{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2023:D63MMBNDNQY2XQ6I5HUATXQWO2","short_pith_number":"pith:D63MMBND","schema_version":"1.0","canonical_sha256":"1fb6c605a36c31abc3c8e9e809de167689bea6b950bb43899b56b7971afd5824","source":{"kind":"arxiv","id":"2311.02172","version":1},"attestation_state":"computed","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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2311.02172","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.CG","submitted_at":"2023-11-03T18:02:15Z","cross_cats_sorted":[],"title_canon_sha256":"4820ae2ee13f28ed888b516f56ad974399756dff0eda3a694a4c97e418ea9f8f","abstract_canon_sha256":"f0fc17b2f4176ea8e713b4d883b813780afb5c316f3cc06326e6001453dce60d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T07:09:06.399683Z","signature_b64":"hFTFsq0yh1o/kYmICX6cZgLjuN79N6bgXrfL8aruhX5GrK3ke9SheOMDHUGlecXIYRKEcybkA04u/rmE8KaCDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1fb6c605a36c31abc3c8e9e809de167689bea6b950bb43899b56b7971afd5824","last_reissued_at":"2026-07-05T07:09:06.399232Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T07:09:06.399232Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2311.02172","created_at":"2026-07-05T07:09:06.399287+00:00"},{"alias_kind":"arxiv_version","alias_value":"2311.02172v1","created_at":"2026-07-05T07:09:06.399287+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2311.02172","created_at":"2026-07-05T07:09:06.399287+00:00"},{"alias_kind":"pith_short_12","alias_value":"D63MMBNDNQY2","created_at":"2026-07-05T07:09:06.399287+00:00"},{"alias_kind":"pith_short_16","alias_value":"D63MMBNDNQY2XQ6I","created_at":"2026-07-05T07:09:06.399287+00:00"},{"alias_kind":"pith_short_8","alias_value":"D63MMBND","created_at":"2026-07-05T07:09:06.399287+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/D63MMBNDNQY2XQ6I5HUATXQWO2","json":"https://pith.science/pith/D63MMBNDNQY2XQ6I5HUATXQWO2.json","graph_json":"https://pith.science/api/pith-number/D63MMBNDNQY2XQ6I5HUATXQWO2/graph.json","events_json":"https://pith.science/api/pith-number/D63MMBNDNQY2XQ6I5HUATXQWO2/events.json","paper":"https://pith.science/paper/D63MMBND"},"agent_actions":{"view_html":"https://pith.science/pith/D63MMBNDNQY2XQ6I5HUATXQWO2","download_json":"https://pith.science/pith/D63MMBNDNQY2XQ6I5HUATXQWO2.json","view_paper":"https://pith.science/paper/D63MMBND","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2311.02172&json=true","fetch_graph":"https://pith.science/api/pith-number/D63MMBNDNQY2XQ6I5HUATXQWO2/graph.json","fetch_events":"https://pith.science/api/pith-number/D63MMBNDNQY2XQ6I5HUATXQWO2/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/D63MMBNDNQY2XQ6I5HUATXQWO2/action/timestamp_anchor","attest_storage":"https://pith.science/pith/D63MMBNDNQY2XQ6I5HUATXQWO2/action/storage_attestation","attest_author":"https://pith.science/pith/D63MMBNDNQY2XQ6I5HUATXQWO2/action/author_attestation","sign_citation":"https://pith.science/pith/D63MMBNDNQY2XQ6I5HUATXQWO2/action/citation_signature","submit_replication":"https://pith.science/pith/D63MMBNDNQY2XQ6I5HUATXQWO2/action/replication_record"}},"created_at":"2026-07-05T07:09:06.399287+00:00","updated_at":"2026-07-05T07:09:06.399287+00:00"}