{"paper":{"title":"A near-linear time approximation scheme for geometric transportation with arbitrary supplies and spread","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CG","authors_text":"Jiashuai Lu (1) ((1) The University of Texas at Dallas), Kyle Fox (1)","submitted_at":"2019-07-09T21:46:01Z","abstract_excerpt":"The geometric transportation problem takes as input a set of points $P$ in $d$-dimensional Euclidean space and a supply function $\\mu : P \\to \\mathbb{R}$. The goal is to find a transportation map, a non-negative assignment $\\tau : P \\times P \\to \\mathbb{R}_{\\geq 0}$ to pairs of points, so the total assignment leaving each point is equal to its supply, i.e., $\\sum_{r \\in P} \\tau(q, r) - \\sum_{p \\in P} \\tau(p, q) = \\mu(q)$ for all points $q \\in P$. The goal is to minimize the weighted sum of Euclidean distances for the pairs, $\\sum_{(p, q) \\in P \\times P} \\tau(p, q) \\cdot ||q - p||_2$.\n  We desc"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.04426","kind":"arxiv","version":5},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1907.04426/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}