{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/efficient-graph-field-integrators-meet-point","title":"Efficient Graph Field Integrators Meet Point Clouds","arxiv_id":"2302.00942","date":"2023-02-02","proceeding":null,"authors":["Krzysztof Choromanski","Arijit Sehanobish","Han Lin","Yunfan Zhao","Eli Berger","Tetiana Parshakova","Alvin Pan","David Watkins","Tianyi Zhang","Valerii Likhosherstov","Somnath Basu Roy Chowdhury","Avinava Dubey","Deepali Jain","Tamas Sarlos","Snigdha Chaturvedi","Adrian Weller"],"abstract":"We present two new classes of algorithms for efficient field integration on graphs encoding point clouds. The first class, SeparatorFactorization(SF), leverages the bounded genus of point cloud mesh graphs, while the second class, RFDiffusion(RFD), uses popular epsilon-nearest-neighbor graph representations for point clouds. Both can be viewed as providing the functionality of Fast Multipole Methods (FMMs), which have had a tremendous impact on efficient integration, but for non-Euclidean spaces. We focus on geometries induced by distributions of walk lengths between points (e.g., shortest-path distance). We provide an extensive theoretical analysis of our algorithms, obtaining new results in structural graph theory as a byproduct. We also perform exhaustive empirical evaluation, including on-surface interpolation for rigid and deformable objects (particularly for mesh-dynamics modeling), Wasserstein distance computations for point clouds, and the Gromov-Wasserstein variant.","url_abs":"https://arxiv.org/abs/2302.00942v6","url_pdf":"https://arxiv.org/pdf/2302.00942v6.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"efficient-graph-field-integrators-meet-point","repo_url":"https://github.com/topographers/efficient_graph_algorithms","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=2302.00942","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"2302.00942"}},"developers":"https://syntology.ai/developers","read_at":"2026-09-24T18:15:14+00:00","read_at_is":"when the build read Syntology's graph, not when any sample ran","claim":"Per-sample execution status on synthesized fixtures; not a correctness claim about the paper. 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