{"paper":{"title":"Faster Algorithms for the Geometric Transportation Problem","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Allen Xiao, Debmalya Panigrahi, Kasturi R. Varadarajan, Kyle Fox, Pankaj K. Agarwal","submitted_at":"2019-03-19T21:37:18Z","abstract_excerpt":"Let $R$ and $B$ be two point sets in $\\mathbb{R}^d$, with $|R|+ |B| = n$ and where $d$ is a constant. Next, let $\\lambda : R \\cup B \\to \\mathbb{N}$ such that $\\sum_{r \\in R } \\lambda(r) = \\sum_{b \\in B} \\lambda(b)$ be demand functions over $R$ and $B$. Let $\\|\\cdot\\|$ be a suitable distance function such as the $L_p$ distance. The transportation problem asks to find a map $\\tau : R \\times B \\to \\mathbb{N}$ such that $\\sum_{b \\in B}\\tau(r,b) = \\lambda(r)$, $\\sum_{r \\in R}\\tau(r,b) = \\lambda(b)$, and $\\sum_{r \\in R, b \\in B} \\tau(r,b) \\|r-b\\|$ is minimized. We present three new results for the t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.08263","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"}