{"paper":{"title":"Approximate Minimum Diameter","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CG","authors_text":"Hamid Homapour, Masoud Seddighin, Mohammad Ghodsi","submitted_at":"2017-03-31T16:40:16Z","abstract_excerpt":"We study the minimum diameter problem for a set of inexact points. By inexact, we mean that the precise location of the points is not known. Instead, the location of each point is restricted to a contineus region ($\\impre$ model) or a finite set of points ($\\indec$ model). Given a set of inexact points in one of $\\impre$ or $\\indec$ models, we wish to provide a lower-bound on the diameter of the real points.\n  In the first part of the paper, we focus on $\\indec$ model. We present an $O(2^{\\frac{1}{\\epsilon^d}} \\cdot \\epsilon^{-2d} \\cdot n^3 )$ time approximation algorithm of factor $(1+\\epsilo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.10976","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"}