{"paper":{"title":"Semi-discrete optimal transport - the case p=1","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.CO"],"primary_cat":"math.NA","authors_text":"Dominic Schuhmacher, Valentin Hartmann","submitted_at":"2017-06-23T11:57:37Z","abstract_excerpt":"We consider the problem of finding an optimal transport plan between an absolutely continuous measure $\\mu$ on $\\mathcal{X} \\subset \\mathbb{R}^d$ and a finitely supported measure $\\nu$ on $\\mathbb{R}^d$ when the transport cost is the Euclidean distance. We may think of this problem as closest distance allocation of some ressource continuously distributed over space to a finite number of processing sites with capacity constraints.\n  This article gives a detailed discussion of the problem, including a comparison with the much better studied case of squared Euclidean cost (\"the case $p=2$\"). We p"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.07650","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"}