistic approach to reducing the algebraic complexity of computing Delaunay triangulations","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","headline":"","cross_cats":[],"primary_cat":"cs.CG","authors_text":"Arijit Ghosh, Jean-Daniel Boissonnat, Ramsay Dyer","submitted_at":"2015-05-20T17:11:41Z","abstract_excerpt":"Computing Delaunay triangulations in $\\mathbb{R}^d$ involves evaluating the so-called in\\_sphere predicate that determines if a point $x$ lies inside, on or outside the sphere circumscribing $d+1$ points $p_0,\\ldots ,p_d$. This predicate reduces to evaluating the sign of a multivariate polynomial of degree $d+2$ in the coordinates of the points $x, \\, p_0,\\, \\ldots,\\, p_d$. Despite much progress on exact geometric computing, the fact that the degree of the polynomial increases with $d$ makes the evaluation of the sign of such a polynomial problematic except in very low dimensions. In this pape"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.05454","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"}