{"paper":{"title":"Fast and Accurate Approximations of the Optimal Transport in Semi-Discrete and Discrete Settings","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.CG","authors_text":"Keegan Yao, Pankaj K. Agarwal, Pouyan Shirzadian, Sharath Raghvendra","submitted_at":"2023-11-03T18:02:15Z","abstract_excerpt":"Given a $d$-dimensional continuous (resp. discrete) probability distribution $\\mu$ and a discrete distribution $\\nu$, the semi-discrete (resp. discrete) Optimal Transport (OT) problem asks for computing a minimum-cost plan to transport mass from $\\mu$ to $\\nu$; we assume $n$ to be the size of the support of the discrete distributions, and we assume we have access to an oracle outputting the mass of $\\mu$ inside a constant-complexity region in $O(1)$ time. In this paper, we present three approximation algorithms for the OT problem.\n  (i) Semi-discrete additive approximation: For any $\\epsilon>0"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2311.02172","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2311.02172/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"}