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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"},"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":"1903.08263","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.DS","submitted_at":"2019-03-19T21:37:18Z","cross_cats_sorted":[],"title_canon_sha256":"fa8f8c64917be18d97f387301ae1533399439563755fab70035ab7a7ba79a34a","abstract_canon_sha256":"82b035c1941cc15da19a12a701050d753a0363732b2f8a83377c0338f3defd21"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:50:49.866950Z","signature_b64":"s4bw2dYtYCy8nJ3Pzw6uHkynaiP7AknXFEN6JdXcDRYHoILVUVBI4/SkbG+VSvaXDiQ+3YgnqcB15TzQ+Ae1Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"df33d3c42f380762d21278949a52e2ca141ae6d5b63ddb820a5fe7b0a4969254","last_reissued_at":"2026-05-17T23:50:49.866234Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:50:49.866234Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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. 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