{"paper":{"title":"Dominance Product and High-Dimensional Closest Pair under $L_\\infty$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CG"],"primary_cat":"cs.DS","authors_text":"Micha Sharir, Omer Gold","submitted_at":"2016-05-26T00:23:34Z","abstract_excerpt":"Given a set $S$ of $n$ points in $\\mathbb{R}^d$, the Closest Pair problem is to find a pair of distinct points in $S$ at minimum distance. When $d$ is constant, there are efficient algorithms that solve this problem, and fast approximate solutions for general $d$. However, obtaining an exact solution in very high dimensions seems to be much less understood. We consider the high-dimensional $L_\\infty$ Closest Pair problem, where $d=n^r$ for some $r > 0$, and the underlying metric is $L_\\infty$.\n  We improve and simplify previous results for $L_\\infty$ Closest Pair, showing that it can be solved"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.08107","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"}