Optimal Transport on Graphs and Stochastically Evolving Trees

[2608.14839] Optimal Transport on Graphs and Stochastically Evolving Trees Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Mathematics > Combinatorics arXiv:2608.14839 (math) [Submitted on 14 Aug 2026] Title: Optimal Transport on Graphs and Stochastically Evolving Trees Authors: Fan Chung , Sawyer Jack Robertson View a PDF of the paper titled Optimal Transport on Graphs and Stochastically Evolving Trees, by Fan Chung and Sawyer Jack Robertson View PDF HTML (experimental) Abstract: We give an effective algorithm for determining the transportation distance between two given probability density functions defined on the vertices of a graph $G=(V,E)$ by analyzing an associated polytope. The vertices of the polytope correspond to feasible flows on spanning trees in $G$, and the $1$-skeleton of the polytope is a projection of the spanning tree state graph associated with the Glauber dynamics on $G$. The optimal value of this transportation problem, known as the $1$-Wasserstein distance, can be computed by tracing the transportation cost along the vertices of this polytope. We show that a local minimum of the transportation cost is also a global minimum, and this leads to a steepest descent algorithm for solving the transportation problem. If the probability density functions take discrete values in $\delta \mathbb{Z}$ for some $\delta>0$, then the optimal transport cost can be reached in at most $\frac{|V|-1}{\delta}$ steps. As an application, we give an efficient algorithm for computing the Ollivier--Ricci curvature of a graph. Comments: 15 pages, 1 figure Subjects: Combinatorics (math.CO) MSC classes: 49Q22, 90C35, 52B05, 05C21 Cite as: arXiv:2608.14839 [math.CO] (or arXiv:2608.14839v1 [math.CO] for this version) https://doi.org/10.48550/arXiv.2608.14839 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Sawyer Robertson [ view email ] [v1] Fri, 14 Aug 2026 19:24:02 UTC (20 KB) Full-text links: Access Paper: View a PDF of the paper titled Optimal Transport on Graphs and Stochastically Evolving Trees, by Fan Chung and Sawyer Jack Robertson View PDF HTML (experimental) TeX Source view license Current browse context: math.CO < prev | next > new | recent | 2026-08 Change to browse by: math References & Citations NASA ADS Google Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs . Which authors of this paper are endorsers? | Disable MathJax ( What is MathJax? ) We gratefully acknowledge support from our major funders , member institutions , , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab) Major funding support from

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