In the regime of bounded transportation costs, additive approximations for the optimal transport problem are reduced (rather simply) to relative approximations for positive linear programs, resulting in faster additive approximation algorithms for optimal transport.
@InProceedings{quanrud:OASIcs.SOSA.2019.6, author = {Quanrud, Kent}, title = {{Approximating Optimal Transport With Linear Programs}}, booktitle = {2nd Symposium on Simplicity in Algorithms (SOSA 2019)}, pages = {6:1--6:9}, series = {Open Access Series in Informatics (OASIcs)}, ISBN = {978-3-95977-099-6}, ISSN = {2190-6807}, year = {2019}, volume = {69}, editor = {Fineman, Jeremy T. and Mitzenmacher, Michael}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.SOSA.2019.6}, URN = {urn:nbn:de:0030-drops-100321}, doi = {10.4230/OASIcs.SOSA.2019.6}, annote = {Keywords: optimal transport, fast approximations, linear programming} }
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