{"paper":{"title":"Near-Linear Time Generalized Sinkhorn Algorithms for Bounded Genus Graphs","license":"http://creativecommons.org/licenses/by/4.0/","headline":"GenusSink delivers near-linear time approximate Sinkhorn algorithms for bounded-genus graphs with shortest-path costs.","cross_cats":["stat.ME"],"primary_cat":"cs.DS","authors_text":"Ananya Parashar, Derek Long, Dwaipayan Saha, Krzysztof Choromanski","submitted_at":"2026-05-10T22:00:42Z","abstract_excerpt":"We present GenusSink, a new class of approximate generalized Sinkhorn algorithms with shortest-path-distance costs for bounded genus (e.g. planar) graphs, providing near-linear time: (1) pre-processing, (2) iteration step, (3) final transport plan matrix querying and near-linear memory. Graphs handled by GenusSink include in particular planar graphs and bounded-genus meshes approximating 3D objects. GenusSink addresses total quadratic time complexity of its brute-force counterpart by leveraging separator-based decomposition of graphs, computational geometry techniques, and new results on fast "},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"GenusSink provides near-linear time (1) pre-processing, (2) iteration step, (3) final transport plan matrix querying and near-linear memory for approximate generalized Sinkhorn algorithms with shortest-path-distance costs on bounded genus graphs, and is numerically equivalent to the brute-force geodesic Sinkhorn algorithm on n-vertex graphs with treewidth O(log log n).","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"Bounded-genus graphs admit separator decompositions that allow approximation of their metrics by small-treewidth metrics while preserving the structure needed for fast generalized distance matrix multiplications without accumulating unacceptable error in the Sinkhorn iterations.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"GenusSink achieves near-linear time approximate generalized Sinkhorn for geodesic optimal transport on bounded-genus graphs by combining separator-based decompositions with Fourier and low-displacement-rank matrix-vector multiplications.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"GenusSink delivers near-linear time approximate Sinkhorn algorithms for bounded-genus graphs with shortest-path costs.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"ba4cc4849adea5d4f6b7668404ea1534cb81b70db99819abcd39d7ccca056575"},"source":{"id":"2605.09782","kind":"arxiv","version":2},"verdict":{"id":"c49c60df-1da7-409e-bc4e-413138513d4f","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-12T03:05:08.325874Z","strongest_claim":"GenusSink provides near-linear time (1) pre-processing, (2) iteration step, (3) final transport plan matrix querying and near-linear memory for approximate generalized Sinkhorn algorithms with shortest-path-distance costs on bounded genus graphs, and is numerically equivalent to the brute-force geodesic Sinkhorn algorithm on n-vertex graphs with treewidth O(log log n).","one_line_summary":"GenusSink achieves near-linear time approximate generalized Sinkhorn for geodesic optimal transport on bounded-genus graphs by combining separator-based decompositions with Fourier and low-displacement-rank matrix-vector multiplications.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"Bounded-genus graphs admit separator decompositions that allow approximation of their metrics by small-treewidth metrics while preserving the structure needed for fast generalized distance matrix multiplications without accumulating unacceptable error in the Sinkhorn iterations.","pith_extraction_headline":"GenusSink delivers near-linear time approximate Sinkhorn algorithms for bounded-genus graphs with shortest-path costs."},"integrity":{"clean":false,"summary":{"advisory":1,"critical":0,"by_detector":{"doi_compliance":{"total":1,"advisory":1,"critical":0,"informational":0}},"informational":0},"endpoint":"/pith/2605.09782/integrity.json","findings":[{"note":"DOI in the printed bibliography is fragmented by whitespace or line breaks. 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