{"paper":{"title":"Efficient Algorithms for Geometric Partial Matching","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.CG"],"primary_cat":"cs.DS","authors_text":"Allen Xiao, Hsien-Chih Chang, Pankaj K. Agarwal","submitted_at":"2019-03-22T05:03:14Z","abstract_excerpt":"Let $A$ and $B$ be two point sets in the plane of sizes $r$ and $n$ respectively (assume $r \\leq n$), and let $k$ be a parameter. A matching between $A$ and $B$ is a family of pairs in $A \\times B$ so that any point of $A \\cup B$ appears in at most one pair. Given two positive integers $p$ and $q$, we define the cost of matching $M$ to be $c(M) = \\sum_{(a, b) \\in M}\\|{a-b}\\|_p^q$ where $\\|{\\cdot}\\|_p$ is the $L_p$-norm. The geometric partial matching problem asks to find the minimum-cost size-$k$ matching between $A$ and $B$.\n  We present efficient algorithms for geometric partial matching pro"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.09358","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"}